WO2009092881A1

WO2009092881A1 - Method and device for improving the resolution of an ultrasound image

Info

Publication number: WO2009092881A1
Application number: PCT/FR2008/001508
Authority: WO
Inventors: Denis Kouame; Jean-Marc Girault
Original assignee: Université François Rabelais
Priority date: 2007-10-24
Filing date: 2008-10-24
Publication date: 2009-07-30
Also published as: FR2923053A1; FR2923053B1

Abstract

The invention relates in particular to a method for improving the resolution of an ultrasound image of a biological tissue or of an object, the method comprising steps in which: radiofrequency lines emanating from the biological tissue or from the object are received so as to generate the ultrasound image in the form of a radiofrequency matrix comprising the radiofrequency lines; a processing based on an autoregressive parametric model is applied so as to determine an autoregressive estimation of an envelope of the radiofrequency lines, the step of processing by an autoregressive parametric model comprising a step of determining the optimal autoregression parameters according to an optimal autoregression order in which: a data vector is created by juxtaposing a transform of the radiofrequency lines; an instrument vector is created by delaying the samples of the data vector by a delay; the covariance matrix M of the data vector and of the instrument vector is calculated; the covariance matrix M is factorized so as to determine the optimal autoregression parameters according to an optimal autoregression order, in which the covariance matrix is factorized in the form M = UDVH, in which D is a diagonal matrix, U is a matrix comprising the parameters of the autoregressive model and V is a matrix of the intermediate parameters, the matrix V being different from the matrix U.

Description

METHOD AND DEVICE FOR IMPROVING THE RESOLUTION OF AN ULTRASONIC IMAGE

The invention relates to the field of processing ultrasound images.

The invention aims to improve the resolution of such ultrasound images.

There are already methods to improve the resolution of such ultrasound images.

One way of improving the resolution of the ultrasound images is to improve the performance of the device generating such ultrasonic images, that is to say in particular the ultrasound transducer.

However, even if the resolutions obtained by increasing the frequency of the transducers are satisfactory, such as 50 MHz transducers in high frequency imaging, known high-resolution ultrasound transducers are complex to develop and therefore expensive.

A second way to improve the resolution of the ultrasound images is to acquire ultrasound images by a standard acquisition device, and to perform a subsequent treatment of the ultrasound images.

Thus, according to this method, the resolution is improved by a method of signal processing on the ultrasound image already generated and not at the level of the acquisition mode of the ultrasound image itself. This type of subsequent treatment of ultrasound images is less expensive than the devices mentioned above.

The present invention relates to such a method using a signal processing on the ultrasound image already generated.

According to the invention, a better resolution can be obtained with an ultrasound transducer, having a lower resolution. Thus an image made with a transducer having a given nominal frequency, for example 20Mhz, will have, after processing using the proposed method, a higher resolution than that obtained intrinsically at the nominal frequency of 20 MHz in this example.

The invention relates more particularly to a method for improving the resolution of an ultrasound image of a biological tissue or an object, the method comprising steps in which:

radiofrequency lines originating from the biological tissue or the object are received so as to generate the ultrasound image in the form of a radiofrequency matrix comprising the radiofrequency lines;

autoregressive parametric model processing is applied so as to determine an autoregressive estimate of a radiofrequency line envelope, the autoregressive parametric model processing step comprising a step of determining the optimal autoregressive parameters according to an optimal autoregressive order.

The invention also relates to a device for improving the resolution of an ultrasound image of a biological tissue or an object, the device comprising:

first means for receiving radio frequency lines derived from the biological tissue or the object, so as to generate the ultrasound image in the form of a radiofrequency matrix comprising the radiofrequency lines;

second means for applying an autoregressive parametric model treatment so as to determine an autoregressive estimate of the radiofrequency line envelope, the autoregressive parametric model processing step comprising a step of determining the autoregressive optimal parameters in a sequence of optimal autoregressions.

Such a method and such a system are described in the document entitled "Improvement of the resolution of high resolution ultrasound images", by Carole Garnier of the EGID BORDEAUX Institute 3. This document notably describes how to use a treatment by model parametric autoregressive improves the resolution of the ultrasound image in the spatial domain.

According to this document, for the determination of the autoregressive model, it is necessary to determine optimal parameters for an optimal order.

Indeed, a poor estimate of the order can lead to a poor determination of the parameters of the model and to an unsatisfactory treatment of the image.

A first object of the invention is therefore to improve the order estimation in the autoregressive parametric model processing of the ultrasound image so as to improve the resolution of the image.

The document entitled "Multidimensional complex number parametric model order and estimate parameters" by Kouamé et al. describes in general terms a method for the estimation of parameters and the order of an autoregressive parametric model. This document, however, does not teach to apply this method to a subsequent treatment of an ultrasound image.

In addition, it has been shown that the application of the method mentioned in the publication of Kouamé et al. does not allow a good improvement of the resolution of the ultrasound image in the presence of colored noise or correlated to the image. Indeed, this method is based on a least squares algorithm deemed unsuited to the presence of colored noise or correlated to the image.

However, in many applications, the ultrasound images pass through different tissues, which causes a creation of colored noise in the ultrasound image.

Similarly, the publication of Kouamé et al., "High resolution processing techniques for ultrasonic Doppler Velocimetry in the presence of colored noise" describes a factorization method for frequency measurements in the context of Doppler velocimetry, but does not teach any apply this method to a treatment of an ultrasound image.

Another object of the invention is therefore to improve the resolution of the ultrasound image when it passes through different tissues.

Another object of the invention is to improve the resolution of the ultrasound image in the presence of colored noise or correlated to the ultrasound image.

At least one of these objects is achieved by the invention by virtue of the fact that in the aforementioned method, the step of determining optimal autoregressive parameters comprises steps in which: a data vector is created by juxtaposing a transform of the radiofrequency lines;

an instrument vector is created by delaying the samples of the data vector by a delay;

the covariance matrix M of the data vector and the instrument vector is calculated;

the covariance matrix M is factorized so as to determine the optimal autoregressive parameters according to an optimal autoregressive order, in which the covariance matrix is factorized in the form M = UDV ^H , in which D is a diagonal matrix, U is a matrix comprising the parameters of the autoregressive model and V is a matrix of the intermediate parameters, the matrix V being different from the matrix U.

Indeed, it has been shown that such a factorization provides a better estimate of the autoregressive parameters, so that a better resolution of the ultrasound image after treatment is obtained, even in the presence of colored or correlated noise. to the ultrasound image. In addition, according to the invention, the optimal autoregressive parameters and the optimal autoregressive order can be determined simultaneously.

According to one embodiment of the invention, the method further comprises steps in which:

the Hilbert transform of the radiofrequency lines of the radiofrequency matrix is calculated so as to generate analytical signals Z _k (u), k = 1, 2, ... N; N being the number of radiofrequency lines, each associated with a radiofrequency line x _k (u), k = 1, 2, ... N;

the inverse Fourier transform of each analytical signal Z _k (u) is calculated so as to generate the transformation of the radio frequency lines. According to one embodiment of the invention, the method further comprises a step in which the envelope of each radio frequency line is generated by calculating a power spectral density from the autoregressive modeling.

This problem is also solved by a device as described above in which the second means are furthermore arranged for:

- create a data vector by juxtaposing the transformed radio frequency lines;

creating an instrument vector by delaying the data vector samples by a delay;

calculating the covariance matrix M of the data vector and the instrument vector;

factoring the covariance matrix M so as to determine the optimal autoregressive parameters according to an optimal autoregressive order, in which the covariance matrix is factorized in the form M = UDV ^H , in which D is a diagonal matrix, U is a matrix comprising the parameters of the autoregressive parametric model, and V is a matrix of the intermediate parameters, the matrix V being different from the matrix U.

According to one embodiment, the second means are furthermore arranged for:

calculating the Hubert transform of the radiofrequency lines of the radiofrequency matrix so as to generate analytical signals Zκ (u) each associated with a radiofrequency line

calculating the inverse Fourier transform of each analytical signal Z _k (u) so as to generate the transformation of the lines radio frequencies.

According to one embodiment, the second means are further arranged to generate the envelope of each radio frequency line by calculating a power spectral density from the autoregressive modeling.

The problem is also solved by a computer program which, when executed on a computer, is able to carry out the steps of the method mentioned above.

An embodiment of the invention will now be described with reference to the appended figures in which:

FIG. 1 represents a device according to one embodiment of the invention;

FIG. 2 illustrates the process carried out in the context of the present invention;

FIG. 3 illustrates the good results of the estimates of autoregressive parameters according to the invention in the context of a colored noise.

As illustrated FIG. 1, a device 1 according to the invention comprises an imaging system 2 for collecting radiofrequency ultrasound signals and a computer 3, for example PC type. These two entities can exist within a single machine.

The ultrasound imaging system 2 makes it possible to collect an ultrasound image consisting of radiofrequency lines.

According to the invention, the computer 3 is arranged to perform a processing of the ultrasound image thus obtained to improve its resolution in the spatial domain. To improve the resolution, an autoregressive model can be used as illustrated FIG. 2. As mentioned in the document entitled "Improvement of resolution of high resolution ultrasound images" cited above, the invention uses the fact that taking the Fourier transform module is equivalent to estimating the power spectral density by a autoregressive model.

In FIG. 2, a Hubert transform is applied to the signal x (u) corresponding to the radiofrequency lines so as to obtain an analytic signal Z (u), associated with x (u).

Mathematically, this transformation of Hubert is expressed as follows:

TH [x (n)] = 1 / (πn) * x (n), the sign * representing a convolution.

In a conventional way, to calculate the envelope, one calculates, in steps 7 and 8, the norm of Z (u), which one smooths by low filtering or by taking the mathematical expectation if one has several realizations, this which is expressed as follows:

e (n) = E | Z (n) | = | x (n) + j TH [x (n)] |

According to the invention, in order to improve the resolution, a super-resolved envelope is calculated by first applying, in a step 9, the inverse of the Fourier transform of the signal Z (u), then, in a step 10 an autoregressive parametric model is applied to determine the optimal parameters to obtain a power spectral density. This power spectral density is equivalent to the super-resolved envelope. In particular, the power spectral density estimated by the autoregressive parametric model provides a spectral resolution better than the classical method of the periodogram if the order is suitably chosen.

The transformed radio frequency lines correspond to the radiofrequency lines for which the analytical signal associated with the line has been calculated, and then the inverse Fourier transform of the analytical signal has been calculated. In a manner known per se, the analytic signal z associated with a real signal x is a complex signal z = x + jy where y is the Hilbert transform of x and j is the pure imaginary complex number.

We now describe how the autoregressive parametric model according to the present invention is applied to determine the optimum order of the model.

According to the invention, to obtain the parametric identification at an optimum order, a data vector is created by juxtaposing the transformed radiofrequency lines and an instrument vector comprising the instrumental variables corresponding to the radiofrequency lines delayed for an arbitrary order m. The delay can be a delay of two or three moments.

The covariance matrix of the data vector and the instrument vector is then calculated. Let M be this covariance matrix.

This matrix M is factored into the form: M = UDV ^H

in which the covariance matrix is factorized in the form M = UDV ^H , wherein D is a diagonal matrix having the cost function, U is an upper triangular matrix whose diagonal elements are equal to 1 and including the parameters of the model parametric autoregressive, and V is an upper triangular matrix of which all the diagonal elements are equal to 1 and including intermediate parameters not used herein; the matrix V being different from the matrix U.

The operator H represents a hermitian transposition corresponding to a transpose followed by the complex conjugation.

The matrix M is not hermitian by construction, since it concerns covariance between the radio frequency lines and the instrumental variables, and U is different from V. U and V contain periodicities of order m + 1.

D is a doubly periodic diagonal matrix of period of order m + 1.

This double periodicity is related to the properties of the image in the direction of propagation of axial and lateral ultrasound.

The minima in each type of periodicity provide the system order, which retrieves the columns of U that contain the optimal parameters. The factor is the optimal order and optimal parameters of the model.

Thanks to these optimal parameters, the power spectral density estimated by the autoregressive parametric model mentioned above is estimated, which provides, as mentioned above, an envelope having a better resolution than the envelope obtained by the mode B. To refine the results, if we have enough computing resources, we can use the decomposition procedure on each line to determine a line-to-line order, calculate a super-resolved envelope line by line and reconstruct the image at the end. the treatment of each line. The mathematical model which underpins the invention is described in detail in particular for an implementation of the invention by a computer program.

Let y (n1, n2) be the image of which one wants to make the parametric modeling autogréssive, that is to say here, what we call here the transformed radiofrequency lines, one models y (n1; n2) by a model 2D autoregressive AR two-dimensional as:

where w (ni, n ₂ ) is a colored noise.

/ is defined so that the estimate is made on the 1 ^st quarter-plane, / = {(k1; k2) / k2 = 0; 1; 2; ...; p1; k2 = 0; 1; 2, ..., p2} and ^4th Quarter- plane, / = {(k1; k2) / / ci = 0; 1,2; ...; p1; k2 = -p2; -p2 + 1; ...; 0} for symmetry reasons.

We detail the calculations for the ^1st quarter plan. Calculations are strictly identical for the 4 ^th quarter plan; only the indices (k'i; Wλ) change range as mentioned above.

UDV factorization ^H allows access to parameters for orders ranging from 0 to m; m fixed a priori and arbitrarily large.

The following data vectors and parameters are defined in which the elements of y and a are juxtaposed independently.

We also define:

Or then

in which z is defined by delaying x, ie z (n _{i 7} n ₂ ) = x (ni-r _o , n ₂ -ro) with for example r _o = 3. And we finally define the instrument vector

Finally, the covariance matrix M that we denote by M _m to denote its dependence with m is defined by:

where n ₁ is the number of radiofrequency lines and n _{2 is} the number of samples per radiofrequency line.

By asking p = (m + 1) ² , the size of this matrix is pxp

We break down M in the form:

where H is the Hermitian transpose.

D is a diagonal matrix with the cost function. It is periodic of period m + 1 in each of the two directions of the image. The minima extracted from each direction provide the optimal order (here pi and p ₂ ), using an Akaike criterion (AIC). U is an upper triangular matrix of which all diagonal elements are equal to 1 and including parameters of the autoregressive parametric model, and V is an upper triangular matrix of which all diagonal elements are equal to 1 and including intermediate parameters not used herein; the matrix V being different from the matrix U.

The optimal parameters are then provided by the column numbers of U provided by the optimal order.

In FIG. 3, there is shown a diagram illustrating the estimates of the real parts of the autoregressive parameters for the second order autoregressive model with colored noise according to:

y (n) = (1 + i) y (n-1) - (0.0625 + 0.5i) y (n-2) + w (n)

with w (n) = - 3rd (n) - 5th (n-2) + 20th (n-1)

with e (n) a Gaussian white noise, and n = 1, 2, ... 2048.

According to this model, the signal w (n) creates a colored noise.

The theoretical parameters are therefore, according to this example, equal to a-i = -1-i and a2 = 0.0625 + 0.5i. Parameter estimation is done recursively moment by moment to illustrate the behavior of the estimates.

In FIG. 3, the lines 4 and 5 represent the theoretical real parts of the parameters a ₁ and a ₂ of the above model respectively equal to -1 and 0.0625.

Curves 13 and 14 represent estimates of these parameters according to the method described in the document "Multidimensional complex number parametric model order and parameters estimation" above in which the covariance matrix M is decomposed in the form M = UDU ^H.

Curves 15 and 16 represent estimates of these parameters. according to the method described above according to the invention in which the covariance matrix M is decomposed in the form M = UDV ^H

On the three curves, the parameters are estimated at times n = 1, 2, ... 2048.

As mentioned above, it is observed in FIG. 3 that the estimates represented by the curves 13 and 14 are strongly biased with respect to the theoretical values. On the contrary, the estimates represented by the curves 15 and 16 are slightly biased with respect to the theoretical values.

According to the invention, the computer 3 illustrated in FIG. 1 comprises a computer program which, when executed, allows the implementation of the processing of the ultrasonic image described above.

The present invention is applicable to two-dimensional images, 3D, or 4D, including images taking into account temporal notions of the type 2D + t, 3D + t, and videos.

Claims

A method for improving resolution of an ultrasound image of a biological tissue or object, the method comprising steps wherein:

radiofrequency lines from the biological tissue or object are received so as to generate the ultrasound image in the form of a radiofrequency matrix comprising the radiofrequency lines; autoregressive parametric model processing is applied so as to determine an autoregressive estimate of a radiofrequency line envelope, the autoregressive parametric model processing step comprising a step of determining the optimal autoregressive parameters according to an optimal autoregressive order;

the method being characterized in that: the step of determining autoregressive optimal parameters comprises steps in which: a data vector is created by juxtaposing a transform of the radio frequency lines; an instrument vector is created by delaying the samples of the data vector by a delay; the covariance matrix M of the data vector and the instrument vector is calculated; the covariance matrix M is factorized so as to determine the optimum autoregressive parameters according to an optimal autoregressive order, in which the covariance matrix is factorized in the form M = UDV ^H , in which D is a diagonal matrix, U is a matrix comprising the parameters of the autoregressive model and V is a matrix of the intermediate parameters, the matrix V being different from the matrix U.

The method of claim 1, wherein the method further comprises steps wherein:

the Hubert transform of the radiofrequency lines of the radiofrequency matrix is calculated so as to generate analytical signals (Z _k (u)) each associated with a radiofrequency line (x _k (u)),;

the inverse Fourier transform of each analytical signal (Z _k (u)) is calculated so as to generate the transformation of the radio frequency lines.

3. Method according to one of claims 1 or 2, wherein the method further comprises a step in which the envelope of each radiofrequency line is generated by calculating a power spectral density from the autoregressive modeling.

4. Device for improving the resolution of an ultrasound image of a biological tissue or an object, the device comprising: first means for receiving radiofrequency lines originating from the biological tissue or the object, so as to generate ultrasound image in the form of a radiofrequency matrix comprising the radio frequency lines; second means for applying an autoregressive parametric model treatment so as to determine an autoregressive estimate of the radiofrequency line envelope, the autoregressive parametric model processing step comprising a step of determining the autoregressive optimal parameters according to an autoregressive order optimal the device being characterized in that: the second means are further arranged to: create a data vector by juxtaposing the transformed radio frequency lines; create an instrument vector by delaying the samples of the data vector by a delay; calculating the covariance matrix M of the data vector and the instrument vector; factorize the covariance matrix M so as to determine the optimal autoregressive parameters according to an optimal autoregressive order, in which the covariance matrix is factorized in the form M = UDV ^H , in which D is a diagonal matrix, U is a matrix comprising parameters of the autoregressive parametric model, and V is a matrix of intermediate parameters, the matrix V being different from the matrix U.

5. Device according to claim 4, wherein the second means are further arranged to: calculate the Hubert transform radiofrequency lines of the radiofrequency matrix so as to generate analytic signals (Z _k (u)) each associated with a line radio frequency (Xk (u)),; calculate the inverse Fourier transform of each analytical signal (Zκ (u)) so as to generate the transformation of the radio frequency lines.

6. Device according to one of claims 4 or 5, wherein the second means are further arranged to generate the envelope of each radiofrequency line by calculating a power spectral density from the autoregressive modeling.

7. Computer program which, when run on a computer, is able to carry out the steps of the method according to one of claims 1 to 3.