CN103983355A - Compressed spectrum imaging system and method based on panchromatic imaging - Google Patents

Abstract

The invention discloses a compressed spectral imaging system and imaging method based on panchromatic imaging, which mainly solves the problems of low spectral image information utilization rate and low spectral image resolution in the existing compressed spectral imaging technology. Its imaging system includes a beam splitter module (1), a compressed spectrum observation module (2), a panchromatic observation module (3) and an image reconstruction processing module (4). The incident beam of the collected spectral image is divided into two beams with the same information and different directions by the beam splitter module (1), one of which passes through the compressed spectral observation module (2) to realize the compressed and coded observation of the spectral image, and the other passes through the panchromatic observation module (3) Realize the panchromatic observation of the spectral image; the image reconstruction processing module (4) perform simultaneous fusion of the output results of these two modules to complete the reconstruction of the spectral image. The invention has the advantages of high utilization rate of spectral information and high resolution of acquired spectral images, and can be used for acquisition and reconstruction of spectral images.

Description

Compressed Spectral Imaging System and Imaging Method Based on Panchromatic Imaging

technical field

The invention belongs to the technical field of image processing, and in particular relates to an imaging technology of compressed spectrum, which can be used for the acquisition and reconstruction of spectral images and improve the spatial resolution of images.

Background technique

With spectral imaging, the power spectral density of light is captured as a function of wavelength λ and spatial position (x,y). That is to say, the spectral image is composed of images of different spectral bands under the same field of view, which contains spatial and spectral dimensional information, while traditional imaging only contains spatial dimensional information. The spectral dimension information of the spatial position of the spectral image is of great significance for indicating the composition and structure of the observed object in the scene. Promote the wide application of spectral imaging technology in geographic remote sensing, atmospheric environment monitoring, military target reconnaissance and surveillance, meteorological observation, disaster prevention and other fields. Researchers have also been working on various spectral imaging systems and imaging methods, but there are still many problems in the existing technology, mainly as follows: the spatial resolution of traditional spectral imaging depends on the density of the detector array, in order to improve the spatial resolution The cost of increasing the density of the detector array is very high, and it is often difficult to achieve high resolution in time, space, and spectrum at the same time. How to use existing detectors to obtain higher resolution spectral images is an urgent problem to be solved.

The CS theory of compressed sensing proposed by E.J.Candes, J.Romberg, T.Tao and D.L.Donoho et al. in 2006 brought new hope to solve the above problems. The theory states that the data should be properly compressed while the signal is being acquired. Compared with the traditional signal acquisition and processing process, under the theoretical framework of compressed sensing, the sampling rate is no longer determined by the bandwidth of the signal, but by the structure and content of the information in the signal, which greatly reduces the sampling and calculation costs of the sensor , and the signal restoration process is a process of optimizing reconstruction.

Suppose the length of the sampled signal X is N, and the sparse transformation basis is Ψ. That is, the representation of signal X on Ψ is sparse. The mathematical model of compressed sensing theory requires the design of an M×N-dimensional observation matrix Φ that is not related to Ψ, where M<N, and the lower-dimensional observation data Y is obtained by multiplying Φ and X:

Y=ΦX

The original signal X is reconstructed by solving the optimization problem under the _l1 norm, and its mathematical expression is:

min||Ψ ^T X|| ₁ stY＝ΦX

According to the above theory, scholars M.E.Gehm and R.Johm of Duke University in the United States designed and proposed the CASSI (Coded Aperture Snapshot Spectral Imagers) system, which uses random coded templates and dispersion elements to realize the observation of spectral images, and finally through compressed sensing Theoretically reconstruct the original image. However, due to the gating effect of the coding template, the spectral image will lose half of the effective information after passing through the coding template, resulting in a low spatial resolution of the final reconstructed spectral image.

Contents of the invention

The purpose of the present invention is to propose a compressed spectral imaging system and imaging method based on panchromatic imaging to reduce the loss of effective information and improve the spatial resolution of the reconstructed spectral image for the low spatial resolution of the existing compressed spectral imaging.

Technical scheme of the present invention is accomplished like this:

The technical principle of the present invention is to learn from the CASSI system proposed by M.E.Gehm, R.Johm, etc., and add panchromatic observation on the basis of the original compressed coding observation to form an imaging system combining panchromatic imaging and compressed spectral imaging.

One. According to the above-mentioned principles, the present invention is based on the compression spectrum imaging system of panchromatic imaging, comprising:

The observation module, the image reconstruction processing module, the observation module observes the spectral image to obtain the observation image, and the image reconstruction processing module reconstructs the observation image to obtain the original spectral image, which is characterized in that the observation module is divided into two, namely The compressed spectrum observation module and the panchromatic observation module are equipped with a beam splitter module at the front end of the two observation modules; the incident beam of the collected spectral image is divided into two beams with the same information and different directions by the beam splitter module, all the way through The compressed spectral observation module realizes the compressed coding observation of the spectral image, and the other channel passes through the panchromatic observation module to realize the panchromatic observation of the spectral image; The reconstruction of the spectral image is completed after simultaneous fusion.

Preferably, the compressed spectrum observation module includes a first lens group, a coding template, a dispersive element and a first area array detector; the coding template is located at the rear end of the first lens group to realize coding of spectral images, and the dispersive element Located at the back end of the encoding template, it is used to translate the spectral dimension information of the spectral image to realize the dispersion of the spectral image. The first area array detector is located at the rear end of the dispersion element, used to observe the image and obtain the encoded image information.

Preferably, the panchromatic observation module includes a second lens group and a second area array detector, and the second area array detector is located at the rear end of the second lens group for observing images and obtaining panchromatic image information, the The panchromatic image information includes spectral information recorded by the first area detector and lost spectral information.

Two. According to the above-mentioned principle, the present invention is based on the compressed spectral imaging method of panchromatic imaging, comprising:

(1) Spectral image observation steps:

(1a) Suppose the size of the original spectral information matrix _f0 is M×N×L, where M×N is the spatial resolution of the spectral information, and L is the spectral resolution of the spectral information;

(1b) Let the spectral information of any point be f ₀ (m,n,k), where m and n represent spatial dimension coordinates, k represents spectral dimension coordinates, where 0≤m≤M-1, 0≤n≤N- 1, 0≤k≤L-1;

(1c) Divide the spectral information into two paths at a ratio of 1:1, where the information f ₁₁ (m,n,k) contained in the first path and the information f ₂₁ (m,n,k) contained in the second path same, ie:

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

(1d) Use the encoding function T(m,n) to encode the first spectral information, and obtain the encoded spectral information f ₁₂ (m,n,k) as:

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

Among them, T(m,n) randomly takes 0 or 1;

(1e) Translate the information of the kth spectral segment in the first encoded spectral information by k pixels, that is, shift the information of the mth row of the kth spectral segment to the mkth row to obtain the spectral information after dispersion f ₁₃ (m,n,k) is:

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

(1f) Simultaneously expose the spectral information of the first path and the second path, and obtain the observation result y ₁ (m,n) of the first path and the observation result y ₂ (m,n) of the second path:

${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

Record the results of these two observations as:

Y=Hf,

Where Y={y ₁ (m,n),y ₂ (m,n)} is the observation image matrix, H is a linear operator, which represents the observation model of the system, and f is the original spectral image;

(2) Spectral image reconstruction steps:

(2a) Send the observed image matrix Y to the image reconstruction processor;

(2b) Set the sparse base Ψ as wavelet base or DCT base or Fourier base, so that the spectral image is sparse under the sparse base Ψ;

(2c) The image reconstruction processor uses a nonlinear optimization method to reconstruct the original spectral image f according to the observed image matrix Y and the sparse basis Ψ.

Compared with the prior art, the present invention has the following advantages

First: Compared with the traditional single-channel compressed spectral imaging technology, the present invention adds full-color imaging, can record all spectral information, and overcomes the shortcomings of low spectral information utilization in existing imaging systems;

Second: the present invention makes full use of the high spatial resolution of panchromatic imaging, so that the present invention has the advantage of high reconstruction accuracy;

Third: the present invention utilizes the sparsity of spectral images, and realizes spectral image reconstruction by solving nonlinear optimization problems, so that the present invention can simultaneously obtain spectral images with high spatial resolution and high inter-spectral resolution.

Description of drawings

Fig. 1 is a system block diagram of the present invention;

Fig. 2 is the structural block diagram of compressed spectrum observation module in the present invention;

Fig. 3 is the structural block diagram of panchromatic observation module among the present invention;

Fig. 4 is a coding template structural diagram among the present invention;

Fig. 5 is the flow chart of imaging method of the present invention;

Fig. 6 is the reconstruction result of observation of the balloons spectral image by the imaging system of the present invention and the CASSI system of Duke University;

Fig. 7 is the reconstruction result of observing the Egyptian_statue spectral image by the imaging system of the present invention and the CASSI system of Duke University.

Detailed ways

The present invention is described in detail below in conjunction with accompanying drawing and example:

Referring to FIG. 1 , the compressed spectrum imaging system based on panchromatic imaging of the present invention includes a beam splitter module 1 , a compressed spectrum observation module 2 , a panchromatic observation module 3 and an image reconstruction processing module 4 . Among them: the beam splitter module 1 is located at the front end of the compressed spectrum observation module 2 and the panchromatic observation module 3; the incident light beam of the collected spectral image is divided into two beams with the same information and different directions by the beam splitter module 1, and one way is compressed The spectral observation module 2 realizes the compressed coding observation of the spectral image, and the other way passes through the panchromatic observation module 3 to realize the panchromatic observation of the spectral image; the image reconstruction processing module 4 converts the compressed coding observation and panchromatic The reconstruction of the spectral image is completed after simultaneous fusion of the observation results.

Referring to FIG. 2 , the compressed spectrum observation module 2 in the present invention includes a first lens group 21 , an encoding template 22 , a dispersive element 23 and a first area array detector 24 . Wherein: the encoding template 22 is located at the rear end of the first lens group 21 to realize the encoding of the spectral image; the dispersion element 23 is located at the rear end of the encoding template 22 and is used to translate the spectral dimension information of the spectral image to realize the dispersion of the spectral image; An array detector 24 is located at the rear end of the dispersive element 23, and is used to observe images and obtain encoded image information.

Referring to FIG. 3 , the panchromatic observation module 3 in the present invention includes a second lens group 31 and a second area array detector 32 . Wherein: the second area array detector 32 is located at the rear end of the second lens group 31, and is used to observe images and obtain panchromatic image information, which includes the spectral information recorded by the first area array detector 24 and the lost spectrum information.

With reference to Fig. 4, coding template 22 among the present invention is the rectangular planar plate that is made up of light-transmitting and opaque grid, and each grid size is identical, and is equal to the size of image pixel point, and light-transmitting grid is opposite to image. The encoding of the image is 1, and the encoding of the image by the opaque grid is 0; whether each grid of the encoding template 22 is transparent is randomly set, and the random encoding of each position information of the image is realized through the encoding template.

Referring to FIG. 5 , the compressed spectral imaging method based on panchromatic imaging in the present invention includes two steps of spectral image observation and spectral image reconstruction.

1. Spectral image observation:

Step 1, initialize the original spectral information, set the size of the original spectral information matrix f ₀ as M×N×L, and set the spectral information of any point as f ₀ (m,n,k), where M×N is the space of spectral information Resolution, L is the spectral resolution of spectral information, that is, the number of spectral segments of spectral information is L; m and n represent spatial dimension coordinates, k represents spectral dimension coordinates, where 0≤m≤M-1, 0≤n≤ N-1, 0≤k≤L-1.

Step 2: Divide the original spectral information into two paths at a ratio of 1:1, wherein the spectral information f ₁₁ (m,n,k) contained in the first path and the spectral information f ₂₁ (m,n,k) contained in the second path ,k) is the same and is equivalent to times the original spectral information, namely:

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; .</span>$

Step 3, set the encoding function as T(m,n), use this encoding function to encode the first path of spectral information f ₁₁ (m,n,k), and obtain the first path of encoded spectral information f ₁₂ ( m,n,k):

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

Among them, T(m,n) randomly takes 0 or 1.

Step 4, translate the spectral information f ₁₂ (m,n,k) after the first encoding, that is, translate the information of the m-th row of the k-th spectral segment to the m-th row, and obtain the shifted spectral information f ₁₃ ( m,n,k) is:

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; .</span>$

Step 5, obtain the observation image matrix.

(5a) Expose the shifted spectral information f ₁₃ (m,n,k) of the first channel and the spectral information f ₂₁ (m,n,k) of the second channel respectively, that is, the spectral information of each spectral segment of each channel Accumulate to get the observation result y ₁ (m,n) of the first path and the observation result y ₂ (m,n) of the second path:

${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

(5b) Record the two observations as:

Y=Hf,

Where Y={y ₁ (m,n),y ₂ (m,n)} is the observation image matrix, H is the observation operator, which represents the observation model of the system, and f is the original spectral information.

2. Spectral image reconstruction:

Step 6: Send the observed image matrix Y to the image reconstruction processor.

Step 7, set the sparse base Ψ as wavelet base, DCT base or Fourier base, so that the original spectral information f is sparse under the sparse base Ψ, that is, the projection coefficient Ψ ^T f of the original spectral information f under the sparse base Ψ is absolutely Most of the values are smaller than a certain threshold, which needs to be set through experiments, and the thresholds corresponding to different sparse transform domains are different. In this example, the sparse base Ψ is set as a wavelet base, and the threshold is set as an adaptive threshold.

Step 8, the image reconstruction processor uses the nonlinear optimization method to reconstruct the original spectral information f according to the observation result Y and the sparse basis Ψ.

(8a) Set _the optimization objective function as min(||Ψ ^T f|| ₁ ), where ^T represents matrix transposition, _|||| ) means to take the minimum value of _l1 norm;

(8b) taking the observed image matrix Y=Hf as a constraint condition;

(8c) Simultaneously optimize the objective function and constraint conditions, and obtain f that satisfies the constraint condition Y=Hf and minimizes ||Ψ ^T f|| ₁ , which is the original spectral information f.

Effect of the present invention can be further illustrated by following simulation

1. Simulation conditions

The hardware test platform of this experiment is: Intel Core i7CPU, main frequency 3.40GHz, memory 8GB; software simulation platform is: windows764 bit operating system and Matlab2013b; test image is: spectral image released by Columbia University, spatial resolution is (512,512) , with an interspectral resolution of 31.

2. Simulation content and result analysis

In order to verify the effectiveness of the present invention, two simulation experiments were carried out. The two simulation experiments used different spectral data cubes as the original spectral images, and then used the two-step iterative algorithm to reconstruct the spectral images, and then calculated the reconstruction results according to the reconstruction results. The peak signal-to-noise ratio (PSNR) of the reconstructed spectral image was compared with the reconstruction result of Duke University's CASSI system.

Simulation 1, using the balloons diagram of Columbia University as the original spectral image, using the CASSI system of Duke University and the system of the present invention for simulation observation, and using two-step iterative algorithms to reconstruct the observation results, the results are shown in Figure (6) , wherein, Figure (6a) is the original spectral image, i.e. balloons figure; Figure (6b) is the reconstruction result after observation by Duke University CASSI system; Figure (6c) is the reconstruction result after observation by the system of the present invention. The PSNR of the reconstruction result of the band is marked under each reconstructed image. Due to the large number of bands, only band 1, band 5, band 22, and band 31 are displayed.

Simulation 2, using the egyptian_statue map of Columbia University as the original spectral image, using the CASSI system of Duke University and the system of the present invention to perform simulation observations, and using two-step iterative algorithms to reconstruct the observation results, the results are shown in Figure (7) Shown, wherein, figure (7a) is the original spectral image, i.e. egyptian_statue figure; Figure (7b) is the reconstruction result after utilizing Duke University CASSI system observation; Figure (7c) is the reconstruction after utilizing the system observation of the present invention result. The PSNR of the reconstruction result of the band is marked under each reconstructed image. Since there are many bands, only band 1, band 5, band 22, and band 31 are displayed.

As can be seen from the experimental results of the simulation, the spectral images obtained by the present invention have clearer details and more complete outlines, which have been greatly improved than the CASSI system of Duke University; as shown in table (1), from the reconstructed image It can be seen that the PSNR of the reconstructed image in the present invention is 7-10dB higher than that of the Duke University CASSI system, with an average of about 8.5dB. These two aspects have fully demonstrated the excellent performance of the present invention.

Table 1. PSNR comparison

PSNR/dB Figure 6 Figure 7 CASSI 31.4079 34.1876 this invention 38.6715 43.9457

Claims (5)

1. A compressed spectral imaging system based on panchromatic imaging, including an observation module, an image reconstruction processing module, the observation module observes the spectral image to obtain an observation image, and the image reconstruction processing module reconstructs the observation image to obtain the original The spectrum image is characterized in that the observation module is divided into two, that is, a compressed spectrum observation module (2) and a panchromatic observation module (3), and the front ends of these two observation modules are provided with a beam splitter module (1); The incident light beam of the spectral image passes through the beam splitter module (1) and is divided into two beams with the same information and different directions, one path passes through the compressed spectral observation module (2) to realize the compressed coding observation of the spectral image, and the other path passes through the panchromatic observation module ( 3) Realize the panchromatic observation of the spectral image; the image reconstruction processing module (4) performs simultaneous fusion of the compressed coding observation and panchromatic observation results of the spectral image output by these two modules to complete the reconstruction of the spectral image. 2. The compressed spectrum imaging system based on panchromatic imaging according to claim 1, characterized in that, the compressed spectrum observation module (2) includes a first lens group (21), a coding template (22), a dispersion element (23) and the first area array detector (24); The coding template (22) is positioned at the rear end of the first lens group (21), realizes the coding to spectral image, and dispersion element (23) is positioned at the coding template (22) The rear end is used to translate the spectral dimension information of the spectral image to realize the dispersion of the spectral image. The first area array detector (24) is located at the rear end of the dispersion element (23) and is used to observe the image and obtain encoded image information. 3. The compressed spectrum imaging system based on panchromatic imaging according to claim 1, wherein the panchromatic observation module (3) includes a second lens group (31) and a second area array detector (32 ), the second area array detector (32) is positioned at the second lens group (31) rear end, is used for observing image, obtains panchromatic image information, and this panchromatic image information comprises first area array detector (24) record Spectral information and missing spectral information. 4. A compressed spectral imaging method based on panchromatic imaging, comprising: (1) Spectral image observation steps: (1a) Suppose the size of the original spectral information matrix _f0 is M×N×L, where M×N is the spatial resolution of the spectral information, and L is the spectral resolution of the spectral information; (1b) Let the spectral information of any point be f ₀ (m,n,k), where m and n represent spatial dimension coordinates, k represents spectral dimension coordinates, where 0≤m≤M-1, 0≤n≤N- 1, 0≤k≤L-1; (1c) Divide the original spectral information into two channels at a ratio of 1:1, where the information f ₁₁ (m,n,k) contained in the first channel and the information f ₂₁ (m,n,k) contained in the second channel ) are the same, namely: ${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$ (1d) Use the encoding function T(m,n) to encode the first spectral information, and obtain the encoded spectral information f ₁₂ (m,n,k) as: ${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$ Among them, T(m,n) randomly takes 0 or 1; (1e) Translate the information of the kth spectral segment in the spectral information of the first channel of encoding by k pixels, that is, translate the information of the mth row of the kth spectral segment to the mkth row, and obtain the spectral information after the shifting f ₁₃ (m,n,k) is: ${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$ (1f) Simultaneously expose the spectral information of the first path and the second path, and obtain the observation result y ₁ (m,n) of the first path and the observation result y ₂ (m,n) of the second path: ${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$ Record the results of these two observations as: Y=Hf, Where Y={y ₁ (m,n),y ₂ (m,n)} is the observation image matrix, H is the observation operator, which represents the observation model of the system, and f is the original spectral information; (2) Spectral image reconstruction steps: (2a) Send the observed image matrix Y to the image reconstruction processor; (2b) Set the sparse base Ψ as wavelet base, DCT base or Fourier base, so that the spectral information is sparse under the sparse base Ψ; (2c) The image reconstruction processor uses a nonlinear optimization method to reconstruct the original spectral information f according to the observed image matrix Y and the sparse basis Ψ. 5. the compressed spectral imaging method based on panchromatic imaging according to claim 4, is characterized in that, utilizes nonlinear optimization method described in step (2c) to reconstruct original image, carries out as follows: (2c1) Set the optimization objective function as min(||Ψ ^T f|| ₁ ), where T represents the matrix transposition, ||·|| ₁ represents the l ₁ norm for the projection coefficient Ψ ^T f, min( ) means to take the minimum value of _l1 norm; (2c2) taking the observed image matrix Y=Hf as a constraint condition; (2c3) Simultaneously optimize the objective function and constraint conditions, and obtain f that satisfies the constraint condition Y=Hf and minimizes ||Ψ ^T f|| ₁ , which is the original spectral information f.