KR101551752B1 - Apparatus and method for recoverying sparse signal using parallel orthogonal matching pursuit - Google Patents

Abstract

A restoration apparatus and a restoration method for restoring a sparse signal in a received signal are disclosed. The restoration apparatus and restoration method restores a sparse signal using an orthogonal matching percess technique, selects a plurality of initial indexes in the orthogonal matching per use technique, and applies an orthogonal matching percess technique to each selected plurality of initial indexes.

Description

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an apparatus and a method for recovering coarse signals using a parallel orthogonal matching per-

The following embodiments relate to the field of compression sensing, and more particularly, to techniques for improving signal restoration performance by applying an orthogonal matching perchoe technique in parallel.

The Nyquist sampling theory is the basis for most current digital devices to acquire analog signals. According to this theory, in order to fully recover the analog signal, it is necessary to sample at a frequency more than twice that of the analog signal frequency bandwidth. This theory is concise and clear, but it is not a sufficient condition to restore the signal completely and therefore does not reflect the characteristics of the signal. Recently, as the amount of data to be sampled rapidly increases as shown in examples of high-resolution image processing and high-speed communication system, the question of efficiency of this theory has been constantly raised.

Candes and Donoho et al. Have shown that if the number of zeros in the signal vector to be restored is large, the original signal can be perfectly restored with a much higher compression ratio than the Nyquist sampling. This theory is often called compression sensing.

The following embodiments are intended to accurately recover a sparse signal from a received signal.

The following embodiments are intended to restore a sparse signal with a small amount of calculation.

According to an exemplary embodiment, there is provided a reconstruction apparatus for reconstructing a sparse signal in a received signal using an orthogonal matching pursuit scheme, the apparatus comprising: an initialization unit for selecting a plurality of initial indexes of the orthogonal matching per- An iterative execution unit that applies the orthogonal matching perchoe technique to a plurality of initial indexes in parallel to generate approximate matrices of the received signal corresponding to each of the initial indexes; And a selection unit for selecting a restoration signal of the restoration unit.

Here, the initialization unit may calculate the correlation between the received signal and the measurement matrix of the orthogonal matching technique, and may select the plurality of initial indexes according to the magnitude of the correlation value.

The iterative execution unit may determine an orthogonal projection over a span of additional indices generated as the initial index and the orthogonal matching fun shoot technique are repeated, and generate an orthogonal projection of the received signal The error between the approximate matrix of the received signal and the received signal can be calculated.

Also, the iterative execution unit may calculate the orthogonality by using a pseudo inverse matrix of the measurement matrix of the orthogonal matching percha technique.

Here, the selector may select the restoration signal according to an error between the approximate matrix and the received signal.

According to another exemplary embodiment, there is provided a reconstruction method for reconstructing a sparse signal in a received signal using an orthogonal matching pursuit technique, the method comprising: selecting a plurality of initial indexes of the orthogonal matching per- Generating approximate matrices of the received signal corresponding to each of the initial indices by applying the orthogonal matching technique in parallel to a selected plurality of initial indexes, The method comprising the steps of:

Here, the step of selecting the initial index may calculate the correlation between the received signal and the measurement matrix of the orthogonal matching perchoe technique, and may select the plurality of initial indexes according to the value of the correlation.

The generating of the candidate signal may include determining an orthogonal projection over a span of additional indices generated as the initial index and the orthogonal matching funspot technique are repeated and generating an orthogonal projection based on the determined orthogonality An error between the approximate matrix of the received signal and the received signal can be calculated.

Also, the step of generating the candidate signal may calculate the orthogonality by using a pseudo inverse matrix of the measurement matrix of the orthogonal matching per-shot technique.

Here, the selecting step may select the restored signal according to an error between the approximate matrix and the received signal.

According to the embodiments described below, a sparse signal in a received signal can be accurately recovered.

According to the embodiments described below, a sparse signal can be restored with a small calculation amount.

1 is a diagram showing a concept of restoring a sparse signal in a received signal.
2 is a diagram illustrating a concept of selecting a plurality of initial indexes according to an exemplary embodiment.
3 is a block diagram showing the structure of a restoration apparatus according to an exemplary embodiment.
FIG. 4 is a flowchart illustrating a restoration method according to an exemplary embodiment.

Hereinafter, embodiments will be described in detail with reference to the accompanying drawings.

According to Compressed Sensing, most of the signals we usually deal with correspond to a sparse signal when transformed into a specific signal space. The coarse signals are mostly '0' in the signal space before the deformation, and the signals other than '0' are only some of the signals. These sparse signals can restore almost perfectly the original signal with only a small number of linear measurements.

1 is a diagram showing a concept of restoring a sparse signal in a received signal. 1, the received signal Y (110) is a signal in which the sparse signal X (130) is transformed by the measurement matrix A (120). The small squares contained in the received signal Y 110, sparse signal X 130 and measurement matrix A 120 correspond to the received signals Y 110, sparse signals X 130 and the elements of the measurement matrix A 120, .

In the coarse signal X 130, white squares are elements with a value of '0', and gray squares are elements whose value is not '0'. According to the embodiment shown in FIG. 1, the coarse signal X 130 has a value of '0' for most of the elements, and a value of '0' for only some of the elements.

According to the compression sensing theory, a sparse signal X (130) can be recovered from a received signal Y (110) by using a measurement matrix A (120) satisfying a specific condition. The embodiment shown in FIG. 1 can be expressed by the following equation (1).

[Equation 1]

, 측정 신호 A는

, 성긴 신호 X는

, 가우시안 잡음 Z는

이다. 또한, n > m 이다.Here, the received signal Y is

, The measurement signal A is

, The sparse signal X

, Gaussian noise Z is

to be. Also, n > m.

The solution of the signal reconstruction problem expressed in Equation (1) can be expressed as Equation (2).

&Quot; (2) "

이고,

은 성긴 신호 X의 행들 중에서 어느 하나의 원소의 값이 '0'이 아닌 행의 개수를 나타낸다.here,

ego,

Represents the number of rows in which the value of any element among the rows of the coarse signal X is not '0'.

The problem of solving Equation (2) is known to be very complex, and various algorithms have been proposed to solve this problem. Among them, the S-OMP algorithm is widely used because of its relatively high restoration performance and low complexity.

Hereinafter, a Parallel Orthogonal Matching Pursuit (S-OMP) algorithm with improved restoration performance will be described with reference to FIGS. 2 to 4. FIG. The parallel orthogonal matching percess technique selects a plurality of initial indexes and applies an orthogonal matching perchoe technique to each initial index in parallel.

2 is a diagram illustrating a concept of selecting a plurality of initial indexes according to an exemplary embodiment. In FIG. 2, the first column represents the number of repetitions of the orthogonal matching funget technique, the second column represents the solution according to the conventional orthogonal matching fun technique, the third column refers to the solution according to the parallel orthogonal matching fun technique according to the exemplary embodiment .

는 t 번째 반복 횟수에서 l번째 인덱스 집합을 나타낸다.2, < EMI ID = 1.0 > represents the i-th column of the measurement matrix,

Represents the lth index set at the t-th iteration.

When the number of repetition is '1', the initial index is selected in the case of the orthogonal matching percess technique. According to the conventional orthogonal matching permutation technique, only one initial index is selected. Here, the orthogonal matching technique may select any one of the columns of the measurement matrix and select the index of the selected column as the initial index. According to the embodiment shown in FIG. 2, '6' is selected as the initial index in the conventional orthogonal matching pershoot technique.

On the other hand, in the case of the parallel orthogonal matching per-shot technique according to the exemplary embodiment, a plurality of initial indexes are selected. According to the embodiment shown in FIG. 2, '6', '3', and '8' are selected as initial indexes in the case of the parallel orthogonal matching permutation technique.

As the number of iterations increases, the orthogonal matching permutation technique selects an additional index. In the conventional orthogonal matching technique, when the number of repetitions is '2', '2' is selected as an additional index. When the number of repetitions is '3', '5' , 5}.

The parallel orthogonal matching percess technique according to the exemplary embodiment applies an orthogonal matching percess technique in parallel to each initial index to generate an additional index corresponding to each initial index. In the embodiment shown in FIG. 2, the additional indexes '2' and '5' are selected for the initial index '6', and the index set is {6, 2, 5}. Further, the index set is {3, 2, 10} by selecting the additional indexes '4' and '10' for the initial index '3'. Finally, the additional indexes '7' and '1' are selected for the initial index '8', and the index set is {8, 7, 1}.

With reference to the embodiment shown in FIG. 2, the parallel orthogonal matching percess technique according to the exemplary embodiment generates an index set corresponding to each selected initial index. A signal that can be composed of these index sets may be a candidate signal of a sparse signal, and a parallel orthogonal matching technique may select a sparse signal restoration signal among a plurality of candidate signals.

According to the embodiment shown in FIG. 2, the parallel orthogonal matching perchoe technique can generate an error signal for a received signal and each reconstructed signal, and select a reconstructed signal from candidate signals according to the magnitude of the generated error signal.

Hereinafter, a signal restoration technique using the parallel orthogonal matching percess technique will be described in detail with reference to FIG. 3 to FIG.

3 is a block diagram showing the structure of a restoration apparatus according to an exemplary embodiment. The restoration apparatus 300 according to the exemplary embodiment includes an initialization unit 310, an iteration unit 320, and a selection unit 330.

의 초기값

, 인덱스 집합

의 초기값

, 반복 횟수 t 를 하기 수학식 3과 같이 초기화할 수 있다.
The initialization unit 310 may include a residual matrix,

The initial value of

, Index set

The initial value of

, The number of repetitions t can be initialized as shown in Equation (3).

&Quot; (3) "

은 l번째 POMP블록을 통해 생성된 수신신호 Y의 근사행렬 (approximation matrix)

과 수신신호 Y간의 오차를 의미한다.Here,

Is an approximation matrix of the received signal Y generated through the 1 < th > POMP block,

And the received signal Y, respectively .

를 선택할 수 있다.
In addition, the initialization unit 310 can receive a received signal and select a plurality of initial indexes for applying the orthogonal matching perchoe technique to the received signal. Here, the initial index may be an index of vectors selected by the initial vector among the column vectors of the measurement matrix. The initialization unit 310 may calculate the correlation between the received signal and the measurement matrix of the orthogonal matching technique and select a plurality of initial indexes according to the magnitude of the correlation value. According to one aspect of the present invention, the initialization unit 310 calculates L initial indexes in order of the correlation between the received signal Y and the measurement matrix A ,

Can be selected.

&Quot; (4) "

는 측정 행렬 A의 i 번째 열을 나타내고,

는 l번째 후보집합을 통해 계산된 잔여행렬의 j번째 열을 의미한다. 수학식 4에서

는 벡터 c, d의 내적을 의미한다.here,

Represents the i-th column of the measurement matrix A ,

Denotes the jth column of the residual matrix calculated through the lth candidate set. In Equation 4,

Denotes the inner product of vectors c and d.

의 내적을 통해 나온 크기의 벡터의 합이 가장 큰 i 가

의 t 번째 '0'이 아닌 열이 된다.Referring to Equation (4), the initialization section 310 includes a column for each of the measurement matrix A,

The sum of the vectors of the magnitudes of the vectors coming out through the inner product of i

0 " of < / RTI >

를 하기 수학식 5에 따라서, 종래의 인덱스 집합과 병합한다.
The initialization unit 310 initializes the generated index

Is merged with the conventional index set according to the following equation (5).

&Quot; (5) "

에 포함된 인덱스들의 스팬(span)위로의 정사영(orthogonal projection)인

를 결정한다.
The initialization unit 310 initializes the index set

Which is the orthogonal projection over the span of the indexes included in the < RTI ID = 0.0 >

.

&Quot; (6) "

은

에 속하는 원소에 해당되는 열들로 구성된 A행렬의 sub-matrix를 의미한다.here,

silver

Matrix of the matrix A consisting of the columns corresponding to the elements belonging to the matrix A.

를 결정할 수 있다.According to one aspect, the initialization unit 310 uses the pseudo inverse matrix of the measurement matrix,

Can be determined.

와 잔여 행렬

를 하기 수학식 7과 같이 업데이트 할 수 있다.
The initialization unit 310 generates an approximation matrix of the received signal based on the determined orthogonality.

And the residual matrix

Can be updated as shown in Equation (7).

&Quot; (7) "

는 수신신호 Y와 상기 수신 신호의 근사 행렬

간의오차를 의미한다.
Here,

Is an approximate matrix of the received signal Y and the received signal

.

The initialization unit 310 performs L initialization procedures of Equations 3 to 7 to select L initial indexes.

와 잔여 행렬

을 업데이트할 수 있다. 일측에 따르면, 반복 수행부(320)는 선택된 복수의 초기 인덱스 각각에 대하여 수학식 4 내지 수학식 7의 절차를 반복할 수 있다. 일측에 따르면, 반복 수행부(320)는 미리 결정된 상수인 K 번 만큼 수학식 4 내지 수학식 7의 절차를 반복할 수 있다.
The iterative execution unit 320 applies an orthogonal matching perchoe technique to a plurality of selected initial indexes in parallel to generate an approximation matrix of a received signal corresponding to each initial index,

And the residual matrix

Can be updated. According to one aspect, the iterative execution unit 320 may repeat the procedure of Equations (4) to (7) for each selected plurality of initial indexes. According to one aspect, the iterative execution unit 320 may repeat the procedure of Equations (4) to (7) by K, which is a predetermined constant.

According to one aspect, the set of indexes may coincide with the repetition of the iterative execution unit 320. For example, if you select index 3 as the initial index, and then add index 2 in a subsequent iteration, The index set corresponding to the initial index '3' is {3, 2} and the index set corresponding to the initial index '2' is the index set corresponding to the initial index '3' when the index 2 is selected as the initial index, 2, 3}. The iterative generation unit 320 may compare index sets including an initial index and additional indexes with each other.

According to one aspect, when there is an index set including the same index, the iterative execution unit 320 calculates an iteration for only one set of the index sets including the same index, It is possible to avoid meaningless iterative calculations.

According to another aspect, when there is an index set including the same index in the t-th iteration, the initialization unit 310 of the t-th iteration process reselects the index in proportion to the number of index sets including the same index . For example, when N sets of indexes exist, the initialization unit 310 may reselect N-1 initial indexes in the t-th iteration. In this case, the iterative execution unit 320 may generate an index set by applying an orthogonal matching per-shot technique to the re-selected initial index.

The selecting unit 330 selects a restored signal of the sparse signal based on the approximate matrices generated by the initializing unit 310 and the iterative performing unit 320. According to one aspect, the selector 330 can select a restoration signal according to an error between each approximate matrix and a received signal. The selector 330 can select a restored signal as a restored signal of a sparse signal through an index set having a minimum size of a residual matrix indicating an error between each approximate matrix and a received signal as shown in Equation (7).

&Quot; (8) "

FIG. 4 is a flowchart illustrating a restoration method according to an exemplary embodiment.

의 초기값

인덱스 집합

의 초기값

, 반복 횟수 t 를 하기 수학식 3과 같이 초기화할 수 있다.
At step 410, the decompression apparatus reconstructs a residual matrix,

The initial value of

Index set

The initial value of

, The number of repetitions t can be initialized as shown in Equation (3).

In addition, the restoration device may receive a received signal and may select a plurality of initial indexes for applying the orthogonal matching perchoe technique to the received signal. Here, the initial index may be an index of vectors selected by the initial vector among the column vectors of the measurement matrix. The decompression apparatus may calculate the correlation between the received signal and the measurement matrix of the orthogonal matching technique and select a plurality of initial indexes according to the magnitude of the correlation value.

를 종래의 인덱스 집합과 병합한다.The restoration device stores the generated index

With the conventional index set.

에 포함된 인덱스들의 스팬(span)위로의 정사영(orthogonal projection)인

를 결정한다. 일측에 따르면, 복원 장치는 측정 행렬의 의사 역행렬(Pseudo Inverse Matrix)을 이용하여 정사영

를 결정할 수 있다.The restoration device includes a set of indexes

Which is the orthogonal projection over the span of the indexes included in the < RTI ID = 0.0 >

. According to one aspect, the restoration device uses a pseudo inverse matrix of the measurement matrix

Can be determined.

와 잔여 행렬

를 업데이트 할 수 있다.
The restoration apparatus calculates an approximation matrix of the received signal based on the decided orthogonality,

And the residual matrix

Can be updated.

와 잔여 행렬

를 업데이트 할 수 있다.
In step 420, the decompression apparatus applies an orthogonal matching per-shot technique in parallel on the selected plurality of initial indexes to obtain an approximation matrix of the received signal corresponding to each initial index,

And the residual matrix

Can be updated.

According to one aspect, the decompressor in step 425 may compare index sets including the initial index and additional indexes to each other. In this case, the index set may match according to the repetition.

According to one aspect, when there is an index set that includes the same index, the decompression apparatus calculates an iteration only for any one of the index sets including the same index in step 420, It is possible to avoid meaningless iterations by stopping iteration.

According to another aspect, when there is an index set including the same index in the t-th iteration, the restoration apparatus of the t-th iteration process calculates an index in proportion to the number of index sets including the same index in step 410 Can be reselected. In this case, the restoration device may generate an index set by applying the orthogonal matching perchoe technique to the initial index re-selected at step 420. [

In step 430, the decompression device selects a reconstructed signal of the coarse signal based on the generated approximate matrices. According to one aspect, the restoration apparatus can select a restoration signal according to an error between each approximation matrix and a received signal. The restoration apparatus can select the restored signal as the restored signal of the sparse signal through the index set having the minimum size of the residual matrix indicating the error between each approximation matrix and the received signal.

The method according to an embodiment may be implemented in the form of a program command that can be executed through various computer means and recorded in a computer-readable medium. The computer-readable medium may include program instructions, data files, data structures, and the like, alone or in combination. The program instructions to be recorded on the medium may be those specially designed and configured for the embodiments or may be available to those skilled in the art of computer software. Examples of computer-readable media include magnetic media such as hard disks, floppy disks and magnetic tape; optical media such as CD-ROMs and DVDs; magnetic media such as floppy disks; Magneto-optical media, and hardware devices 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 those 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 devices described above may be configured to operate as one or more software modules to perform the operations of the embodiments, and vice versa.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. For example, it is to be understood that the techniques described may be performed in a different order than the described methods, and / or that components of the described systems, structures, devices, circuits, Lt; / RTI > or equivalents, even if it is replaced or replaced.

Therefore, other implementations, other embodiments, and equivalents to the claims are also within the scope of the following claims.

110: received signal
120: measurement matrix
130: Sparkling signal

Claims (15)

1. A restoration apparatus for restoring a coarse signal in a received signal using an orthogonal matching pursuit scheme,
An initialization unit for selecting a plurality of initial indexes of the orthogonal matching per use technique;
An iterative execution unit that applies the orthogonal matching perchoe technique to the selected plurality of initial indexes in parallel to generate approximate matrices of the received signals corresponding to each of the initial indexes;
A selector for selecting a restored signal of the sparse signal based on the plurality of approximate matrices;
.
The method according to claim 1,
Wherein the initialization unit calculates the correlation between the received signal and the measurement matrix of the orthogonal matching perchture technique and selects the plurality of initial indexes according to the magnitude of the correlation value.
The method according to claim 1,
Wherein the iterative execution unit determines an orthogonal projection over a span of additional indices generated as the initial index and the orthogonal matching perchture technique are repeated and generates an approximation of the received signal based on the determined orthogonality And calculates an error between the matrix and the received signal.
The method of claim 3,
Wherein the iterative execution unit computes the orthogonal projection using a pseudo inverse matrix of a measurement matrix of the orthogonal matching technique.
The method of claim 3,
And the selector selects the restoration signal according to an error between the approximate matrix and the received signal.
2. The apparatus of claim 1, wherein the repetition performing unit
The initial indexes and the orthogonal matching permutation techniques are repeated, and the orthogonal matching permutation technique is applied to only one of the sets of indexes including the same index Restoration device. 2. The apparatus of claim 1, wherein the repetition performing unit
Comparing the index sets including additional indexes generated as the initial index and the orthogonal matching permit technique are repeated,
The initialization unit reselects the initial index according to the number of elements of the index set including the same index to maintain the number of the index sets when there is an index set including the same index among the index sets,
Wherein the iterative execution unit applies the orthogonal matching perchoe technique to the re-selected initial index. A restoration method for restoring a coarse signal in a received signal using an orthogonal matching pursuit technique,
Selecting a plurality of initial indices of the orthogonal matching perchoe technique;
Generating approximate matrices of the received signals corresponding to each of the initial indices by applying the orthogonal matching perchoe technique to the selected plurality of initial indexes in parallel; And
Selecting a restored signal of the coarse signal based on the plurality of approximate matrices
/ RTI >
9. The method of claim 8,
Wherein the selecting the initial index comprises: calculating a correlation between the received signal and a measurement matrix of the orthogonal matching perchoe technique; and selecting the plurality of initial indexes according to a value of the correlation.
9. The method of claim 8,
Wherein generating the approximate matrices of the received signal comprises determining an orthogonal projection over a span of additional indices generated as the initial index and the orthogonal matching funspot technique are repeated, And an error between the generated approximate matrix of the received signal and the received signal is calculated. 11. The method of claim 10,
Wherein the generating of the approximate matrices of the received signal comprises calculating an orthogonal projection using a pseudo inverse matrix of a measurement matrix of the orthogonal matching per use technique. 9. The method of claim 8,
Wherein the step of selecting the restored signal of the sparse signal selects the restored signal according to an error between the approximate matrix and the received signal. 9. The method of claim 8, wherein generating the approximate matrices comprises:
The initial indexes and the orthogonal matching permutation techniques are repeated, and the orthogonal matching permutation technique is applied to only one of the sets of indexes including the same index How to restore. 9. The method of claim 8,
Further comprising comparing index sets including additional indexes generated as the initial index and the orthogonal matching permit technique are repeated,
Wherein the step of selecting the initial index includes the step of re-selecting the initial index according to the number of elements of the index set including the same index, if there is an index set including the same index among the index sets, Keep the number,
Wherein generating the approximate matrices comprises applying the orthogonal matching perchoe technique to a re-selected initial index. A computer readable recording medium on which a program for executing the method of any one of claims 8 to 14 is recorded.

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