WO2016204451A1

WO2016204451A1 - Method and apparatus for beamforming

Info

Publication number: WO2016204451A1
Application number: PCT/KR2016/006148
Authority: WO
Inventors: 박종인; 이진수; 위석민
Original assignee: 포항공과대학교 산학협력단
Priority date: 2015-06-16
Filing date: 2016-06-10
Publication date: 2016-12-22
Also published as: KR101604570B1

Abstract

Disclosed are a beamforming apparatus and a beamforming method. The beamforming method comprises the steps of: setting an array data, a first subarray data matrix, and a first steering matrix; obtaining a conversion matrix for converting, on the basis of the first subarray data matrix, a covariance matrix to a constant multiple of an identity matrix; obtaining an apodization weight by using the conversion matrix; obtaining the average of a second subarray data matrix by using the first subarray data matrix and the conversion matrix; and performing a beamforming. Accordingly, a minimum variance beamforming can be performed with a low level of computational complexity.

Description

Beamforming method and apparatus

The present invention relates to a beamforming method and apparatus, and more particularly, to a minimum variance beamforming method having a low level of computational complexity and a beamforming apparatus using the same.

Beamforming is one of the essential elements in the field of ultrasonic imaging. Generally, delay-and-sum beamforming (DAS) is widely used. According to the time delay beamforming, predetermined apodization weights are applied to the obtained array data, and a beamforming output is generated by combining the array data and the apodization weight into one. Time-delay beamforming is robust in a simple and general environment, making it well suited for real-time ultrasound imaging. However, time delay beamforming has relatively low resolution and lack of side lobe suppression.

In order to overcome this drawback of time delay beamforming, adaptive beamforming using data-dependent apodization weighting has been studied. One representative method is minimum variance beamforming (MVB). Minimal distributed beamforming is a method of finding an optimized apodization weighting that minimizes the beamforming output average power while the signal coming from the user's direction is kept constant. According to the minimum distributed beamforming, an interference signal coming from a direction other than the user wants to view is suppressed and cancellation of the signal coming from the direction to be viewed is prevented, so that a high level of resolution and contrast can be achieved.

Despite yielding high performance, minimally distributed beamforming is not currently widely used. The reason is that a high level of computation is required for minimum distributed beamforming. While time-delayed beamforming has a low level of computational complexity that is proportional to the array size, minimally distributed beamforming yields a subarray size (usually one of the size of the array). / 3 or 1/4) has a high level of computational complexity proportional to three squares. This computational complexity is due to the fact that, in minimum distributed beamforming implementations, a covariance matrix and its inverse matrix must be computed from the array data. Therefore, minimum distributed beamforming is not widely used in real equipment because of the high level of computational complexity.

An object of the present invention for solving the above problems is to provide a minimum variance beamforming method having a low level of computational complexity and a beamforming apparatus using the same.

According to an embodiment of the present invention for achieving the above object, in the beamforming method performed in the beamforming apparatus, the beamforming method, the array data, the first sub-array data defined in the array data Establishing a matrix and a first steering matrix; Obtaining a transformation matrix for converting a covariance matrix into a constant multiple of an identity matrix based on the first subarray data matrix; Obtaining an apodization weight using the transformation matrix; Obtaining an average of a second subarray data matrix using the first subarray data matrix and the transformation matrix; And performing beamforming based on the average of the second subarray data matrix and the apodization weighting.

In the obtaining of the transformation matrix, the transformation matrix may be obtained through an orthogonalization algorithm of the first subarray data matrix.

Here, the orthogonalization algorithm may be QR decomposition expressed as a product of an orthogonal matrix and an upper triangular matrix.

The acquiring of the transformation matrix may include a method of obtaining the upper triangular matrix with respect to the first subarray data matrix having a form of a Toeplitz matrix.

The acquiring weight using the transform matrix may include obtaining a second steering matrix by applying a forward substitution algorithm to the upper triangular matrix and the first steering matrix. ; And acquiring the apodization weighting using the second steering matrix.

The obtaining of the average of the second subarray data matrix may include: obtaining an average of column vectors in the first subarray data matrix; And calculating an average of the second subarray data matrix using a forward substitution algorithm based on the mean of the column vectors and the transformation matrix.

According to one embodiment of the present invention, a beamforming apparatus apparatus includes: a processor that performs an operation related to performing beamforming; And a memory in which at least one instruction executed by the processor is stored, wherein the at least one instruction comprises: setting array data, a first subarray data matrix and a first steering matrix defined within the array data; Obtaining a transformation matrix for converting a covariance matrix to a constant multiple of an identity matrix based on the first subarray data matrix, obtaining an apodization weight using the transformation matrix, Obtaining an average of a second subarray data matrix using a subarray data matrix and the transformation matrix, and performing beamforming based on the average of the second subarray data matrix and the apodization weighting It is executable to

According to the present invention, minimum distributed beamforming can be achieved through a low level of computational complexity. In addition, it can exhibit the same performance as the existing minimum distributed beamforming.

1 is a block diagram showing the configuration of a beamforming apparatus according to an embodiment of the present invention.

2 is a flowchart illustrating a beamforming method according to an embodiment of the present invention.

3 is an exemplary view showing arrangement data according to an embodiment of the present invention.

4 is an exemplary view showing arrangement data according to an embodiment of the present invention.

As the present invention allows for various changes and numerous embodiments, particular embodiments will be illustrated in the drawings and described in detail in the written description. However, this is not intended to limit the present invention to specific embodiments, it should be understood to include all modifications, equivalents, and substitutes included in the spirit and scope of the present invention.

Terms such as first and second may be used to describe various components, but the components should not be limited by the terms. The terms are used only for the purpose of distinguishing one component from another. For example, without departing from the scope of the present invention, the first component may be referred to as the second component, and similarly, the second component may also be referred to as the first component. The term and / or includes a combination of a plurality of related items or any item of a plurality of related items.

When a component is referred to as being "connected" or "connected" to another component, it may be directly connected to or connected to that other component, but it may be understood that other components may be present in between. Should be. On the other hand, when a component is said to be "directly connected" or "directly connected" to another component, it should be understood that there is no other component in between.

The terminology used herein is for the purpose of describing particular example embodiments only and is not intended to be limiting of the present invention. Singular expressions include plural expressions unless the context clearly indicates otherwise. In this application, the terms "comprise" or "have" are intended to indicate that there is a feature, number, step, operation, component, part, or combination thereof described in the specification, and one or more other features. It is to be understood that the present invention does not exclude the possibility of the presence or the addition of numbers, steps, operations, components, components, or a combination thereof.

Unless defined otherwise, all terms used herein, including technical or scientific terms, have the same meaning as commonly understood by one of ordinary skill in the art. Terms such as those defined in the commonly used dictionaries should be construed as having meanings consistent with the meanings in the context of the related art and shall not be construed in ideal or excessively formal meanings unless expressly defined in this application. Do not.

Hereinafter, with reference to the accompanying drawings, it will be described in detail a preferred embodiment of the present invention. In the following description of the present invention, the same reference numerals are used for the same elements in the drawings and redundant descriptions of the same elements will be omitted.

Referring to FIG. 1, the beamforming apparatus 100 according to an exemplary embodiment of the present invention may include a processor 110 that performs operations related to beamforming, and a memory 120 in which at least one instruction executed by the processor is stored. Include. In addition, the beamforming apparatus 100 according to the embodiment of the present invention may further include a network interface device 130 connected to a network to perform communication. In addition, the beamforming apparatus 100 may further include an input interface device 140, an output interface device 150, a storage device 160, and the like. Each component included in the beamforming apparatus 100 may be connected by a bus 170 to communicate with each other.

The processor 110 may execute a program command stored in the memory 120 and / or the storage device 160. The processor 110 may mean a central processing unit (CPU), a graphics processing unit (GPU), or a dedicated processor on which methods according to the present invention are performed. The memory 120 and the storage device 160 may be configured of a volatile storage medium and / or a nonvolatile storage medium. For example, the memory 120 may be configured as read only memory (ROM) and / or random access memory (RAM).

The at least one instruction includes setting array data, a first subarray data matrix and a first steering matrix defined within the array data; Obtaining a transformation matrix for converting a covariance matrix into a constant multiple of an identity matrix based on the first subarray data matrix; Obtaining an apodization weight using the transformation matrix; Obtaining an average of a second subarray data matrix using the first subarray data matrix and the transformation matrix; And beamforming based on the average of the second subarray data matrix and the apodization weighting.

Hereinafter, a beamforming method according to an embodiment of the present invention will be described in detail.

For an array with M channels, the beamforming output for one point n of one scanline can be expressed as follows.

Here, w _m [n] is apodization weighting, and x _m [n] is array data obtained for each array. And [Delta] _m [n] is a time-delay for focusing during beamforming.

For simpler development, Equation 1 may be expressed in the form of a matrix as follows.

here,

In addition, * represents a complex conjugate, and H is a Hermitian operator of the matrix. Afterwards, a term indicating a time delay may be omitted for convenience in formula expansion.

Unlike time-delayed beamforming, minimally distributed beamforming is a method of finding optimized apodization weighting that minimizes beamforming output average power while maintaining a constant signal coming from a user's desired direction. That is, minimum distributed beamforming may be considered a limited optimization problem, which may be described mathematically as follows.

Here, E [] is an expectation operator, R [n] = E [x [n] x [n] ^H ] represents a spatial covariance matrix, and a represents a steering matrix. In the case of an ultrasound image, it is assumed that there is a time delay. a is [1 1... 1] can be defined as ^T.

The solution of the optimization problem described in Equation 3 can be obtained by the Lagrange multipliers method as follows.

In practice, however, the exact value of R [n] cannot be calculated and must be estimated. The most widely used method for this is estimation of R [n] by subarray averaging.

Where x _l [n] is a subarray data vector,

Is defined as L is the subarray vector size.

As a result, the beamforming output is as shown in Equation 4 and Equation 5 below.

In addition, a diagonal loading method can be applied to obtain a more robust spatial covariance matrix. This is to normalize the optimized apodization weightings by adding a constant doubling identity matrix to the original spatial covariance matrix.

As described in equations (4) and (5), according to the conventional lowest distributed beamforming method, the beamforming output is obtained only when the spatial covariance matrix and its inverse matrix are obtained. Both calculations require a high level of computational complexity, which is proportional to the cube of the array size. More precisely, it is proportional to the cube of the subarray size (L).

In order to solve this problem, an embodiment of the present invention discloses a method of converting a spatial covariance matrix into a constant multiple of an identity matrix by applying a specific transformation to array data.

If the spatial co-injection matrix is converted to a constant multiple of the identity matrix, its inverse is also converted to a constant multiple of the identity matrix, so that the apodization weight can be simply calculated without performing an inverse matrix operation as shown in Equation (5).

In general, transformation can be implemented as follows by multiplying an array data transformation matrix.

Where z _l [n] is the transformed l-th subarray data vector. The clause matrix and the spatial covariance matrix can also be transformed as follows.

As a result, the optimization problem of the lowest distributed beamforming may be expressed as follows in the transformed region.

If you look at the optimization solution earlier,

Therefore, the beamforming output is as follows.

As mentioned earlier, if

If there is a transform matrix that converts to a constant multiple of the identity matrix, the apodization weighting can be easily computed as

That is, the apodization weighting can be simply calculated using only a _z [n].

Referring to FIG. 2, the beamforming apparatus 100 may set array data necessary for performing beamforming, a first subarray data matrix defined in the array data, and a first steering matrix (S210).

For one point n of each scanline, the array size is M and the subarray size is L. Array data is x _i [n], i = 0, 1,... , M-1, subarray data matrix is U [n] = [u ₀ [n] u ₁ [n]. u _L-1 [n]]. Where u _k [n] = [x _M _{-L + K} [n] x _M _{-L + K-1} [n]. x _k [n]] ^T , k = 0, 1,... , L-1. The steering matrix is a [n] = [1 1... 1] ^T.

Here, the subarray data matrix before conversion is referred to as a first subarray data matrix, and the subarray data matrix transformed by the conversion matrix is referred to as a second subarray data matrix. In addition, also about a steering matrix, the steering matrix before transformation is called a 1st steering matrix, and the steering matrix converted by the transformation matrix is called a 2nd steering matrix.

Next, the beamforming apparatus 100 may obtain a transformation matrix for converting the covariance matrix into a constant multiple of the identity matrix based on the first subarray data matrix (S220).

Prior to obtaining the transformation matrix, the spatial covariance matrix first

The structural characteristics of the system should be investigated in detail. for teeth

Can be expressed in the extended form as follows.

bracket

The component of may be expressed as the sum of the products of matrix data. The following subarray data vector can be defined.

Can be expressed by u _k [n] as follows.

3 and 4 are exemplary views showing arrangement data according to an embodiment of the present invention.

As shown in Figs. 3 and 4, the subarray data vector u _k [n] is distinguished from the subarray data vector x _l [n]. Detailed description thereof will be described later.

The diagonal components of can all be expressed as the inner product of themselves with the vectors of u _k [n].

Components other than the diagonal of can be represented internally of different vectors of u _k [n].

IF subarray data vector set

If a transformation matrix can be obtained by finding a set of orthogonal basis of the space represented by

Can be converted to a constant multiple of the identity matrix. In other words, an orthogonal basis set that satisfies the property of equation (16).

Once this is saved,

Can be converted to a constant multiple of the identity matrix.

In general, finding an orthogonal basis for a set of vectors is called an orthogonalization algorithm. The most representative of this orthogonalization algorithm is QR decompostion. Assuming that m × n (m ≧ n) matrix A is given, the QR decomposition of A is given by

Where Q is an m × n orthogonal matrix, and R is n × n an upper triangular matrix. If A has a full column rank, then Q represents the orthogonal basis of the range of A.

In order to apply QR decomposition to an embodiment according to the present invention, first

A first subarray data matrix U [n] having a size of (M−L + 1) × L may be generated as follows.

The transformation matrix may be obtained through an orthogonalization algorithm of the subarray data matrix. That is, the QR decomposition of U [n] is given by

Where S [n] is the L × L phase triangular matrix, and Q [n] is

An orthogonal matrix of size (M-L + 1) × L consisting of the orthogonal basis of can be expressed as

Here, the upper triangular matrix is denoted as S [n] to avoid confusion with the spatial covariance matrix R [n].

Note that the previous series of conversion

Has been applied for. In order to apply the transformation to the array data, and to obtain the beamforming output,

A conversion matrix for is required. In other words, through the QR decomposition process

The transformation matrix for must be obtained.

This is solved relatively simply. Looking again at U [n] expressed in Equation 18, the row components of U [n]

You can confirm that That is, U [n] can be expressed as follows.

The transpose matrix of U [n] can be expressed as follows.

Eventually U ^T [n]

May be regarded as a first subarray data matrix composed of columns. If the transposed process is performed on both sides of Equation 19, and S ^-T [n] is multiplied by the front side of the equation, the following result can be obtained.

Here, since S ^T [n] is a lower triangular matrix whose diagonal component is not 0, it necessarily has an inverse matrix. According to equations (7), (22), and (22), S- ^T [n] can be regarded as a transformation matrix T [n]. As a result, the transformation matrix T [n] can be obtained simply through the QR decomposition process of U [n].

Based on the previous results,

Subarray data vector transformed from

It can also be defined from orthogonal matrix Q.

here,

Next, the beamforming apparatus 100 may obtain the apodization weighting using the transformation matrix (S230).

Here, obtaining the apodization weighting using the transform matrix may include obtaining a second steering matrix by applying a forward substitution algorithm to the upper triangular matrix and the first steering matrix (S231); And obtaining the apodization weighting using the second steering matrix (S232).

As shown in Equation 12, the beamforming apparatus 100 may obtain the apodization weighting when the second steering vector a _z [n] is obtained. As described in Equation 8, a _z [n] is easily obtained by multiplying a by a transformation matrix.

Here, the feature of S ^T [n] may be used for a solution for a _z [n] that does not include operations on inverse matrices. Based on the property that S ^T [n] is a lower triangular matrix, a _z [n] can be easily obtained with a low level of computational complexity by the following equation according to the forward substitution method.

In relation to the solution of S ^T [n] here, due to the special structure of U [n], QR decomposition can proceed quickly. Referring to Equation 18, the diagonal components of U [n] have the same value in the upper left to the lower right. In other words, U [n] is a tapered matrix. This fetch matrix configuration is based on arranging u _k [n] backwards in (14). Regarding the tapped matrix, a QR decomposition method is known which has a low level of computational complexity.

As a result, the apodization weighting may be obtained as shown below by Equation 12 based on the obtained _az [n].

Next, the beamforming apparatus 100 may obtain an average of the second subarray data matrix using the first subarray data matrix and the transformation matrix (S240).

Referring to Equation 23, an average z _mean [n] of the second subarray data matrix may be obtained by obtaining an average of thermal components of Q ^T [n].

That is, the beamforming output may be calculated as follows.

here,

to be.

In general, the apodization weighting and the average of the second subarray data matrix are obtained through the orthogonal matrix and the upper triangular matrix computed through QR decomposition of U [n], thereby obtaining a beamforming output simply.

However, QR decomposition requires a significant amount of computational complexity. Of course, the method according to the embodiment of the present invention shows a low level of computational complexity compared to the conventional method, but still shows a computational complexity proportional to the cube of the size of the subarray.

In the method according to the embodiment of the present invention, an element for reducing the computational complexity may be applied.

First, the beamforming output can be stroked without using the orthogonal matrix Q [n] as shown in the following equation.

here,

to be.

For reference, x _mean [n] may be obtained by a solution for calculating an average of the column vectors of U ^T [n] (S241).

As a result, the average of the second subarray data matrix may be obtained from the equations 26 and 27 using the average of the column vectors and the transformation matrix (S242).

As in the case of obtaining the second steering matrix in equations (24) and (25), a forward substitution algorithm may be used for the solution of z _mean [n] as shown in equation (29).

Also, due to the special structure of U [n], QR decomposition can proceed correctly. Referring to Equation 18, the diagonal components of U [n] have the same value in the upper left to the lower right. In other words, U [n] is a tapered matrix.

Regarding the tapped matrix, a QR decomposition method is known which has a low level of computational complexity. In general, QR decomposition may be performed at a computation level of 13 mm + O (n ² ) for m × n (m ≧ n) matrices.

Next, the beamforming apparatus 100 may perform beamforming based on the average and apodization weights of the second subarray data matrix (S250).

That is, the beamforming output in Equation 26 is as follows.

Since U [n] is a matrix of size (M-L + 1) × L, QR decomposition can be performed with a computational complexity of 13 (M-L + 1) L + O (L ² ). In addition, in the case of the present invention, the beamforming output may be obtained through only an upper triangular matrix without an orthogonal matrix. That is, when only the upper triangular matrix is included in the beamforming output acquisition according to the embodiment of the present invention, the computational complexity of mn + O (n ² ) level, that is, (M-L + 1) L + O (L ² ) The beamforming output can be obtained with a level of computational complexity. This computational complexity is a level proportional to the square of the size of the subarray (O (L ² )), which is significant compared to the square of the size of the subarray of the existing least distributed beamforming (O (L ³ )). It is a computational complexity that has been reduced to a level

Table 1 compares the computational complexity of the existing method and the method according to an embodiment of the present invention in detail. Computational complexity was quantified by floating-point operations.

The methods according to the invention can be implemented in the form of program instructions that can be executed by various computer means and recorded on a computer readable medium. Computer-readable media may include, alone or in combination with the program instructions, data files, data structures, and the like. The program instructions recorded on the computer readable medium may be those specially designed and constructed for the present invention, or may be known and available to those skilled in computer software.

Examples of computer readable media include hardware devices that are specifically configured to store and execute program instructions, such as ROM, RAM, flash memory, and the like. Examples of program instructions include machine language code, such as produced by a compiler, as well as high-level language code that can be executed by a computer using an interpreter or the like. The hardware device described above may be configured to operate with at least one software module to perform the operations of the present invention, and vice versa.

Although it has been described above with reference to the preferred embodiment of the present invention, those skilled in the art will be able to variously modify and change the present invention without departing from the spirit and scope of the invention described in the claims below. It will be appreciated.

Claims

In the beamforming method performed in the beamforming apparatus,

Setting array data, a first subarray data matrix and a first steering matrix defined within the array data;

Obtaining a transformation matrix for converting a covariance matrix into a constant multiple of an identity matrix based on the first subarray data matrix;

Obtaining an apodization weight using the transformation matrix;

Obtaining an average of a second subarray data matrix using the first subarray data matrix and the transformation matrix; And

And performing beamforming based on the average of the second subarray data matrix and the apodization weighting.
The method according to claim 1,

Obtaining the transformation matrix,

And obtaining the transformation matrix through an orthogonalization algorithm of the first subarray data matrix.
The method according to claim 2,

The orthogonalization algorithm,

A beamforming method, which is QR decomposition represented by the product of an orthogonal matrix and an upper triangular matrix.
The method according to claim 3,

Obtaining the transformation matrix,

And obtaining the upper triangular matrix for the first subarray data matrix in the form of a toeplitz matrix.
The method according to claim 4,

Acquiring an apodization weighting using the transform matrix,

Obtaining a second steering matrix by applying a forward substitution algorithm to the upper triangular matrix and the first steering matrix; And

Obtaining the apodization weighting using the second steering matrix.
The method according to claim 2,

Obtaining an average of the second subarray data matrix,

Obtaining an average of column vectors in the first subarray data matrix; And

Computing an average of a second subarray data matrix using a forward substitution algorithm based on the mean of the column vectors and the transformation matrix.
A beamforming apparatus for generating beamforming output,

A processor configured to perform operations related to the beamforming; And

A memory having stored therein at least one instruction executed by the processor,

The at least one command is

Setting array data, a first subarray data matrix and a first steering matrix defined within the array data;

Obtaining a transformation matrix for converting a covariance matrix into a constant multiple of an identity matrix based on the first subarray data matrix;

Obtaining an apodization weight using the transformation matrix;

Obtaining an average of a second subarray data matrix using the first subarray data matrix and the transformation matrix; And

And beamforming based on the average of the second subarray data matrix and the apodization weighting.
The method according to claim 7,

Obtaining the transformation matrix,

And obtaining the transformation matrix through an orthogonalization algorithm of the first subarray data matrix.
The method according to claim 8,

The orthogonalization algorithm,

A beamforming apparatus, which is QR decomposition represented by the product of an orthogonal matrix and an upper triangular matrix.
The method according to claim 9,

Obtaining the transformation matrix,

And obtaining the upper triangular matrix with respect to the first subarray data matrix in the form of a toeplitz matrix.
The method according to claim 10,

Acquiring an apodization weighting using the transform matrix,

Obtaining a second steering matrix by applying a forward substitution algorithm to the upper triangular matrix and the first steering matrix; And

Obtaining the apodization weighting using the second steering matrix.
The method according to claim 8,

Obtaining an average of the second subarray data matrix,

Obtaining an average of column vectors in the first subarray data matrix; And

And calculating an average of a second subarray data matrix using a forward substitution algorithm based on the mean of the column vectors and the transformation matrix.