CN111466949A - MMSE (minimum mean square error) beam former, MMSE beam forming method and computer-readable storage medium - Google Patents

MMSE (minimum mean square error) beam former, MMSE beam forming method and computer-readable storage medium Download PDF

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CN111466949A
CN111466949A CN202010288748.1A CN202010288748A CN111466949A CN 111466949 A CN111466949 A CN 111466949A CN 202010288748 A CN202010288748 A CN 202010288748A CN 111466949 A CN111466949 A CN 111466949A
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阮义
理查德普拉格
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Cambridge University Nanjing Science And Technology Innovation Center Co ltd
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Abstract

The invention provides an MMSE (minimum mean square error) beam former, an MMSE beam forming method and a computer readable storage medium, which improve the technical scheme of realizing the MMSE (minimum mean square error) criterion of synthesized beam approximation based on a Minimum Variance Distortionless Response (MVDR) beam former and a scalar filter in the prior art, and rebuild a coherent factor calculation model and a covariance estimation model. The method solves the technical problem of low quality of the synthesized image caused by covariance estimation and coherence factor calculation deviation in the existing Minimum Variance Distortionless Response (MVDR) beam forming method, can adaptively inhibit the influence of data noise and interference on the imaging contrast ratio, and improves the quality of the synthesized image.

Description

MMSE (minimum mean square error) beam former, MMSE beam forming method and computer-readable storage medium
Technical Field
The invention relates to the technical field of coherent plane compounding, in particular to an MMSE (minimum mean square error) beam former, an MMSE beam forming method and a computer-readable storage medium.
Background
Coherent plane wave synthesis (CPWC), a method to achieve high frame rate and uniform resolution throughout the imaging region, can use plane wave transmission to generate the entire image within one pulse-echo sequence, unlike conventional systems that generate images row by row.
The Minimum Mean Square Error (MMSE) beamformer, which is an array processing technique for enhancing ultrasound coherent plane wave synthesis (CPWC) image quality, typically approximates the minimum mean square error criterion MMSE using a Minimum Variance Distortionless Response (MVDR) beamformer and a scalar filter. In actual practice, scalar filters are typically approximated using a coherence factor whose calculation is based on the incident signal, which is estimated with errors. On the other hand, a minimum variance distortion free response (MVDR) beamformer generally obtains a data covariance matrix in the MVDR algorithm by a spatial smooth approximation estimation, which makes the calculated weight vector smaller, and thus the quality of the synthesized image is lower.
Disclosure of Invention
The purpose of the invention is as follows: to overcome the defects of the prior art, the invention provides an MMSE beam former, an MMSE beam forming method and a computer readable storage medium.
The technical scheme is as follows: the technical scheme provided by the invention is as follows:
an MMSE beam former is applied to coherent plane wave synthesis, receives echo data of plane waves of M different angles transmitted by a transducer through an N-line linear array, and performs beam synthesis; the echo data matrix is recorded as: u (n) ═ u1(n)，u2(n)，…，uM(n)]TThen the synthesized beam is:
Figure BDA0002448974750000011
wherein u isi(n) echo data representing a plane wave i,
Figure BDA0002448974750000012
xi，j(n) echo data representing a plane wave i received at time instant n, jth array element; w is aDCR-MMSEAs a weight vector, wDCR-MMSEThe expression of (a) is:
Figure BDA0002448974750000021
Figure BDA0002448974750000022
Figure BDA0002448974750000023
wherein r isk(n) represents an intermediate parameter which is,
Figure BDA0002448974750000024
qk(N) a set of snapshots of the N array element output signals of the beamformer, qk(n)＝[qk，1(n)，qk，2(n)，…，qk，N(n)]，
Figure BDA0002448974750000025
For the diagonal loading parameters, I denotes the identity matrix and a denotes the time delay vector of all echo data.
An MMSE beamforming method comprising the steps of:
(1) exciting N element linear array transducers to emit M plane waves at different angles, and receiving echo data through N array elements;
(2) the output signal of each array element is acquired through snapshot and is recorded as qk(n)，qk(n)＝[qk，1(n)，qk，2(n)，…，qk，N(n)]，
Figure BDA0002448974750000026
Wherein x isi，j(n) echo data representing a plane wave i received at time instant n, jth array element;
(3) selecting diagonal line loading parameters according to requirements, and obtaining q according to the step (2)k(n) calculating a covariance matrix:
Figure BDA0002448974750000027
wherein I represents an identity matrix;
(4) defining an intermediate parameter rk(n)，
Figure BDA0002448974750000028
a represents the time delay of all echo dataVector quantity; q obtained according to step (2)k(n) and obtained in step (3)
Figure BDA0002448974750000029
Calculate rk(n)，
(5) Calculating a coherence factor:
Figure BDA0002448974750000031
(6) calculating a weight vector:
Figure BDA0002448974750000032
(7) the synthetic beam of the echo is calculated as:
Figure BDA0002448974750000033
a computer readable storage medium having stored thereon at least one instruction executable by a processor, the at least one instruction, when executed by the processor, implementing the MMSE beamforming method.
Has the advantages that: compared with the prior art, the invention has the following advantages: the MMSE beam forming scheme provided by the invention improves the technical scheme of the MMSE based on the Minimum Variance Distortionless Response (MVDR) beam former and a scalar filter to realize the approach of a synthesized beam to a minimum mean square error criterion, overcomes the technical problem of low quality of a synthesized image caused by covariance estimation and coherence factor calculation deviation in the existing Minimum Variance Distortionless Response (MVDR) beam forming method, can adaptively inhibit the influence of data noise and interference on imaging contrast and improve the quality of the synthesized image.
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Fig. 1 is a flowchart of an MMSE beamforming method according to the present invention.
FIG. 2 is a simulated image of 9 ideal lesions generated with different beamformers as involved in the example; wherein, fig. 2(a) is a simulated image of 9 ideal lesions generated by using a CPWC beamformer, with the value of M being 75; FIG. 2(b) is a simulated image of 9 ideal lesions generated using an SS-MVDR beamformer with M taken at 75; fig. 2(c) is a simulated image of 9 ideal lesions generated using a CPWC beamformer, with M taking the value 15; FIG. 2(d) is a simulated image of 9 ideal lesions generated using an SC-MVDR + CF beamformer with M taking the value of 15; FIG. 2(e) is a simulated image of 9 ideal lesions generated using an SS-MVDR + HRCF beamformer with M taking the value of 15; FIG. 2(f) is a simulated image of 9 ideal lesions generated by the joint SC-MVDR beamformer with M taking the value of 15; FIG. 2(g) is a simulated image of 9 ideal lesions generated by the DCR-MVDR beamformer with M being 15; FIG. 2(h) is a simulated image of 9 ideal lesions generated by the DCR-MMSE beamformer, where M is 15; fig. 2(a) to (h) all undergo log compression, showing a dynamic range of 60 dB.
FIG. 3 is an experimental image generated with different beamformers for resolution evaluation as referred to in the examples; fig. 3(a) is an experimental image generated by the CPWC beamformer, with the value of M being 75; FIG. 3(b) is an experimental image generated by the SS-MVDR beamformer with M taking the value of 75; fig. 3(c) is an experimental image generated by the CPWC beamformer, with the value of M being 15; FIG. 3(d) is an experimental image generated by the SC-MVDR + CF beamformer with a value of M of 15; FIG. 3(e) is an experimental image generated by the SS-MVDR + HRCF beamformer with M taking the value of 15; FIG. 3(f) is an experimental image generated by the joint SC-MVDR beamformer with a value of M of 15; FIG. 3(g) is an experimental image generated by the DCR-MVDR beamformer with the value of M being 15; FIG. 3(h) is an experimental image generated by the DCR-MMSE beamformer with the value of M being 15; fig. 3(a) to (h) are log compressed and displayed with a dynamic range of 70 dB.
Fig. 4 is a graph comparing the response of beams generated by a pair of CPWC beamformer (M75), SS-MVDR beamformer (M15) and CPWC beamformer (M15) on a scan centerline with nylon monofilament wire pairs having ordinates of 10mm, 30mm and 50mm, respectively; wherein, fig. 4(a) is a beam response contrast diagram on the cross section of the nylon monofilament metal wire at the ordinate 10mm on the scanning center line; FIG. 4(b) is a plot of the beam response versus a cross-section of a nylon monofilament wire at 30mm ordinate on the scan center line; fig. 4(c) is a plot of the beam response versus the cross-section of a nylon monofilament wire at 50mm ordinate on the scan center line.
Fig. 5 is a response comparison graph of beams generated by a nylon monofilament wire pair CPWC beamformer (M15), a joint SC-MVDR beamformer (M15), an SS-MVDR + CF beamformer (M15), an SS-MVDR + HRCF beamformer (M15), a DCR-MVDR beamformer (M15), and a DCR-MMSE beamformer (M15) at the scanning center line with ordinate of 10mm, 30mm, and 50mm, respectively; wherein, fig. 5(a) shows a response distribution comparison graph of a beam generated by a CPWC beamformer (M15) and a beam generated by a joint SC-MVDR beamformer (M15) on a cross section of a nylon monofilament metal wire at an ordinate of 10mm on a scanning center line; fig. 5(b) shows a graph of the response profile of the beam generated by the SS-MVDR + CF beamformer (M15) and the beam generated by the SS-MVDR + HRCF beamformer (M15) in a cross-section of a nylon monofilament wire at an ordinate of 30mm on the scan center line; fig. 5(c) shows a graph of response distributions of beams generated by the DCR-MVDR beamformer (M15) and beams generated by the DCR-MMSE beamformer (M15) in a cross-section of a nylon monofilament wire at an ordinate of 50mm on a scan center line.
Fig. 6 is an experimental image generated with different beamformers for evaluating contrast, where fig. 6(a) is an experimental image generated with a CPWC beamformer with M taking the value 75; FIG. 6(b) is an experimental image generated using an SS-MVDR beamformer with M taking the value 75; fig. 6(c) is an experimental image generated by using a CPWC beamformer, with the value of M being 15; FIG. 6(d) is an experimental image generated using an SC-MVDR + CF beamformer with a value of M of 15; FIG. 6(e) is an experimental image generated using a SS-MVDR + HRCF beamformer with the value of M being 15; FIG. 6(f) is an experimental image generated by the joint SC-MVDR beamformer with a value of M of 15; FIG. 6(g) is an experimental image generated by the DCR-MVDR beamformer with the value of M being 15; FIG. 6(h) is an experimental image generated by the DCR-MMSE beamformer with the value of M being 15; fig. 6(a) to (h) all undergo log compression, showing a dynamic range of 70 dB.
Fig. 7 is a carotid ultrasound image obtained by scanning the carotid artery with different beamformers, wherein fig. 7(a) is a carotid ultrasound image generated by using a CPWC beamformer with the M value being 75; FIG. 7(b) is a carotid ultrasound image generated using an SS-MVDR beamformer with M taken at 75; FIG. 7(c) is a carotid ultrasound image generated using a CPWC beamformer with M taking the value 15; FIG. 7(d) is a carotid ultrasound image generated using an SC-MVDR + CF beamformer with M taken as 15; FIG. 7(e) is a carotid ultrasound image generated using a SS-MVDR + HRCF beamformer with M taken at 15; FIG. 7(f) is a carotid ultrasound image generated by the combined SC-MVDR beamformer with M taken at 15; FIG. 7(g) is a carotid ultrasound image generated by the DCR-MVDR beamformer with M taken as 15; FIG. 7(h) is a carotid ultrasound image generated by the DCR-MMSE beamformer with M taken as 15; fig. 7(a) to (h) all undergo log compression, showing a dynamic range of 60 dB.
FIG. 8 is a table of experimental results referred to in the examples.
Detailed Description
The invention will be further described with reference to the accompanying drawings and specific embodiments. It is to be understood that the present invention may be embodied in various forms, and that there is no intention to limit the invention to the specific embodiments illustrated, but on the contrary, the intention is to cover some exemplary and non-limiting embodiments shown in the attached drawings and described below.
It is to be understood that the features listed above for the different embodiments may be combined with each other to form further embodiments within the scope of the invention, where technically feasible. Furthermore, the particular examples and embodiments of the invention described are non-limiting, and various modifications may be made in the structure, steps, and sequence set forth above without departing from the scope of the invention.
The invention provides an MMSE (minimum mean square error) beam former which is applied to coherent plane wave synthesis, wherein the beam former receives echo data of plane waves of M different angles transmitted by a transducer through an N-line linear array and performs beam synthesis; the echo data matrix is recorded as: u (n) ═ u1(n)，u2(n)，…，uM(n)]TThen, then are combinedThe beam forming is:
Figure BDA0002448974750000051
wherein u isi(n) echo data representing a plane wave i,
Figure BDA0002448974750000052
xi，j(n) echo data representing a plane wave i received at time instant n, jth array element; w is aDCR-MMSEAs a weight vector, wDCR-MMSEThe expression of (a) is:
Figure BDA0002448974750000061
Figure BDA0002448974750000062
Figure BDA0002448974750000063
wherein r isk(n) represents an intermediate parameter which is,
Figure BDA0002448974750000064
qk(N) a set of snapshots of the N array element output signals of the beamformer, qk(n)＝[qk，1(n)，qk，2(n)，…，qk，N(n)]，
Figure BDA0002448974750000065
For the diagonal loading parameters, I denotes the identity matrix and a denotes the time delay vector of all echo data.
The present invention also provides an MMSE beam forming method, the flow of which is shown in fig. 1, including the steps of:
(1) exciting N element linear array transducers to emit M plane waves at different angles, and receiving echo data through N array elements;
(2) by capturing each element by snap-shotOutput signal, noted qk(n)，qk(n)＝[qk，1(n)，qk，2(n)，…，qk，N(n)]，
Figure BDA0002448974750000066
Wherein x isi，j(n) echo data representing a plane wave i received at time instant n, jth array element;
(3) selecting diagonal line loading parameters according to requirements, and obtaining q according to the step (2)k(n) calculating a covariance matrix:
Figure BDA0002448974750000067
wherein I represents an identity matrix;
(4) defining an intermediate parameter rk(n)，
Figure BDA0002448974750000068
a represents the time delay vector of all echo data; q obtained according to step (2)k(n) and obtained in step (3)
Figure BDA0002448974750000069
Calculate rk(n)，
(5) Calculating a coherence factor:
Figure BDA0002448974750000071
(6) calculating a weight vector:
Figure BDA0002448974750000072
(7) the synthetic beam of the echo is calculated as:
Figure BDA0002448974750000073
the following illustrates the design principles of the present invention.
A. Coherent plane composite CPWC
In the CPWC, the echo data of the plane waves emitted at different angles are acquired by emitting the plane waves at a plurality of angles and beam-forming is performed to obtain an ultrasound image. Assuming that a linear array comprises N array elements, and the linear array transmits M plane waves with different angles, echo data received by the linear array is represented by a two-dimensional matrix:
Figure BDA0002448974750000074
wherein x isi，j(n) echo data representing a plane wave i received at time instant n, jth array element;
the coherent composite beam for obtaining the echo data is:
Figure BDA0002448974750000075
B. MVDR beam former with space smoothing function
The MVDR algorithm can be integrated into the coherent combining process, and not only can combine the data in each plane wave transmission (MVDR upon reception), but also can combine the data at different emission angles (MVDR upon emission).
An MVDR beamformer is used, echo data of each plane wave emitted by the DAS beamformer forms a corresponding low-resolution image, and then the low-resolution images are combined through an MVDR algorithm to obtain a composite image. The echo data of each plane wave is recorded as uiThen the echo data matrix is represented as: u (n) ═ u1(n)，u2(n)，…，uM(n)]TWherein u isi(n) echo data of plane wave i, uiThe expression of (n) is:
Figure BDA0002448974750000081
during source propagation we observe the presence of spatial correlation at different reception points (sensor elements). Whereas in ultrasound imaging the light source is not self-radiating, but is formed by reflection of the incident light beam. A general MVDR beamformer processes echo signals of a single shot plane wave. However, for the current array, the components generated by the reflection of different plane waves included in the input vector u (N) can be described by the reciprocity of acoustics theorem, and based on this, u (N) can be regarded as the echo data of M plane waves emitted from different angles received by N linear arrays.
To find a beamformer to be applied to u (n), we modeled u (n):
u(n)＝spa+v(n) (4)
wherein s ispRepresenting signal amplitude, v (n) is a combination of noise and non-target interference, and a represents a time delay vector.
Then, a beam forming weight vector calculation model is given:
Figure BDA0002448974750000082
the model satisfies the constraint: w is aHa＝1；
Solving the formula (5) to obtain a weight vector:
Figure BDA0002448974750000083
wherein R isvIs a noise plus interference covariance matrix;
in practice, we usually use a data covariance matrix R containing the desired signaluReplacement of RvObtaining:
Figure BDA0002448974750000084
the output signal of the beamformer is then:
Figure BDA0002448974750000085
in general, we passObtaining a data covariance matrix R in the MVDR algorithm by space smooth approximate estimationuHowever, this approximation method results in a calculated weight vector wMVDRTo eliminate this effect, w needs to be reducedMVDRBy multiplying by the average of the elements in u (n), we turn this beamformer into a spatially smooth beamformer.
C. Coherence factor
In the prior art, the MVDR and the coherence factor are generally used in combination to enhance the performance of composite imaging. The coherence factor CF is defined as representing the ratio of the sum of the amount of coherent data to the sum of the amount of incoherent data in the data vector. This way of combining MVDR with coherence factors can be used to approximate the minimum mean square error criterion MMSE. The formula for calculating the coherence factor CF is:
Figure BDA0002448974750000091
wherein the content of the first and second substances,
Figure BDA0002448974750000092
the value of CF ranges from 0 to 1, the lower the value of CF as the coherence of the signal received at the transducer element is lower. Based on this property, we use CF as a post-filter to suppress blurring artifacts. To form a better filtered scalar, CF is modified to create two variants: high-resolution coherence coefficient (HRCF) and scale coefficient (scCF):
Figure BDA0002448974750000093
using y in the formulaMVDR(n) replaces yavg(n), to understand the effect of doing so on the imaging results, we note yavg(n) weight vector
Figure BDA0002448974750000094
Also satisfies the corresponding condition of no distortion
Figure BDA0002448974750000095
In such a beamforming weight vector, wMVDRSatisfy the minimum output power or yMVDR(n)|2≤|yavg(n)|2. Thus, the high resolution coherence factor can reduce the effect of the post-filter scalar on the imaging contrast.
The scaling factor (scCF) is expressed as:
Figure BDA0002448974750000096
η is a parameter that ranges from 0 to 1, scCF (n) is less than 1 but greater than CF. therefore, it reduces the effect of the post-filter scalar on the imaging contrast and makes the image synthesis result closer to that of the MVDR beamformer.
D. MVDR algorithm based on space consistency
In the invention, a new method is developed to estimate the covariance of u (n), and a plurality of snapshots q are collectedk(n) covariance for estimating u (n), qk(n)＝[qk，1(n)，qk，2(n)，…，qk，N(n)]，
Figure BDA0002448974750000097
u (n) and qk(n) statistical similarity between them complies with the Van Satt-Zernike theorem. We first detect the spatial coherence between the elements in u (N), and based on the acoustic reciprocity of coherent plane wave complex imaging (CPWC) when receiving signals, we consider u (N) as the backscattered signals from point targets received by N linear arrays, and then use the fourier transform of the beam pattern and the distance between two elements in the array to calculate the spatial coherence between the corresponding two signals in u (N) by using the van-zernike theorem. Compared with u (n), qk(N) is the back scattered signal from the point target received by all but the k-th element of the N element linear arrays, when N is large enough, we consider u (N) and qkThe difference between (n) is small enough for u (n) and qk(n) have similar second order statistics, therefore, we estimate the covariance matrix using the following formulaArraying:
Figure BDA0002448974750000101
wherein, I represents an identity matrix for diagonal loading parameters.
In formula (7)
Figure BDA0002448974750000102
Replacement of RuThen obtain the weight vector
Figure BDA0002448974750000103
The output signal is then:
Figure BDA0002448974750000104
e MMSE beamformer
In the invention, a spatial coherence method is expanded, and a new MMSE beam former suitable for CPWC is developed. We first assume that the main signal is deterministic and that the backscatter data is a narrowband signal. The output signals y and s of the beamformer are according to equation (4)pThe mean square error MSE between is calculated as:
E{|y-sp|2)＝wHRvw+|sp|2|1-wHa|2(15)
where E represents the expected value operator.
According to the minimum mean square error MSE, calculating a weight vector as follows:
Figure BDA0002448974750000105
further obtaining:
Figure BDA0002448974750000106
of these, β(s)p) As a post-filter scalar, β(s)p) The expression of (a) is:
Figure BDA0002448974750000111
substituting formula (17) for formula (15) yields:
Figure BDA0002448974750000112
for w in formula (6)MVDRWe pass the MSEMVDRError between the main signal and the MVDR beamformer output signal is described:
Figure BDA0002448974750000113
comparing equation (19) with equation (20), we find MSEout≤MSEMVDRThus for the main signal spThe output of the MMSE beamformer is more accurate.
However, according to equation (18), calculating the weight vector of MMSE also requires estimating spAnd
Figure BDA0002448974750000114
the output signal of the MVDR beamformer is spIs estimated unbiased, and
Figure BDA0002448974750000115
and MSEMVDRDirect correlation (e.g., equation (20)), and thus β(s)p) Can be expressed in terms of the mean square error of the output signal of the MVDR beamformer. Based on this analysis, we used the DCR-MVDR beamformer and the snapshot set q in equation (12)k(n) to estimate β(s)p)。
In the space phase drying method, u (n) and qk(n) have similar covariance matrices, and therefore,
Figure BDA0002448974750000116
can be regarded as qk(n) covariance matrix, and wDCR-MVDRCan be used as weight vector of MVDR beam former. ByIn that
Figure BDA0002448974750000117
And
Figure BDA0002448974750000118
mean value s ofpThe same applies, therefore,
Figure BDA0002448974750000119
and
Figure BDA00024489747500001110
so β(s)p) May be used with qk(n) is estimated as the mean square error of the input output signal of the DCR-MVDR beamformer.
Order to
Figure BDA00024489747500001111
By { rkThe mean and variance of (n) are substituted into (18) as spAnd
Figure BDA00024489747500001112
to obtain an approximation of:
Figure BDA0002448974750000121
Figure BDA0002448974750000122
in the form of a coherence factor, but
Figure BDA0002448974750000123
Are calculated from the output data of the beamformer rather than from the input data. The new MMSE beamformer has weight vectors of
Figure BDA0002448974750000124
The output signal is:
Figure BDA0002448974750000125
the above is the design principle of the MMSE beamformer and beamforming method proposed by the present invention.
Further, the present invention also provides a computer-readable storage medium storing at least one instruction executable by a processor, where the at least one instruction, when executed by the processor, implements the MMSE beamforming method.
The technical effects of the present invention are illustrated by specific experimental data below.
We first generated simulated images of 9 ideal lesions through the beamformer to assess the resolution of the images generated by the different beamformers. FIG. 2 shows simulated images of 9 ideal lesions generated with different beamformers; wherein, fig. 2(a) is a simulated image of 9 ideal lesions generated by using a CPWC beamformer, with the value of M being 75; FIG. 2(b) is a simulated image of 9 ideal lesions generated using an SS-MVDR beamformer with M taken at 75; fig. 2(c) is a simulated image of 9 ideal lesions generated using a CPWC beamformer, with M taking the value 15; FIG. 2(d) is a simulated image of 9 ideal lesions generated using an SC-MVDR + CF beamformer with M taking the value of 15; FIG. 2(e) is a simulated image of 9 ideal lesions generated using an SS-MVDR + HRCF beamformer with M taking the value of 15; FIG. 2(f) is a simulated image of 9 ideal lesions generated by the joint SC-MVDR beamformer with M taking the value of 15; FIG. 2(g) is a simulated image of 9 ideal lesions generated by the DCR-MVDR beamformer with M being 15; FIG. 2(h) is a simulated image of 9 ideal lesions generated by the DCR-MMSE beamformer, where M is 15; fig. 2(a) to (h) all undergo log compression, showing a dynamic range of 60 dB.
In fig. 2(a) to (h), the lesions are uniformly distributed, with centers located at 17mm, 30mm and 43mm in the longitudinal direction and at-12 mm, Omm and 12mm in the transverse direction. Fig. 2(a) and 2(b) are images generated based on a full dataset (the full dataset is plane wave echo data at 75 different angles), whereas fig. (c) to (h) employ only plane wave echo data at 15 angles.
Comparing fig. 2(a) and fig. 2(b), it can be seen that the SS-MVDR beamformer is effective in improving the resolution of the lesion compared to the CPWC beamformer. Comparing fig. 2(c) to (h), when M is 15, the resolution of the CPWC beamformer is lowest (as in fig. 2(c)), and the DCR-MVDR beamformer has a higher resolution (as in fig. 2(e)), especially at a depth of 17mm at the transducer surface (near field region). The resolution of the SC-MVDR + CF beamformer, the SS-MVDR + HRCF beamformer, and the joint SC-MVDR beamformer is comparable to the resolution of the DCR-MVDR beamformer. However, by carefully observing these images, we find that some artifacts are introduced inside the lesion located in the near field region or at the edge of the image, while the DCR-MMSE beamformer proposed by the present invention has the highest image quality, the DCR-MMSE beamformer can not only improve the resolution of the lesion, but also suppress the artifacts, further improving the image quality.
For fig. 2(a) to 2(h), we use the following formula to quantify the image quality:
Figure BDA0002448974750000131
wherein IinAnd IoutThe average intensity (in decibels) measured inside and outside the focus respectively, the value range of CR is 0 to 1, and the larger the value of CR, the higher the resolution is. The table shown in fig. 8 shows the image quality average values in fig. 2(a) to 2 (h). From the calculation results, the DCR-MMSE beamformer has the highest peak response compared to the other beamformers.
Next, we scan the tissue phantom with different beamformers, yielding experimental data for evaluating the spatial resolution performance of the beamformers. Setting the sound velocity of the scanning to 1540 +/-10 m/s and the slope of the background attenuation coefficient to 0.5dBcm- 1MH-1. The scanned objects are 7 nylon monofilament metal wires with the diameter of 100 mm which are hung in the mottled background, the 7 nylon monofilament metal wires are arranged in parallel, and the beam emission direction is parallel to the length direction of the nylon monofilament metal wires during scanning. One end of the nylon monofilament metal wire is regarded as a point, and after scanning, 5 points are positioned in the scanningOn the axis (i.e. the abscissa on the scanned image is 0), the 5 points have the ordinate positions of 10mm, 20 mm, 30mm, 40 mm and 50mm on the scanned image, and the other two points are located on the abscissa of-10 mm and the ordinate of 40 mm on the scanned image, and the other point is located on the abscissa of 10mm and the ordinate of 40 mm on the scanned image. Specific scanning data is shown in fig. 3, fig. 3(a) is an experimental image generated by a CPWC beamformer, and M takes a value of 75; FIG. 3(b) is an experimental image generated by the SS-MVDR beamformer with M taking the value of 75; fig. 3(c) is an experimental image generated by the CPWC beamformer, with the value of M being 15; FIG. 3(d) is an experimental image generated by the SC-MVDR + CF beamformer with a value of M of 15; FIG. 3(e) is an experimental image generated by the SS-MVDR + HRCF beamformer with M taking the value of 15; FIG. 3(f) is an experimental image generated by the joint SC-MVDR beamformer with a value of M of 15; FIG. 3(g) is an experimental image generated by the DCR-MVDR beamformer with the value of M being 15; FIG. 3(h) is an experimental image generated by the DCR-MMSE beamformer with the value of M being 15; fig. 3(a) to (h) are log compressed and displayed with a dynamic range of 70 dB.
Fig. 3(a) and 3(b) are experimental images obtained from full-angle data, and from fig. 3, the SS-MVDR beamformer has a higher line resolution than the CPWC beamformer. Fig. 3(c) to 3(h) are beamformers calculated based on echo data of 15 angles, wherein the line resolution of the remaining beamformers, except the SC-MVDR + CF beamformer, is higher than that of the CPWC beamformer (fig. 3 (c)). Due to the coherence of the signals received by the individual beamformer array elements, coherent spots may be formed in the imaging region, resulting in artifacts in the entire imaging region, thereby affecting image quality.
The DCR-MMSE (in fig. 3 (h)) achieves the highest line resolution, but it is equivalent to the line resolution obtained with DCR-MVDR (in fig. 3 (g)). Whereas the line resolution of MVDR + CF and MVDR + HRCF is better than that of CPWC, but worse than that of DCR-MMSE.
We present the beam profiles of the above-described beamformer in fig. 4 and 5. Fig. 4 is a graph comparing the response of beams generated by a pair of CPWC beamformer (M75), SS-MVDR beamformer (M15) and CPWC beamformer (M15) on a scan centerline with nylon monofilament wire pairs having ordinates of 10mm, 30mm and 50mm, respectively; wherein, fig. 4(a) is a beam response contrast diagram on the cross section of the nylon monofilament metal wire at the ordinate 10mm on the scanning center line; FIG. 4(b) is a plot of the beam response versus a cross-section of a nylon monofilament wire at 30mm ordinate on the scan center line; fig. 4(c) is a plot of the beam response versus the cross-section of a nylon monofilament wire at 50mm ordinate on the scan center line. As can be seen from fig. 4, the reduction of the transmitted plane wave (compare M75 and M15) results in an increase of the side lobes of the response signal, which is particularly significant in the near field region.
Fig. 5 is a response comparison graph of beams generated by a nylon monofilament wire pair CPWC beamformer (M15), a joint SC-MVDR beamformer (M15), an SS-MVDR + CF beamformer (M15), an SS-MVDR + HRCF beamformer (M15), a DCR-MVDR beamformer (M15), and a DCR-MMSE beamformer (M15) at the scanning center line with ordinate of 10mm, 30mm, and 50mm, respectively; wherein, fig. 5(a) shows a response distribution comparison graph of a beam generated by a CPWC beamformer (M15) and a beam generated by a joint SC-MVDR beamformer (M15) on a cross section of a nylon monofilament metal wire at an ordinate of 10mm on a scanning center line; fig. 5(b) shows a graph of the response profile of the beam generated by the SS-MVDR + CF beamformer (M15) and the beam generated by the SS-MVDR + HRCF beamformer (M15) in a cross-section of a nylon monofilament wire at an ordinate of 30mm on the scan center line; fig. 5(c) shows a graph of response distributions of beams generated by the DCR-MVDR beamformer (M15) and beams generated by the DCR-MMSE beamformer (M15) in a cross-section of a nylon monofilament wire at an ordinate of 50mm on a scan center line.
As can be seen from fig. 5, when the number of transmitted plane waves is all 15, the main lobe of the DCR-MMSE beamformer is narrowest, indicating that its radiation is most concentrated. We measure the pulse width of all responses with FWHM, calculate the mean FWHM of each beamformer, and record the calculation results in the table shown in fig. 8.
To evaluate contrast resolution, we scanned two anechoic cysts in the speckle background with the beamformer described above, and the obtained scan data is shown in fig. 6, where fig. 6(a) is an experimental image generated with a CPWC beamformer and M is 75; FIG. 6(b) is an experimental image generated using an SS-MVDR beamformer with M taking the value 75; fig. 6(c) is an experimental image generated by using a CPWC beamformer, with the value of M being 15; FIG. 6(d) is an experimental image generated using an SC-MVDR + CF beamformer with a value of M of 15; FIG. 6(e) is an experimental image generated using a SS-MVDR + HRCF beamformer with the value of M being 15; FIG. 6(f) is an experimental image generated by the joint SC-MVDR beamformer with a value of M of 15; FIG. 6(g) is an experimental image generated by the DCR-MVDR beamformer with the value of M being 15; FIG. 6(h) is an experimental image generated by the DCR-MMSE beamformer with the value of M being 15; fig. 6(a) to (h) all undergo log compression, showing a dynamic range of 70 dB.
As can be seen from fig. 6, the diameter of the cyst is about 3mm, and the two cysts are located at positions 15 mm and 45 mm on the ordinate of the scanning center line, respectively. As can be seen from fig. 6, the DCR-MMSE beamformer generates experimental images with optimal contrast for the two cysts. We calculate the mean value of the image quality CR of each cyst, and then record the calculation result in the table shown in fig. 8.
Fig. 7 is a carotid ultrasound image obtained by scanning the carotid artery with different beamformers, wherein fig. 7(a) is a carotid ultrasound image generated by using a CPWC beamformer with the M value being 75; FIG. 7(b) is a carotid ultrasound image generated using an SS-MVDR beamformer with M taken at 75; FIG. 7(c) is a carotid ultrasound image generated using a CPWC beamformer with M taking the value 15; FIG. 7(d) is a carotid ultrasound image generated using an SC-MVDR + CF beamformer with M taken as 15; FIG. 7(e) is a carotid ultrasound image generated using a SS-MVDR + HRCF beamformer with M taken at 15; FIG. 7(f) is a carotid ultrasound image generated by the combined SC-MVDR beamformer with M taken at 15; FIG. 7(g) is a carotid ultrasound image generated by the DCR-MVDR beamformer with M taken as 15; FIG. 7(h) is a carotid ultrasound image generated by the DCR-MMSE beamformer with M taken as 15; fig. 7(a) to (h) all undergo log compression, showing a dynamic range of 60 dB.
Under normal circumstances, the artery appears as a circular structure on the sonogram, with the lumen appearing as an anechoic region surrounded by specular scattering from the artery wall. The intra-cavity contrast was calculated for each image and the calculation was recorded in the table of fig. 8.
In fig. 7, the carotid ultrasound image generated by the CPWC beamformer (fig. 7(a)) and the carotid ultrasound image generated by the SS-MVDR beamformer (fig. 7(b)) are both generated with complete data sets, and the image quality is relatively close. The image quality of carotid ultrasound images generated by the DCR-MVDR beamformer is significantly higher than that of the CPWC beamformer and the SS-MVDR beamformer. When M is 15, the contrast of the carotid ultrasound image generated by the CPWC beamformer and the contrast of the carotid ultrasound image generated by the DCR-MVDR beamformer are both low. Between the SC-MVDR + CF beam former and the joint SC-MVDR beam former, the contrast of the carotid artery ultrasonic image generated by the joint SC-MVDR beam former is higher, even exceeds the DCR-MMSE beam former, but the carotid artery ultrasonic image generated by the joint SC-MVDR beam former has an artifact in a near field area, so that the image quality is poor. The SC-MVDR + CF beamformer and the joint SC-MVDR beamformer can also improve the imaging contrast to some extent, but there are also artifacts in the near field region. While the DCR-MMSE beamformer can provide both high imaging contrast and high image quality, as can be seen in fig. 7(h), the entire lumen and artery boundaries are very clear.
The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.

Claims (3)

1. An MMSE beam former is applied to coherent plane wave synthesis and is characterized in that the beam former receives echo data of plane waves of M different angles transmitted by a transducer through an N-line linear array and carries out beam synthesis; the echo data matrix is recorded as: u (n) ═ u1(n)，u2(n)，…，uM(n)]TThen the synthesized beam is:
Figure FDA0002448974740000011
wherein u isi(n) echo data representing a plane wave i,
Figure FDA0002448974740000012
xi，j(n) echo data representing a plane wave i received at time instant n, jth array element; w is aDCR-MMSEAs a weight vector, wDCR-MMSEThe expression of (a) is:
Figure FDA0002448974740000013
Figure FDA0002448974740000014
Figure FDA0002448974740000015
wherein r isk(n) represents an intermediate parameter which is,
Figure FDA0002448974740000016
qk(N) a set of snapshots of the N array element output signals of the beamformer, qk(n)＝[qk，1(n)，qk，2(n)，…，qk，N(n)]，
Figure FDA0002448974740000017
For the diagonal loading parameters, I denotes the identity matrix and a denotes the time delay vector of all echo data.
2. An MMSE beamforming method, comprising the steps of:
(1) exciting N element linear array transducers to emit M plane waves at different angles, and receiving echo data through N array elements;
(2) the output signal of each array element is acquired through snapshot and is recorded as qk(n)，qk(n)＝[qk，1(n)，qk，2(n)，…，qk，N(n)]，
Figure FDA0002448974740000018
Wherein x isi，j(n) echo data representing a plane wave i received at time instant n, jth array element;
(3) selecting diagonal line loading parameters according to requirements, and obtaining q according to the step (2)k(n) calculating a covariance matrix:
Figure FDA0002448974740000021
wherein I represents an identity matrix;
(4) defining an intermediate parameter rk(n)，
Figure FDA0002448974740000022
a represents the time delay vector of all echo data; q obtained according to step (2)k(n) and obtained in step (3)
Figure FDA0002448974740000023
Calculate rk(n)，
(5) Calculating a coherence factor:
Figure FDA0002448974740000024
(6) calculating a weight vector:
Figure FDA0002448974740000025
(7) the synthetic beam of the echo is calculated as:
Figure FDA0002448974740000026
3. a computer-readable storage medium having stored thereon at least one instruction executable by a processor, the at least one instruction when executed by the processor implementing the MMSE beamforming method of claim 2.
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