WO1998055882A1

WO1998055882A1 - Imaging system having numerical residual focusing

Info

Publication number: WO1998055882A1
Application number: PCT/NL1998/000330
Authority: WO
Inventors: Augustinus Johannes Berkhout; Maurits Sebastiaan Van Der Heiden; Leo Ongkiehong
Original assignee: Stichting voor de Technische Wetenschappen STW
Current assignee: Stichting voor de Technische Wetenschappen STW
Priority date: 1997-06-04
Filing date: 1998-06-04
Publication date: 1998-12-10
Anticipated expiration: 1999-12-04
Also published as: NL1006229C2; AU8040298A

Abstract

Method and device for forming an image of an object, in which the following steps are performed: generating and transmitting a transmitted beam (B+) to a medium; receiving echo signals caused by the medium within a received beam (B-); converting the echo signals into incoming electrical signals to form an image (P(r,z¿0?,φ); p(x,t), P(kx,φ)); wherein the transmitted beam and the received beam, respectively, is transformed into a virtual transmitted beam of a predetermined desired shape and a virtual received beam of a predetermined shape, respectively, to form the image (P(r,z0,φ); p(x,t), P(kx,φ)) and during the transformation at least one spatial phase adjustment is applied.

Description

Imaging system having numerical residual focusing

The present invention relates to a device for forming an image of an object, comprising: - transmitting means for generating and transmitting a transmitted beam having a certain transmitted-beam property to a medium; receiving means for receiving echo signals caused by the medium within a received beam having a certain received-beam property; conversion means for converting the echo signals into incoming electrical signals; a processor which is connected to the conversion means and is designed to receive the incoming electrical signals and to transform the transmitted beam and the received beam, respectively, into a virtual transmitted beam of a predetermined desired shape and a virtual received beam of a predetermined shape, respectively, for the formation of an image.

Such a device is disclosed in "Digital Processing for Improvement of Ultrasonic Abdominal Images", IEEE Transactions on Medical Imaging, Vol. MI-2, No. 2, June 1983, pages 66-75 by CN. Liu et al.

Ultrasonic imaging systems use transducers for generating and registering acoustic waves. Sometimes, such imaging systems have separate transmitting transducers and receiving transducers. The transmitting transducers generate a high- frequency acoustic wave which irradiates the medium, which, in medical applications, may be tissue. The acoustic wave is reflected by acoustic inhomogeneities. The receiving transducer detects the reflected signal and converts it into electrical signals, which can be made visible. In many ultrasonic applications, the transmitting transducer and receiving transducer form one unit and reference is made to "single-transducer pulse echo measurements". In applications in which the transducer comprises a plurality of elements, reference is made to a transducer array. As a result of moving the single transducer or driving the individual elements of a transducer array differently, the medium is irradiated differently during each measurement and an image is obtained by combining and visualizing all the measured signals.

In practice, it is desirable to form images having a high resolution. Imaging with a high resolution means the formation of an image with a high separation power, both radially and axially. High axial resolution means that, viewed from the transducer, inhomogeneities just behind one another can be distinguished. High radial resolution means that, viewed from the transducer, inhomogeneities just next to one another can be imaged separately. A high axial resolution is generally achieved by irradiating the medium with a short acoustic pulse. Spectrally, this means that the transmitting transducer has to generate a broad-band acoustic pulse.

A high radial resolution is generally achieved by keeping the width of the generated beams of the transmitting and receiving transducers as small as possible in a focal zone. Thus, a focusing beam having one fixed focus has the shape of an "hourglass" which is narrowest in the focal zone. In practice, the focus does not have infinitely small dimensions. Thus, punctiform particles at the focus undergo a widening. Particles outside the focal zone are spread out still more severely.

The above applies not only to ultrasonic imaging systems, but to all types of imaging systems in which use is made either of sound or of electromagnetic radiation. The present invention therefore relates to all such imaging systems.

With systems according to the prior art, the best imaging is obtained of those particles in the medium which are situated in the focal zone. In order, therefore, to obtain as good images as possible at different distances from the imaging system, it is proposed in the prior art to vary the distance from the focal zone to the imaging system with the aid of electromechanical or electrical means (dynamic focusing). However, this results in complex systems.

For imaging systems not having a focusing beam, the above drawbacks apply to an even greater extent. The above paper by Liu et al. describes how an improvement in ultrasonic images can be achieved by digital data processing of the transmitted and received beams. The digital data processing relates solely to the adjustment of the amplitudes of transmitted and received beams.

It is the object of the present invention to achieve a more far-reaching improvement in ultrasonic images by providing an imaging system having a maximum achievable separation capability, both inside and outside the focal zone.

To achieve said object, the present invention proposes a device for forming an image of an object as defined above, which device is characterized in that the processor is designed to apply at least one spatial phase adjustment during the transformation for the formation of the image.

Where the amplitude of the beams is adjusted according to the prior art, the invention therefore applies at least one spatial phase matching. The beam shape in the entire space can be adjusted more satisfactorily in calculating the image. As a result, a more accurate image can be obtained. In addition, the application of spatial phase adjustment proves to be faster in the sense that a mathematically desired shape of the beams can be obtained more quickly.

In an exemplary embodiment, the invention relates to a device as defined above and which is characterized in that the spatial phase adjustment takes place as a component of a residual focusing process according to:

^⁽ = ^ 2-πf^F _m ⁽ ><*^)p(K><^»)d«

where:

P is the Fourier transform of an unprocessed image, r_m is the residual Fourier-transformed focusing result for a time value t_m and F_m is a Fourier-transformed focusing operator which is given by

where:

2k_z(t_m -tf) = spatial phase factor,

Am = amplitude factor,

k_z ⁼ ^_x ²-ω

k_x = wave number, ω = angular frequency, c = wave velocity,

z_rz₀ = distance between focus and transmitting means.

A device according to the invention avoids dynamic focusing during the measuring process and focusing takes place virtually both in transmission and reception after the measuring process, namely during the processing of the incoming electrical signals by the processor. As a result, the physical imaging system can remain robust and simple. As stated, it is possible, for example, to use a device which has only one focal zone during transmission and reception. In this connection, use is made of the high power and flexibility of modern processors. Thus, an image can be obtained which has high resolution at all levels of depth.

In a preferred embodiment, the virtual transmitted beam and/or the virtual received beam have a constant cross-section. The cross-section of the beams may be circular or ellipsoidal, or have any other desired shape. The cross-section of the said virtual beams is preferably chosen to be as small as possible, the minimum size depending on the transducer(s) used and the frequency content of the transmitted signal.

To transform the beam(s) into the said virtual beam(s), the shape of the beam(s) must be known to the processor. The shape of the beam(s) may be derived, for example, analytically by the processor on the basis of data relating to the type of transducer(s) used. As an alternative, the shape of the beam(s) can be measured in one plane in the medium. With the aid of wave theory, the entire three-dimensional shape of the beam(s) can then be determined unambiguously. The measurement of the shape of the beam(s) has the advantage that deviations of the transducer(s) are automatically allowed for in the measurement process.

Preferably, the processor is designed to perform a lateral deconvolution process on the image, which deconvolution process depends on the distance in the medium from the imaging system and which deconvolution process yields a filtered image.

The operations performed by the processor preferably take place in the Fourier domain. As a result, the lateral deconvolution process can be replaced by a simple multiplication process. In such an embodiment, the processor is therefore designed to perform the following processing steps on the image: a. calculation of the Fourier transform of the image; b. performance of lateral deconvolution on the Fourier-transformed image as a multiplication process in the Fourier domain; c. performance of an inverse Fourier transformation on the result of step b. In general, the transmitted beam will have too long a pulse shape. In an embodiment, the processor is also designed to perform a temporal deconvolution step so that the pulse shape in the filtered image is shortened in time. This results in a higher axial resolution. The present invention is not restricted to a device. The invention also relates to a method for forming an image of an object, comprising:

- generating and transmitting a transmitted beam having a certain transmitted-beam property to a medium;

- receiving echo signals caused by the medium within a received beam having a certain received-beam property;

- converting the echo signals into incoming electrical signals;

- processing the incoming electrical signals to form an image by transforming the transmitted beam and the received beam, respectively, into a virtual transmitted beam of a predetermined desired shape and a virtual received beam of a predetermined shape, respectively, characterized in that at least one spatial phase adjustment is applied during the transformation for the formation of the image.

Further embodiments of the method emerge from the dependent method claims. The present invention is explained by reference to some figures which are intended for the purpose of more detailed illustration and not of restricting the scope of protection thereof.

Figure 1 shows a beam generated by a focusing transducer in an arrangement known per se; Figure 2 shows a diagrammatic image of six fully reflecting point diffractors, such as are produced by an imaging system having one fixed focus, such as is also known per se;

Figure 3 shows a diagram for the more detailed illustration of the invention.

Ultrasonic imaging systems use transmitting and receiving transducers for generating and registering acoustic waves. The essence of the invention will be explained below by reference to an acoustic pulse-echo imaging system in which use is made of a transmitted/received beam having an "hourglass shape" with one focus. As stated, the general applicability of the mathematical formulation is, however, not restricted hereto. The shape of the beam may be any one, provided it is known to the processor 4 (see Figure 3) of the system.

Figure 1 shows a transmitting transducer 1 which generates a beam B⁺ in an axis system in which the lateral positions are indicated by r and the axial positions are indicated by z. In the arrangement shown in Figure 1, the origin of the beam B¹ emitted by the transducer 1 is situated at the position (r_k,z₀). The transmitting transducer 1 shown generates a focusing beam B', whose focus is situated at position (r_k,z_f).

The radial resolution is determined by the width of the transmitting/receiving transducer. Thus, a focusing beam B⁺ having a fixed focus has the shape of an "hourglass" which is narrowest in the focus zone at a distance z_rz₀ from the transmitting transducer 1, as shown in Figure 1.

In order to obtain as high as possible radial and lateral resolution with the systems according to the prior art, electromechanical or electrical measures are taken in order to displace the position of the focus of the beam during the measurement process.

This electromechanical or electrical solution proves, however, to be unnecessary. It proves to be possible to apply a numerical focusing to the received image with the aid of a processor after performing the measurement process without actually displacing the focus of the transducer(s) during the measurement.

First of all, the general mathematical formulation of the invention is given below. An example of the general mathematical formulation for an application in two dimensions then follows.

The process, the mathematical formulation The beams of a transmitting transducer at the position (r„z₀) and a receiving transducer at the position (r ,z₀) can be represented in any plane (z=z_m) respectively by the functions B⁺(r,z_m; r„z₀; ω) and B^"(r_j,z₀; r,z_m; ω). The effective beam of the transmission/reception combination is given by the product of the two beams.

This means that, in a single-transducer system (pulse-echo system), the effective beam at position (r,z₀) of one perfectly reflecting point diffractor at the point (r_k,z_m) is represented by ^G*^^zc»^ω) =^{B ~}(r,z₀;r_k,z_m,ω)B ⁺(r_k,z_m;r,z₀;ω) O)

or, for a medium without lateral variations,

^G W^ω) = ^{B ~}(^₀;r_k,z_m ω)B ⁺(r_Λ;r,z₀;ω) (lb)

Any image P at position (r,ζ₀) can be represented as the summation of images P_m(r,z₀) due to all the point diffractions in all the planes z_m:

P(r,z₀,ω) = ∑ P_m(r,z₀,ω)

(2a) = Σ ⁵»Σ Gi(r-r_k,z₀, )R _k_z_m_ )e ^~2jωt- m k

where R⁺(r_k,z_m,co) represents the reflectivity distribution for depth level z_m. S_m(ω) is equal to the pulse shape for depth level z_m, G_m = G,{-e^"2jωt<" and t_m = (z₀-z_m)/c.

All this is explained in greater detail in Figure 2. Figure 2 shows a diagrammatic image of six fully reflecting point diffractors, that is to say R⁺ = 1, which are located at lateral position r_k in an imaging system having one fixed focus. Note that, in Figure 2, the vertical axis is now the time axis and that the beam has its most restricted size at time t = t_f, that is to say at the time at which the beam reaches the focus.

Note that Formula 2a represents a lateral convolution process:

P(r,z₀,ω) = ∑ 5_m(ω)[G_m(r,z₀,ω)*R⁺(r,z_m,ω)] (2b) m

In the focal zone, the function G_m has the smallest width and this depends on the dimensions, the shape and the frequency range of the transducer(s). Outside the focal zone, G_m becomes wider as a consequence of a wave-propagation-dependent spreading. Said spreading is not transducer-dependent and can be calculated from wave theory if G_m is known at only one z-plane.

A filter F_m can therefore be determined which, for any reflection depth z_m having vertical reflection time 2t_m = 2(z₀-z_m)/c, the function G^ can be compressed at any depth to a size Go which the function G' has at the focus: (3)

^Gi = ^F _m*

Filter process (3) means the application of a depth-dependent lateral deconvolution process to the measured image:

E₀(r,z_0.ω) = ∑ F_m(r,z₀,ω) *P_m(r,z₀_ω)

(4a)

G₀( ,ω) * S_m(ω)R ,z_m_ ω)e ^~2^"'

where Gό(r,ω) represents a narrow depth-independent beam which can be termed a "pencil beam". Optionally, the filter F_m could also shorten the time pulse (temporal deconvolution) and/or alter the shape of the beam at the focus, for example virtually reduce the intensity of side lobes and narrow the width of the main lobe:

P₀(r,z₀,ω) = S₀(ω)G₀'(r,ω) *∑ R r_.z_m,ω)e ^"2yωt'^« (4b) m

where S₀(ω) represents the resulting pulse after the optional temporal "pulse shaping" process and GO(r,ω) represents the resulting beam after the optional lateral "beam shaping" process.

Result (4b) represents the result of an integrated hybrid imaging process which simulates a virtual imaging system having a narrow depth-independent beam ("pencil beam"), a variable focus being simulated, as it were, during transmission and reception with the aid of numerical methods. Example

The invention is now explained further by reference to an example with reference to Figure 3. With the aid of a physical imaging system 2, an analog electrical signal is generated which is fed to an A/D converter 3. The digitized output signal of the A/D converter 3 is fed to a digital processor 4. The physical imaging system 2 may be any known imaging system. Thus, the A/D converter 3 and the digital processor 4 can also be commercially obtainable instruments.

Figure 3 indicates, with the aid of an ellipsoidal line 5 that the physical imaging system 3 gives a "rough" image. Said image is an image which can be obtained using systems according to the prior art. Another ellipsoidal line 6 indicates diagrammatically that the digital processor 4 is programmed so that an image having high resolution is obtained. For this purpose, the digital processor is provided with a program which uses the theory given above. The digital processor 4 comprises residual focusing operators which are associated with the filter process F_m(r,z₀,ω). The rough image is treated with said operators (lateral deconvolution) to obtain a result having an unprecedentedly high separation capability which results in a completely variable focus during transmission and reception. The theory given above is now illustrated in two dimensions (r therefore becomes x) for the situation of a single-transducer system having one fixed focus, whose position is given by the double-path transit time t_f = 2(z_rz₀)/c. If p(x,t) represents the "rough" image and P(k_x,ω) represents the two-dimensional Fourier transform thereof, the residual Fourier-transformed focusing result for the time level t_m = mΔt (m = 0,1,2,...,M; Δt = predetermined time duration) can be written as:

where F_m is the Fourier-transformed focusing operator which is given by

+2jk _m-t_f) (5b)

F_m(k_χ,ω) =A_me

where

Using the amplitude factor A_m and the value of 2k_z(t_m-t_f), both the amplitude and the phase of the "rough" image can be adjusted mathematically. In view of the factor t_m-t_f in the phase, the phase itself can be adjusted in a depth-dependent manner, which promotes the accuracy and speed.

The amplitude factor A_m in the Fourier-transformed focusing operator F_m can optionally be used for the transducer-dependent "pulse shaping process", that is to say the abovementioned time pulse shortening (temporal deconvolution) and/or the "beam shaping" process, that is to say the abovementioned adjustment of the beam at the focus. If A_m = 1, the residual focusing operator is a wave-field operator and is dependent only on the wave velocity c and the position of the focus z_f.

In this example, the entire process therefore comprises a double Fourier transformation: p(x,t) → P(k_x,ω) and a residual focusing process (5a) for m = 1,2,...,M, followed by single inverse Fourier transformation r_m(k_x,t_m) — > r(x,t_m) for m = 1,2, ...,M.

If a time-dependent focusing process has already been used in the physical imaging system 2 in the receiving phase, (5b) has to be replaced by

If no focusing transducers are used in the physical imaging process 2 and the beam therefore immediately becomes wider starting from position z₀ as a consequence of a wave-propagation- independent spreading, t_f must be taken as t_f = 0 in (5b).

List of the most important symbols

ω = angular frequency c = wave velocity (r,z) = position expressed as lateral position r and axial position z with respect to an origin; B⁺(r,z;r_k,z₀;ω) = transmitted beam at position (r,z) due to transmitting transducer at position (r_k,z₀) having angular frequency ω; B^"(r.,z₀,r,z;ω) = received beam at position (r,z) due to receiving transducer at position (r.,z₀) having angular frequency ω;

G_m(r-r_k,z₀,ω) = B\B = effective beam at position (r_k,z_m) due to a single-transducer system at position (r,z₀); P(r,z₀,ω) = unprocessed image at position (r,z₀);

P_m(r,z₀,ω) = unprocessed image of all the individual point reflections in plane (z = z_m);

P₀(r,z₀,ω) = image after depth-dependent lateral deconvolution of P(r,z₀,ω);

S_m(ω) = pulse shape in plane (z = z ;

S₀(ω) = pulse shape after temporal deconvolution;

R⁺(r,z_m,ω) = reflectivity distribution in plane (z = z_m); Gό(r,ω) = narrow depth-independent beam (pencil beam) as a function of r and ω; F_m(r,z₀,ω) = filter process to make the depth-dependent beam G_(,(r,z₀,ω) into a depth-independent beam Gό(r,ω).

Claims

1. Device for forming an image of an object, comprising: transmitting means (1) for generating and transmitting a transmitted beam having a certain transmitted-beam property (B⁺) to a medium; receiving means (2) for receiving echo signals caused by the medium within a received beam having a certain received-beam property (B^"); conversion means (2) for converting the echo signals into incoming electrical signals; - a processor (4) which is connected to the conversion means (2) and is designed to receive the incoming electrical signals and to form an image (P(r,z₀,ω); p(x,t), P(k_x,ω)) by transforming the transmitted beam and the received beam, respectively, into a virtual transmitted beam of a predetermined desired shape and a virtual received beam of a predetermined shape, respectively; characterized in that the processor is designed to apply at least one spatial phase adjustment during the transformation for the formation of the image.

2. Device according to Claim 1, characterized in that the spatial phase adjustment takes place as a component of a residual focusing process according to:

,W=^Λ^U ^

where:

P is the Fourier transform of an unprocessed image, r_m is the residual Fourier-transformed focusing result for a time value t_m and

F_m is a Fourier-transformed focusing operator which is given by

where: 2k_z(t_m-t_f) = spatial phase factor, Am = amplitude factor,

k_x = wave number, ω = angular frequency, c = wave velocity, t_f = 2(z_rz₀)/c, z_rz₀ = distance between focus and transmitting means.

3. Device according to Claim 1 or 2, wherein the virtual transmitted beam and the virtual received beam have a substantially constant cross-section.

4. Device according to one of Claims 1, 2 or 3, wherein the processor (4) is designed to perform a lateral deconvolution process (F_m(k_x,ω)) on the image (P(r,z₀,ω); p(x,t), P(k_x,ω)), which deconvolution process (F_m(k_x,ω)) depends on the distance in the medium from the imaging system and which deconvolution process (F_m(k_x,ω)) yields a filtered image (P₀; r(x,t_m), r_m(k_x,t ).

5. Device according to Claim 4 wherein the processor is designed to perform the following processing steps on the image (p(x,t)): a. calculation of the Fourier transform (P(k_x,ω)) of the image (p(x,t)); b. performance of lateral deconvolution (F_m(k_x,ω)) on the Fourier- transformed image (P(k_x,ω)) as a multiplication process in the Fourier domain; c. performance of an inverse Fourier transformation on the result of step b.

6. Device according to one of the preceding claims, wherein the image (P(r,z₀,ω); p(x,t), P(k_x,ω)) has a predetermined pulse shape (S_m(ω)) which depends on the distance in the medium from the imaging system (2) and the processor (4) is also designed to perform a temporal deconvolution step so that the pulse shape in the filtered image (P₀; r(x,t_m), r_m(k_x,t_m)) is shortened in time.

7. Device according to one of the preceding claims, wherein the processor (4) is also designed for subsequently mathematically altering the shape of the original transmitted beam and the original received beam at the focus, for example, by reducing the intensity of side lobes and narrowing the width of a main lobe.

8. Method for forming an image of an object, comprising:

- generating and transmitting a transmitted beam having a certain transmitted-beam property (B ) to a medium;

- receiving echo signals caused by the medium within a received beam having a certain received-beam property (B );

- converting the echo signals into incoming electrical signals;

- processing the incoming electrical signals to form an image (P(r,z₀,ω); p(x,t), P(k_x,ω)) by transforming the transmitted beam and the received beam, respectively, into a virtual transmitted beam of a predetermined desired shape and a virtual received beam of a predetermined shape, respectively, characterized in that at least one spatial phase adjustment is applied during the transformation for the formation of the image.

9. Method according to Claim 8, characterized in that the spatial phase adjustment takes place as a component of a residual focusing process according to:

where: P is the Fourier transform of an unprocessed image, r_ιn is the residual Fourier-transformed focusing result for a time value t_m and F_nι is a Fourier-transformed focusing operator which is given by

F_m(k_χ,ω) =A_me ^H'AP

where: 2k_z(t,„-t_r) spatial phase factor, Am amplitude factor,

K = wave number,

CO = angular frequency, c = wave velocity, t. = 2(z_rz₀)/c, z_t-z_υ = distance between focus and transmitting means

10. Method according to Claim 8 or 9, wherein the virtual transmitted beam and the virtual received beam have a substantially constant cross-section.

11. Method according to one of Claims 8, 9 or 10, wherein the processor (4) is designed to perform a lateral deconvolution process (F_m(k_x,ω)) on the image (P(r,z₀,ω); p(x,t), P(k_x,ω)), which deconvolution process (F_m(k_x,co)) depends on the distance in the medium from the imaging system and which deconvolution process (F_m(k_x,ω)) yields a filtered image (P₀; r(x,t ,^'r_m(k_x,t_m)).

12. Method according to Claim 11, wherein the processor is designed to perform the following processing steps on the image (p(x,t)): a. calculation of the Fourier transform (P(k_x,ω)) of the image (p(x,t)); b. performance of lateral deconvolution (F_m(k_x,ω)) on the Fourier-transformed image (P(k_x,ω)) as a multiplication process in the Fourier domain; c. performance of an inverse Fourier transformation on the result of step b.

13. Method according to one of the preceding Claims 9 to 12, inclusive, wherein the image (P(r,z₀,ω); p(x,t), P(k_x,ω)) has a predetermined pulse shape (S_m(ω)) which depends on the distance in the medium from the imaging system (2) and the processor (4) is also designed to perform a temporal deconvolution step so that the pulse shape in the filtered image (P₀; r(x,t_m), r_m(k_x,t_m)) is shortened in time .

14. Method according to one of the preceding Claims 9 to 13 inclusive, wherein the processor (4) is also designed for subsequently mathematically altering the shape of the original transmitted beam and the original received beam at the focus, for example, by reducing the intensity of side lobes and narrowing the width of a main lobe.