WO2015100598A1

WO2015100598A1 - Compressed sensing-based signal reconstruction method and device

Info

Publication number: WO2015100598A1
Application number: PCT/CN2013/091066
Authority: WO
Inventors: 王悦
Original assignee: 华为技术有限公司
Priority date: 2013-12-31
Filing date: 2013-12-31
Publication date: 2015-07-09
Also published as: CN104904122B; CN104904122A

Abstract

Provided are a compressed sensing-based signal reconstruction method and device. The method comprises: calculating inner product values of all column vectors within a residual vector and a processing matrix; determining a largest inner product value within the inner product values; according to the largest inner product value, an inner product threshold factor and a preset maximum number of search paths, determining the number of search paths within an iteration; within all the column vectors of the processing matrix, according to the inner product values in descending order, selecting corresponding column vectors, the number of column vectors being identical to the number of search paths; according to index positions of the column vectors, the number of column vectors being identical to the number of search paths, sequentially updating an index set of each search path, and obtaining updated index sets; according to the updated index sets, respectively performing an iteration update operation on each search path, and obtaining an updated residual vector. In the present invention, the number of processing targets of an iteration update is reduced, thereby significantly decreasing workload and complexity.

Description

Signal reconstruction method and device based on compressed sensing

The present invention relates to communication technologies, and in particular, to a signal reconstruction method and apparatus based on compressed sensing. Background technique

In the traditional signal processing theory, according to the Shannon sampling theorem: the sampling rate used to acquire the signal should be at least equal to twice the signal bandwidth to recover the original signal without distortion, and the sampling rate is called Nyquist. Sample rate. However, with today's demand for data volume and the rapid growth of data to be processed, the signal bandwidth of the data carrying data will become wider and wider, resulting in higher and higher Nyquist sampling rates, while existing hardware. The analog-to-digital conversion and signal processing capabilities of the device are not yet able to meet the rapid growth in demand for broadband signals. Moreover, on the other hand, even if the level of hardware implementation is greatly improved in the future, high-energy mass data collection is not essential. Taking the existing image signal processing as an example, in order to reduce the storage and transmission overhead, the data obtained after sampling is usually compressed, and the important information in the image is represented by a small amount of data, that is, only important data is retained and the remaining non-important is discarded. The data is reconstructed from the original image after being stored or transmitted. This method of first high speed sampling and then compression and discarding actually causes a great waste of sampling resources.

In order to combine sampling and compression simultaneously, that is, to directly collect data at a sampling rate lower than Nyquist, Compressive Sensing (CS) technology is proposed. In CS technology, the original input information (ie, the high-dimensional original input signal) is reconstructed based on the sampled data obtained after the low-speed sampling process (ie, the dimensionally reduced sampled signal). This process is called compression-sensing signal reconstruction. The CS signal reconstruction method mainly includes the greedy search method. The most commonly used subclass of this method is Orthogonal Matching Pursuit (OMP), but the accuracy of the signal reconstruction of this method is not high.

In the prior art, a K-best-OMP signal reconstruction method is proposed to improve the accuracy of CS signal reconstruction. In the K-best-OMP signal reconstruction method, a fixed K path is searched for each iteration, and all K bars are retained. Path, and then expand K new sub-search paths based on each path, that is, a common search path, and then retain K paths satisfying the conditions in the search path, and then perform new A round of path expansion until the iteration stops.

However, the CS signal reconstruction using the prior art has high complexity and is difficult to implement. Summary of the invention

Embodiments of the present invention provide a signal reconstruction method and apparatus based on compressed sensing, which are used to solve the problem of high complexity of existing CS signal reconstruction.

A first aspect of the embodiments of the present invention provides a signal reconstruction apparatus based on compressed sensing, which includes:

a calculation module, configured to calculate a residual vector and an inner product value of all column vectors in the processing matrix; a determining module, configured to determine a maximum inner product value in the inner product value; according to the maximum inner product value, inner product a threshold factor and a preset maximum number of search paths, determining a number of search paths in the iteration; a screening module, configured to select corresponding ones in the column vectors of the processing matrix according to the inner product values from large to small a column number of the same number as the number of search paths;

And an update module, configured to sequentially update an index set of each search path according to the index position of the column number of the same number of the search path, and obtain an updated index set;

An iterative module is configured to perform an iterative update operation on each search path according to the updated index set to obtain an updated residual vector.

With reference to the first aspect, in a first possible implementation manner of the first aspect, the determining module is specifically configured to determine an inner product threshold according to the maximum inner product value and an inner product threshold factor; And the number of inner product values of the inner product value that is greater than the inner product threshold value; comparing the number of inner product values greater than the inner product threshold value and the size of the preset maximum search path number, The smaller of these values is taken as the number of search paths in the iteration.

With reference to the first aspect, in a second possible implementation manner of the second aspect, the calculating module is further configured to: when the iterative update operation is a non-first iterative update operation, according to the updated index set And performing an iterative update operation on each search path to obtain an updated residual vector, calculating a second norm of the updated residual vector on all the search paths, and determining a minimum of all the second norms Two norm;

The determining module is further configured to determine, according to the minimum two norm, the two norm threshold factor, and the maximum search path, the number of search path reservations in the iteration; in the search path, according to the second norm To a large number of search paths that retain the same number of numbers as the search path, In order to preserve the search path; when the number of times of the iterative update operation is equal to the preset parameter signal sparsity, the corresponding search path with the smallest two norm is selected from the reserved search path, and the two norms are The iterative update signal corresponding to the smallest search path is used as the reconstruction signal.

With reference to the first aspect, in a third possible implementation manner of the second aspect, the device further includes: an checking module, configured to: when the iterative update operation is a non-first iterative update operation, An index position of the same number of column vectors as the number of search paths, sequentially updating an index set of each search path, and after obtaining the updated index set, checking the index sets of all the search paths to determine whether the index set exists The duplicate path, if it exists, deletes the duplicate path, and updates the index set again according to the search path remaining after the deletion to obtain the index set of the secondary update.

A second aspect of the embodiments of the present invention provides a signal reconstruction method based on compressed sensing, which includes:

Calculating the residual vector and the inner product of all column vectors in the processing matrix;

Determining a maximum inner product value of the inner product values;

Determining the number of search paths in the iteration according to the maximum inner product value, the inner product threshold factor, and the preset maximum search path number;

In all the column vectors of the processing matrix, the corresponding number of column vectors corresponding to the number of the search paths are sequentially selected according to the inner product value from large to small;

And updating, according to the index position of the column number of the same number of the search path, the index sets of each search path, and obtaining the updated index set;

According to the updated index set, an iterative update operation is performed on each search path to obtain an updated residual vector.

With reference to the second aspect, in a first possible implementation manner of the second aspect, the determining, according to the maximum inner product value, an inner product threshold factor, and a preset maximum search path number, determining a number of search paths in an iteration, Includes:

Determining an inner product threshold according to the maximum inner product value and the inner product threshold factor;

Counting the number of inner product values of all the inner product values that are greater than the inner product threshold; comparing the number of inner product values greater than the inner product threshold value and the preset maximum number of search paths The size of the smaller number is used as the number of search paths in the iteration.

In conjunction with the second aspect, in a second possible implementation of the second aspect, the iterative The new operation is a non-first iteration update operation, and accordingly,

According to the updated index set, performing an iterative update operation on each search path separately, and obtaining an updated residual vector, the method further includes:

Calculating a two norm of the updated residual vector on all of the search paths, and determining a minimum two norm of all of the two norms;

Determining the number of search path reservations in the iteration according to the minimum two norm, the two norm threshold factor, and the maximum search path;

In the search path, a corresponding search path having the same number of retaining numbers as the search path is retained as a reserved search path according to the second norm;

If the number of times of the iterative update operation is equal to the preset parameter signal sparsity, the corresponding search path with the smallest two norm is filtered out from the reserved search path, and the search path with the minimum of the two norms is selected. The corresponding iterative update signal is used as the reconstruction signal.

With reference to the second aspect, in a third possible implementation manner of the second aspect, the iterative update operation is a non-first iterative update operation, and accordingly,

And updating, according to the index position of the column number of the same number of the search path, the index set of each search path, and obtaining the updated index set, further comprising: checking all the search path locations The index set determines whether there is a duplicate path. If yes, the duplicate path is deleted, the search path and the index set are updated again, and the search path and the index set of the secondary update are obtained.

A third aspect of the embodiments of the present invention provides a signal reconstruction apparatus based on compressed sensing, including:

a memory for storing instructions;

a processor, coupled to the memory, configured to execute instructions stored in the memory for calculating a residual vector and an inner product value of all column vectors in the processing matrix; determining a maximum of the inner product values An inner product value; determining, according to the maximum inner product value, an inner product threshold factor, and a preset maximum search path number, a number of search paths in an iteration; in all column vectors of the processing matrix, according to the inner product value Sorting the corresponding number of column vectors corresponding to the number of the search paths from the largest to the smallest; and sequentially updating the indexes of the search paths according to the index positions of the column numbers of the same number of the search paths Collecting, obtaining an updated index set; performing an iterative update operation on each search path according to the updated index set, and obtaining an updated Residual vector.

With reference to the third aspect, in a first possible implementation manner of the third aspect, the processor is configured to determine an inner product threshold according to the maximum inner product value and an inner product threshold factor; And the number of inner product values of the inner product value that is greater than the inner product threshold value; comparing the number of inner product values greater than the inner product threshold value and the size of the preset maximum search path number, The smaller of these values is taken as the number of search paths in the iteration.

With reference to the third aspect, in a second possible implementation manner of the third aspect, the processor is further configured to: when the iterative update operation is a non-first iterative update operation, according to the updated index set And performing an iterative update operation on each search path to obtain an updated residual vector, calculating a second norm of the updated residual vector on all the search paths, and determining a minimum of all the second norms a second norm; determining, according to the minimum two norm, a two norm threshold factor, a maximum search path, a number of search path reservations in the iteration; in the search path, retaining from the second norm according to the second norm The search path retains the same number of search paths as the reserved search path. When the number of times of the iterative update operation is equal to the preset parameter signal sparsity, the corresponding searched path is selected from the reserved search path. The search path with the smallest norm is used as the reconstruction signal for the iterative update signal corresponding to the search path with the smallest two norm.

With reference to the third aspect, in a third possible implementation manner of the third aspect, the processor is further configured to: when the iterative update operation is a non-first iterative update operation, according to the number of the search paths Index positions of the same number of column vectors, sequentially updating the index sets of the search paths, and after obtaining the updated index sets, checking the index sets of all the search paths to determine whether there is a duplicate path, if any, The path deletion is repeated, and the index set is updated again according to the search path remaining after the deletion, and the index set of the secondary update is obtained.

In the embodiment of the present invention, the number of search paths in the iteration is determined according to the maximum inner product value, the inner product threshold factor, and the preset maximum search path number, that is, the search path is filtered, and according to the determined search path. The number determines the index set, so the processing objects of subsequent iteration updates are reduced, and the workload and complexity are greatly reduced. DRAWINGS

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following will The drawings used in the embodiments or the description of the prior art are briefly described. It is obvious that the drawings in the following description are some embodiments of the present invention, and are not creative to those skilled in the art. Other drawings can also be obtained from these drawings on the premise of labor.

1 is a schematic structural diagram of Embodiment 1 of a signal reconstruction apparatus based on compressed sensing provided by the present invention;

2 is a schematic structural diagram of Embodiment 2 of a signal reconstruction apparatus based on compressed sensing provided by the present invention;

3 is a schematic flow chart of Embodiment 1 of a method for reconstructing a compressed sensing based signal according to the present invention;

4 is a schematic flow chart of Embodiment 2 of a method for reconstructing a compressed sensing based signal according to the present invention;

FIG. 5 is a schematic structural diagram of Embodiment 3 of a signal reconstruction apparatus based on compressed sensing provided by the present invention. The technical solutions in the embodiments of the present invention are clearly and completely described in the following with reference to the accompanying drawings in the embodiments of the present invention. The embodiments are a part of the embodiments of the invention, and not all of the embodiments. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments of the present invention without creative efforts are within the scope of the present invention.

FIG. 1 is a schematic structural diagram of Embodiment 1 of a compression-aware signal reconstruction apparatus according to the present invention. As shown in FIG. 1, the apparatus includes: a calculation module 101, a determination module 102, a screening module 103, an update module 104, and an iteration module 105. , among them:

The calculation module 101 is configured to calculate an inner product value of the residual vector and all the column vectors in the processing matrix. The residual vector may be an initial residual vector or a residual vector during subsequent iterations. For example, to initialize the residual vector, denoted as r ^[ ° ^] , and 0 in the upper corner indicates initialization. r ^[ ° ^] and each column vector of the processing matrix A are subjected to inner product calculation one by one, expressed as < , 4 > , where A „ denotes the nth 歹U of the processing matrix A, and the processing matrix A has a total of N columns, n Can be 1, 2, ..., N, 〈> Inner product operation. Finally, N inner product values are obtained. The determining module 102 is configured to determine a maximum inner product value of the inner product values; and determine the number of search paths in the iteration according to the maximum inner product value, the inner product threshold factor, and the preset maximum search path number.

The filtering module 103 is configured to select, in the column vectors of the processing matrix, the same number of column vectors corresponding to the number of the search paths in order from the inner product value.

The updating module 104 is configured to sequentially update the index sets of the search paths according to the index positions of the column numbers of the same number of the search paths as above, and obtain the updated index sets.

The iteration module 105 is configured to perform an iterative update operation on each search path according to the updated index set to obtain an updated residual vector.

In this embodiment, the number of search paths in the iteration is determined according to the maximum inner product value, the inner product threshold factor, and the preset maximum search path number, that is, the search path is filtered, and the number of search paths is determined according to the determined number of search paths. The index set is determined, so the processing objects of subsequent iterations are reduced, and the workload and complexity are greatly reduced. And according to experiments, the reconstructed signal obtained by the method of the embodiment of the invention has high accuracy.

Further, the determining module 102 is specifically configured to determine an inner product threshold according to the maximum inner product value and the inner product threshold factor; and calculate an inner product of all the inner product values that is greater than the inner product threshold value. The number of values is compared; the number of inner product values greater than the inner product threshold value and the size of the preset maximum search path number are compared, and the smaller one is used as the number of search paths in the iteration.

The calculating module 101 is further configured to: after the iterative update operation is a non-first iterative update operation, perform an iterative update operation on each search path according to the updated index set, and obtain an updated residual vector, Calculating a two norm of the updated residual vector on all of the search paths and determining a minimum two norm of all of the two norms. Correspondingly, the determining module 102 is further configured to determine, according to the minimum two norm, the two norm threshold factor, and the maximum search path, the number of search path reservations in the iteration; in the search path, according to the second norm a number of search paths retaining the same number of search paths as the reserved search path from small to large, and filtering from the reserved search path when the number of times of the iterative update operation is equal to the preset parameter signal sparsity Corresponding to the second norm minimum search path, and the iterative update signal corresponding to the second norm minimum search path is used as a reconstruction signal.

2 is a schematic structural diagram of Embodiment 2 of a signal reconstruction apparatus based on compressed sensing provided by the present invention As shown in FIG. 2, on the basis of FIG. 1, the apparatus further includes: an checking module 106, configured to: when the iterative update operation is a non-first iterative update operation, according to the number of the search paths according to the The index position of the number of column vectors, the index set of each search path is sequentially updated, and after the updated index set is obtained, the index sets of all the search paths are checked to determine whether there is a duplicate path, and if it exists, it will be repeated. The path is deleted, and the index set is updated again according to the search path remaining after the deletion, and the index set of the second update is obtained.

The apparatus is for performing the method embodiments described below.

FIG. 3 is a schematic flowchart of Embodiment 1 of a method for reconstructing a compressed sensing based signal according to the present invention. As shown in FIG. 3, the method includes:

S301. Calculate a residual vector and an inner product value of all column vectors in the processing matrix.

The residual vector may be an initialization residual vector, or may refer to a residual vector in a subsequent iteration. Taking the initialization residual vector as an example, it is denoted as r ^[ ° ^] , and 0 in the upper corner indicates initialization. r ^[ ° ^] is calculated internally by each column vector of the processing matrix A, expressed as < \ , 4 ⁿ > I , where represents the nth column of the processing matrix A, the processing matrix A - a total of N columns, n It can be 1, 2, ..., N, ( > means inner product operation. Finally, N inner product values are obtained.

5302. Determine a maximum inner product value of the inner product values. The largest one is selected from the above N inner product values, denoted as v ^[1] = ma _X ( [< , 〉]), and the superscript 1 indicates the first step.

S303. Determine, according to the maximum inner product value, the inner product threshold factor, and the preset maximum search path number, the number of search paths in the iteration.

S304. In all the column vectors of the processing matrix, select the same number of column vectors corresponding to the number of the search paths according to the inner product value from the largest to the smallest.

Assuming that the number of search paths determined for the first time is ^1] , in the above processing matrix ,, the corresponding column vectors are selected according to the N inner product values from large to small.

S305. Update the index sets of the search paths in turn according to the index positions of the column numbers of the same number of the search paths, and obtain the updated index sets.

The index position of the same number of column vectors as the number of search paths, that is, the number of these column vectors, updates ^ ^[1] index positions one by one to the index set, and obtains ^[1] updated index sets. {Ω , subscript k denotes the kth search path, where fc = l, 2,..., ^ ^1] , ie each index bit Set the corresponding index set added to its corresponding search path.

S306. Perform an iterative update operation on each search path according to the updated index set, and obtain an updated residual vector.

Taking the kth search path as an example, the iterative update signal vector ^ is obtained according to the index set {Ω of the search path, and the iterative update process can be expressed as a formula ^ A y, where y is a pre-entered sample signal vector, A is a processing matrix input in advance, and A is a matrix composed of column vectors corresponding to index positions included in the index set {Ω in the processing matrix A, which is a conjugate transposed matrix of A, (Α^ Α _Ω is Α _Ω The inverse matrix is then updated according to ^, and the updated residual vector i can be obtained according to the formula i = yA. Further, the updated residual vector is used to enter the next iteration loop until the last reconstruction is obtained. The signal, which is described in more detail below.

The determining the number of search paths in the iteration according to the maximum inner product value, the inner product threshold factor, and the maximum search path number, specifically: determining an inner product threshold according to the maximum inner product value and the inner product threshold factor; And the number of inner product values of all the inner product values greater than the inner product threshold value; comparing the number of inner product values greater than the inner product threshold value and the size of the preset maximum search path number, The small value is used as the number of search paths in the iteration.

Taking the first iterative process as an example, the product of the maximum inner product value max /" ^[ ° „ and the inner product threshold factor "multiplied by is used as the inner product threshold value, and all the inner product values are larger than the inner product gate. The number of inner product values of the limit, comparison; 7 ^[1] and the size of K, the smaller value is used as the number of search paths in the first iteration. Where 7 ^[1] can use the formula = {[< r ^[0] , A >] > v ^m a where {[ < r ^[0] , A >1 > v ^[1] a ; set {[ < r ^[0] , A >1 > v ^[1] The number of elements in a ₍ Further, if the iterative update operation is not the first iterative update operation, the index position of each search path is sequentially updated according to the index position of the column number of the same number of the search path, and the updated index set is obtained. The index set of all search paths may also be checked to determine whether there is a duplicate path. If yes, the duplicate path is deleted, and the search set is updated according to the search path remaining after the deletion, and the index set of the second update is obtained. After filtering in this way, unnecessary calculations can be avoided during subsequent iteration operations to reduce complexity.

For the iterative update operation is a non-first iteration update operation, according to the updated index set, performing an iterative update operation on each search path separately, and obtaining the updated residual vector, the method further includes: calculating the residual of the update on all the search paths. a two norm of the vector, and determining a minimum two norm of all the two norms; determining the number of search path reservations in the iteration according to the minimum two norm, the two norm threshold factor, and the maximum search path; According to the above two norm, from small to large, the corresponding search path retaining the same number as the above search path is reserved as the reserved search path; if the number of times of the above iterative update operation is equal to the preset parameter signal sparsity S, then the above reservation is performed. The search path corresponding to the second norm number is selected in the search path, and the iterative update signal corresponding to the search path with the smallest two norm is used as the reconstruction signal.

FIG. 4 is a schematic flowchart of Embodiment 2 of a method for reconstructing a compressed sensing based signal according to the present invention. As shown in FIG. 4, the entire process of the signal reconstruction method provided by the embodiment of the present invention includes:

5401. Receive input data and parameters. Specifically, it can be manually input by the user or imported by other devices. The above data includes: sampling signal (denoted as y, y is a vector), processing matrix (remembered; the above parameters include: preset signal sparsity (remarked as, preset maximum number of search paths (denoted as J, inner product threshold) Factor (denoted as ") and two-norm threshold factor (denoted as.

5402. Initialize a residual vector and an index set. The initialization residual vector is to assign the initial value of the residual vector to the input sample signal, that is, r ^[ ° ^] = _{y; to} initialize the index set, the initial value of the index set is assigned to the empty set, that is, Ω = 0.

S403. Find an initial residual vector and an inner product value of all column vectors in the processing matrix. Through the formula

(r ^[01 , A ) find N inner product values. S404. Determine a maximum inner product value among the inner product values. Write the maximum inner product value as

S405. Determine, according to the maximum inner product value, the inner product threshold factor, and the preset maximum search path number, the number of search paths in the first iteration. Specifically, the product of V (r ^[0] , A ) and " is used as the inner product threshold value, and the number of inner product values of the above Ν is greater than the inner product threshold value; / ^[1] , And the smaller one is used as the number of search paths in the first iteration, and is recorded as ^[1] , ie Κ ^ί1] = Ώΐιη (η ^ί1] , κ).

5406. Select, from all the vectors of the processing matrix, the same number of column vectors corresponding to the number of search paths in the first iteration according to the inner product value from the largest to the smallest. Specifically, in the processing selection matrix A ^ column vector product of greater value within ^1] correspond.

5407. Update the index set of each search path sequentially according to the index position of the selected column vector. The index position of the selected column vector is the corresponding position number of each column vector. The ^1] index positions are updated one by one into ^ ^[1] index sets, and ^1] updated index set {Ω is obtained, and the subscript k represents the kth search path, where = 1, υ ^[1] .

5408. Perform an iterative update operation on each search path according to the updated index set, and obtain an updated residual vector. With the method of the previous embodiment, each search path acquires an updated residual vector i .

5409. In each search path, use the updated residual vector to obtain an inner product value of the updated residual vector and all the column vectors of the processing matrix. That is, by the formula <ιΤ ^1] , Α^ _ obtains N inner product values. s indicates the number of times of this iteration (that is, the current iteration is the sth iteration), - "represents the residual vector obtained after the last iteration update; the subscript k is represented in the kth path.

It should be noted that each path is performed in parallel and does not interfere with each other, and the same is true in the following methods. S410. Determine, in each of the foregoing search paths, a maximum inner product value among the inner product values. Record the maximum inner product value as v ^s] = .

s indicates the number of times of this iteration (ie, when Before the Sth iteration)

S411. Determine, according to the maximum inner product value, the inner product threshold factor, and the preset maximum search path number, the number of sub-search paths in each search path in the current iteration. Specifically, the product of v _k = max — — ^{1 ]} , 4 > ] and “ is used as the inner product threshold value, and the number of inner product values of the above N is greater than the inner product threshold value; Where; ^ = {[<r ^] , A„ >] > v^a) The smaller of ^ and ^ is the number of sub-search paths in this iteration, and is denoted as ^s] , ^s] =min( ;^, .

S412. Select, from all the vectors of the processing matrix, the same number of column vectors corresponding to the number of the sub-search paths in order from the inner product value. That is, in each search path, ^s] corresponding column vectors having larger inner product values are selected from the above processing matrix A.

S413. Update the index set of each search path sequentially according to the index position of the selected column vector. The index positions are updated one by one into the index set, and ^s] updated index sets {Ω _Α , .}., j = l, 2,..., K _k ^[s

5414. Check the current index set in all the search paths, and determine whether there is a duplicate path. If yes, delete the duplicate path, and return to execution S413, that is, re-index the set according to the search path remaining after the deletion; if not, execute S415.

5415. Perform respective iterative update operations on each of the sub-search paths according to the updated index set, and obtain an updated residual vector.

Taking the jth sub-search path of the kth path as an example, first, an iterative update signal vector is obtained according to the index set {Ω^.}., where =(Α^Α ·) - ¹ A^.y, A _ntj The moment composed of the column vectors corresponding to the index positions contained in the index set {Ω^.}. in the matrix A. Then, according to the residual vector update, the residual vector of this update is = - ^A n ^[ nl.

5416. Calculate a second norm of the updated residual vector on all search paths, and determine a minimum two norm of all the two norms. The minimum two norm is recorded as ^

The two norms. It should be noted that all search paths include all the above search paths and each Each sub-search path under a search path.

S417. Determine, according to the minimum two norm, the two norm threshold factor, and the maximum search path, the number of search path reservations in the iteration. Specifically, the ratio of ^] = min | and is used as a two-norm threshold value, and a number of two norms that are less than or equal to the second norm threshold value is determined from the above two norms ^[5] , that is, 1 ^[ then Use the smaller values in ^ and K as the search path in this iteration

The number of paths is reserved, denoted as t/ ^[s] , ί/ ^Μ = ηιίη( ^] , ^ί:).

5418. In all the foregoing search paths, the search path with the same number of retaining numbers as the above search path is kept from small to large according to the above two norms, as a reserved search path. That is, in all search paths, the t/ ^[s] search path is reserved as a reserved search path from small to large according to the two norm.

5419. Determine whether the iteration stop condition is met, and if yes, execute S420; if not, return to execute S409. When the execution returns to S409, the residual vector updated in S415 is used.

Wherein, determining whether the iteration stop condition is satisfied, specifically, determining whether the current iteration update number is equal to the preset signal sparsity S, indicating that the iteration stop condition is not satisfied; s = S indicates that the iteration stop condition is satisfied.

5420. Filter out the corresponding search path with the smallest two norm from the reserved search path, and use the iterative update signal corresponding to the search path with the smallest two norm as the reconstruction signal.

The above-mentioned corresponding second norm minimum search path can be expressed as = ar _g mi _n [S] arg min [S] is an identifier for obtaining the corresponding search path with the smallest two norm, and the iteration corresponding to the search path Updating the signal as the final reconstruction signal δ, specifically

0[ ^s] ,when e Ω

Oh, yes

0, when i i. Ω- In this embodiment, the working objects of the subsequent steps are sequentially filtered by S405, S411, S414, and S417, so that the workload of the subsequent steps is gradually reduced, so that the complexity of the entire signal reconstruction process is greatly increased. reduce. The accuracy of the reconstructed signal obtained by the method provided by the embodiment of the present invention can also be ensured according to a large amount of experimental data. FIG. 5 is a schematic structural diagram of Embodiment 3 of a compressed sensing-based signal reconstruction apparatus according to the present invention. As shown in FIG. 5, the apparatus includes: a memory 501 and a processor 502, where:

a memory 501, configured to store instructions; a processor 502, coupled to the memory 501, configured to execute instructions stored in the memory 501 for calculating an inner product value of the residual vector and all column vectors in the processing matrix; Determining a maximum inner product value in the inner product value; determining a number of search paths in the iteration according to the maximum inner product value, an inner product threshold factor, and a preset maximum search path number; in all column vectors of the processing matrix And selecting, according to the inner product value, the same number of column vectors corresponding to the number of the search paths; according to the index position of the column number of the same number of the search path, The index set of each search path is sequentially updated to obtain an updated index set. According to the updated index set, an iterative update operation is performed on each search path to obtain an updated residual vector.

Further, the processor 502 is specifically configured to determine an inner product threshold according to the maximum inner product value and the inner product threshold factor; and calculate an inner product of all the inner product values that is greater than the inner product threshold value. The number of values is compared; the number of inner product values greater than the inner product threshold value and the size of the preset maximum search path number are compared, and the smaller one is used as the number of search paths in the iteration.

In a specific implementation process, the processor 502 is further configured to: when the iterative update operation is a non-first iterative update operation, perform an iterative update operation on each search path according to the updated index set, and obtain an updated After the residual vector, calculating a two norm of the updated residual vector on all of the search paths, and determining a minimum two norm of all of the two norms; according to the minimum two norm, two norm a threshold factor, a maximum search path, determining a number of search path reservations in the iteration; in the search path, retaining the same number of search paths as the search path keeps according to the two norms, as Retaining a search path; when the number of times of the iterative update operation is equal to a preset parameter signal sparsity degree, selecting a corresponding search path with the smallest two norm from the reserved search path, and minimizing the two norm The iterative update signal corresponding to the search path is used as the reconstruction signal.

Further, the processor 502 is further configured to: when the iterative update operation is a non-first iteration update operation, sequentially update the search paths according to the index position of the same number of column vectors as the number of the search paths. After obtaining the updated index set, the index set is checked, and the index set of all the search paths is checked to determine whether there is a duplicate path. If yes, the duplicate path is deleted, and the index set is updated again according to the search path remaining after the deletion. , get twice more New index collection.

A person skilled in the art can understand that all or part of the steps of implementing the above method embodiments may be completed by using hardware related to program instructions, and the foregoing program may be stored in a computer readable storage medium, and the program is executed when executed. The foregoing steps include the steps of the foregoing method embodiments; and the foregoing storage medium includes: a medium that can store program codes, such as a ROM, a RAM, a magnetic disk, or an optical disk.

Finally, it should be noted that the above embodiments are only for explaining the technical solutions of the present invention, and are not intended to be limiting thereof; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art will understand that The technical solutions described in the foregoing embodiments may be modified, or some or all of the technical features may be equivalently replaced; and the modifications or substitutions do not deviate from the technical solutions of the embodiments of the present invention. range.

Claims

claims

1. A signal reconstruction device based on compressed sensing, characterized by including:

Calculation module, used to calculate the inner product value of the residual vector and all column vectors in the processing matrix; Determination module, used to determine the maximum inner product value among the inner product values; According to the maximum inner product value, inner product The threshold factor and the preset maximum number of search paths determine the number of search paths in the iteration;

A screening module, configured to select the corresponding number of column vectors that are the same as the number of search paths according to the inner product value from large to small among all column vectors of the processing matrix;

An update module, configured to sequentially update the index set of each search path according to the index positions of the column vectors with the same number as the search path, and obtain the updated index set; an iteration module, used to update the index set according to the update After obtaining the index set, iterative update operations are performed on each search path to obtain the updated residual vector.

2. The device according to claim 1, characterized in that, the determination module is specifically configured to determine the inner product threshold value according to the maximum inner product value and the inner product threshold factor; and count all the inner products The number of inner product values that are greater than the inner product threshold value; compare the number of inner product values that are greater than the inner product threshold value with the size of the preset maximum search path number, and select the smaller one The value of is used as the number of search paths in the iteration.

3. The device according to claim 1, characterized in that, the calculation module is further configured to calculate each item according to the updated index set when the iterative update operation is not the first iterative update operation. The search paths perform iterative update operations respectively, and after obtaining the updated residual vectors, calculate the second norm of the updated residual vectors on all the search paths, and determine the minimum second norm among all the two norms;

The determination module is also configured to determine the number of search paths to retain in the iteration based on the minimum second norm, the second norm threshold factor, and the maximum search path; in the search path, according to the second norm, from Retain the same number of search paths as the number of reserved search paths as the retained search paths; when the number of iterative update operations is equal to the preset parameter signal sparsity, filter out the corresponding search paths from the reserved search paths The search path with the smallest two norms is obtained, and the iterative update signal corresponding to the search path with the smallest two norms is used as the reconstructed signal.

4. The device according to claim 1, further comprising: a checking module; the checking module is configured to, when the iterative update operation is not the first iterative update operation, based on the Describe the index positions of the same number of column vectors as the number of search paths, update the index sets of each search path in turn, and after obtaining the updated index set, check the index sets of all the search paths to determine whether they exist If a duplicate path exists, the duplicate path will be deleted, and the index set will be updated again based on the remaining search paths after deletion to obtain a twice updated index set.

5. A signal reconstruction method based on compressed sensing, characterized by: calculating the inner product value of the residual vector and all column vectors in the processing matrix;

Determine the maximum inner product value among the inner product values;

Determine the number of search paths in the iteration according to the maximum inner product value, the inner product threshold factor and the preset maximum number of search paths;

Among all the column vectors of the processing matrix, select the corresponding column vectors with the same number as the number of search paths in order from large to small according to the inner product value;

According to the index positions of the column vectors with the same number as the search paths, update the index set of each search path in sequence, and obtain the updated index set;

According to the updated index set, iterative update operations are performed on each search path to obtain an updated residual vector.

6. The method according to claim 5, wherein determining the number of search paths in the iteration based on the maximum inner product value, the inner product threshold factor and the preset maximum number of search paths includes:

Determine the inner product threshold value according to the maximum inner product value and the inner product threshold factor;

Counting the number of inner product values greater than the inner product threshold among all inner product values; comparing the number of inner product values greater than the inner product threshold with the preset maximum number of search paths The size of , the smaller value is used as the number of search paths in the iteration.

7. The method according to claim 5, characterized in that the iterative update operation is a non-first iterative update operation, and accordingly,

According to the updated index set, iterative update operations are performed on each search path respectively, and after obtaining the updated residual vector, it also includes:

Calculate the second norm of the updated residual vector on all the search paths, and determine the minimum second norm among all the two norms;

According to the minimum second norm, the second norm threshold factor, and the maximum search path, determine the number of search paths to retain in the iteration; In the search path, the same number of corresponding search paths as the number reserved in the search path is reserved according to the two norms from small to large as the reserved search paths;

If the number of iterative update operations is equal to the preset parameter signal sparsity, then the corresponding search path with the smallest two norms is filtered out from the retained search paths, and the search path with the smallest two norms is selected. The corresponding iteratively updated signal is used as the reconstructed signal.

8. The method according to claim 5, characterized in that the iterative update operation is a non-first iterative update operation, and accordingly,

The step of updating the index set of each search path sequentially according to the index positions of the column vectors with the same number as the search paths. After obtaining the updated index set, it also includes: checking all the search paths. The above-mentioned index set is used to determine whether there are duplicate paths. If there are duplicate paths, the duplicate paths are deleted, the search path and the index set are updated again, and the second updated search path and index set are obtained.

9. A signal reconstruction device based on compressed sensing, characterized by including: a memory for storing instructions;

a processor, coupled to the memory, configured to execute instructions stored in the memory for calculating an inner product value of a residual vector and all column vectors in the processing matrix; determining a maximum of the inner product values Inner product value; Determine the number of search paths in the iteration according to the maximum inner product value, inner product threshold factor and the preset maximum number of search paths; Among all column vectors of the processing matrix, according to the inner product value Select the corresponding column vectors that are the same number as the number of search paths in order from large to small; update the index of each search path sequentially according to the index positions of the column vectors that are the same number as the number of search paths. set to obtain an updated index set; according to the updated index set, iterative update operations are performed on each search path to obtain an updated residual vector.

10. The device according to claim 9, wherein the processor is specifically configured to determine the inner product threshold value based on the maximum inner product value and the inner product threshold factor; and to count all the inner products. The number of inner product values that are greater than the inner product threshold value; compare the number of inner product values that are greater than the inner product threshold value with the size of the preset maximum search path number, and select the smaller one The value of is used as the number of search paths in the iteration.

11. The device according to claim 9, characterized in that, the processor is further configured to: when the iterative update operation is not the first iterative update operation, based on the updated index Set, perform an iterative update operation on each search path respectively, and after obtaining the updated residual vector, calculate the second norm of the updated residual vector on all the search paths, and determine the second norm of all the second norms Minimum second norm; According to the minimum second norm, the second norm threshold factor, and the maximum search path, determine the number of search paths to retain in the iteration; In the search path, retain the second norm from small to large The same number of search paths as the number of reserved search paths is used as the reserved search path; when the number of iterative update operations is equal to the preset parameter signal sparsity, the corresponding search paths are filtered out from the reserved search paths. The search path with the smallest two norms is used, and the iterative update signal corresponding to the search path with the smallest two norms is used as the reconstructed signal.

12. The apparatus according to claim 9, wherein the processor is further configured to: when the iterative update operation is a non-first iterative update operation, based on the same number of search paths as the number of search paths, The index position of the column vector, update the index set of each search path in turn, and after obtaining the updated index set, check the index sets of all the search paths to determine whether there are duplicate paths, and if so, delete the duplicate paths. And update the index set again according to the remaining search path after deletion, and obtain the second updated index set.