CN112202452A

CN112202452A - Compressed sensing signal reconstruction method and system based on block sparsity and binary tree search

Info

Publication number: CN112202452A
Application number: CN202010911892.6A
Authority: CN
Inventors: 徐弘毅; 吴天昊; 张英静; 李阳
Original assignee: Beijing Institute of Electronic System Engineering
Current assignee: Beijing Institute of Electronic System Engineering
Priority date: 2020-09-02
Filing date: 2020-09-02
Publication date: 2021-01-08

Abstract

The invention discloses a compressed sensing signal reconstruction method and a system based on block sparsity and binary tree search, wherein the method comprises the following steps: uniformly partitioning a received signal to construct a block sparse signal model; carrying out block sparse signal reconstruction on the block sparse signal model to determine a support block with a signal and form a support block index set; the invention provides a blind block orthogonal matching tracking algorithm based on a binary tree search and supervision mechanism, which has considerable accurate reconstruction probability in a same-class block adaptive greedy algorithm and has stronger robustness advantage in signal reconstruction under the blind receiving scene of a CS receiver.

Description

Compressed sensing signal reconstruction method and system based on block sparsity and binary tree search

Technical Field

The invention relates to the technical field of communication. And more particularly, to a compressed sensing signal reconstruction method and system based on block sparsity and binary tree search.

Background

Compressed Sensing (CS) information acquisition theory is widely used in the field of communications. Compared with the traditional signal sampling method, the CS method can ensure that the sampling rate of the signal is not limited by the Nyquist sampling theorem any more, but is determined by the characteristics and the information content of the signal. The CS receiver constructed based on the CS method can greatly reduce the sampling rate required by a third party (namely a non-partner) in communication to obtain unknown signals, and avoids the high-speed sampling bottleneck of the receiver in the traditional blind receiving. Meanwhile, because the low-speed ADC can provide higher effective digits, the CS blind receiving method expands the receiving bandwidth and simultaneously considers the large dynamic range necessary for subsequent signal processing.

In order to effectively utilize the multi-narrow-band distribution characteristics of the communication signal spectrum, the block sparse model is an effective improved form in the CS method. By utilizing the structural prior information of the non-zero value blocking distribution of the signals in the sparse domain (namely, the frequency domain), the undersampling efficiency, the reconstruction precision and the reconstruction speed of the signals can be greatly improved. However, the block sparsity greedy reconstruction algorithm with better performance, such as BCoSaMP, BSAMP, and FBBP, is very sensitive to the initialization of the block sparsity and the block length in terms of reconstruction performance. The unmatched block lengths can greatly deteriorate the reconstruction performance of the algorithm, and the block resolution is always fixed and unchangeable in the whole reconstruction process. For CS blind reception, the block distribution, block sparsity, and block length of the signal are usually unknown or not accurately acquired, which greatly limits the use of structured information, multiple narrowband features, by CS receivers.

Disclosure of Invention

The invention aims to provide a compressed sensing signal reconstruction method based on block sparsity and binary tree search, and provides a blind block orthogonal matching pursuit (BTSM-B) based on a binary tree search and supervision mechanism²OMP) algorithm, which has considerable accurate reconstruction probability in the same-class block self-adaptive greedy algorithm, and has stronger robustness advantage in signal reconstruction under the blind receiving scene of a CS receiver. Another object of the present invention is to provide a compressed sensing signal reconstruction system based on block sparsity and binary tree search. It is a further object of this invention to provide such a computer apparatus. It is a further object of this invention to provide such a readable medium.

In order to achieve the purpose, the invention adopts the following technical scheme:

the invention discloses a compressed sensing signal reconstruction method based on block sparsity and binary tree search, which comprises the following steps:

uniformly partitioning a received signal to construct a block sparse signal model;

carrying out block sparse signal reconstruction on the block sparse signal model to determine a support block with a signal and form a support block index set;

and uniformly partitioning the supporting blocks of the supporting block index set again and constructing a block sparse signal model, reconstructing the reconstructed block sparse signal model to update the supporting block index set, repeatedly updating the supporting block index set until an iteration stop condition is met, and reconstructing signals according to the supporting blocks after iteration is stopped.

Preferably, the uniformly blocking the received signal, and the constructing a block sparse signal model specifically includes:

uniformly partitioning the received signals according to a preset block length;

forming a recovery sub-matrix and a sparse sub-vector corresponding to each sub-signal after uniform blocking to obtain an observation vector;

and establishing a block sparse signal model according to the block sparse constraint of the mixed norm of each block of sub-signals after uniform blocking and the observation vector.

Preferably, the reconstructing the block sparse signal model to determine the support block having the signal and forming the support block index set specifically includes:

carrying out block correlation detection on the block sparse signal model through a block orthogonal matching pursuit algorithm to obtain a supporting block with a detected signal;

adding a support block of the detected presence signal to a support block index set to update the support block index set;

and repeating the process of updating the supporting block index set until the search residual of the current block signal meets a preset supervision condition.

Preferably, the re-uniformly partitioning the support blocks of the support block index set and constructing the block sparse signal model specifically includes:

taking half of the block length of the current sub-signal as the decomposed block length;

uniformly partitioning the supporting blocks of the supporting block index set again according to the length of the decomposed block;

and establishing a block sparse signal model for the sub-signals obtained by uniformly partitioning again according to the length of the decomposed block.

The invention also discloses a compressed sensing signal reconstruction system based on block sparsity and binary tree search, which comprises the following steps:

the model building unit is used for uniformly partitioning the received signals to build a block sparse signal model;

the supporting block screening unit is used for reconstructing a block sparse signal of the block sparse signal model to determine a supporting block with a signal and form a supporting block index set;

and the signal reconstruction unit is used for uniformly partitioning the supporting blocks of the supporting block index set again and constructing a block sparse signal model, reconstructing the reconstructed block sparse signal model to update the supporting block index set, repeatedly updating the supporting block index set until an iteration stop condition is met, and reconstructing signals according to the supporting blocks after iteration is stopped.

Preferably, the model building unit is specifically configured to uniformly block the received signal according to a preset block length; forming a recovery sub-matrix and a sparse sub-vector corresponding to each sub-signal after uniform blocking to obtain an observation vector; and establishing a block sparse signal model according to the block sparse constraint of the mixed norm of each block of sub-signals after uniform blocking and the observation vector.

Preferably, the supporting block screening unit is specifically configured to perform block correlation detection on the block sparse signal model through a block orthogonal matching pursuit algorithm to obtain a supporting block with a detected signal; adding a support block of the detected presence signal to a support block index set to update the support block index set; and repeating the process of updating the supporting block index set until the search residual of the current block signal meets a preset supervision condition.

Preferably, the signal reconstruction unit is specifically configured to take half of the block length of the current sub-signal as the decomposed block length; uniformly partitioning the supporting blocks of the supporting block index set again according to the length of the decomposed block; and establishing a block sparse signal model for the sub-signals obtained by uniformly partitioning again according to the length of the decomposed block.

The invention also discloses a computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor,

the processor, when executing the program, implements the method as described above.

The invention also discloses a computer-readable medium, having stored thereon a computer program,

which when executed by a processor implements the method as described above.

In blind signal receiving based on compressed sensing, aiming at signal reconstruction with block sparse characteristics, the invention provides a blind block orthogonal matching pursuit (BTSM-B) based on a binary tree search and supervision mechanism²OMP) algorithm. The invention is divided into an internal circulation part and an external circulation part. In the outer loop, the received signals are uniformly partitioned and then subjected to signal detection, and then the obtained supporting blocks are partitioned again, so that the block resolution of the signal detection is gradually increased (namely the partition length is gradually reduced), the interval where the signal supporting blocks exist is continuously reduced and refined, and the process is substantially a binary search tree downward search process. In the inner loop, a Block Orthogonal Matching Pursuit (BOMP) algorithm with a supervision condition is utilized to carry out signal support search on an original signal under the fixed block resolution (namely, the same-layer child nodes of the binary search tree), and the method is substantially transverse search of the binary search tree in the same-layer nodes. Experiments prove that the method has considerable accurate reconstruction probability in the same-class block self-adaptive greedy algorithm. Meanwhile, under the condition of blind receiving of the CS receiver, the experimental result shows that the method has stronger robustness advantage on the premise of self-adaptive reconstruction.

Drawings

The following describes embodiments of the present invention in further detail with reference to the accompanying drawings.

FIG. 1 is a flowchart illustrating one embodiment of a compressed sensing signal reconstruction method based on block sparsity and binary tree search according to the present invention;

FIG. 2 is a second flowchart illustrating a compressed sensing signal reconstruction method based on block sparseness and binary tree search according to an embodiment of the present invention;

FIG. 3 is a third flowchart illustrating a compressed sensing signal reconstruction method based on block sparsity and binary tree search according to an embodiment of the present invention;

FIG. 4 is a flow chart of a specific implementation of the compressed sensing signal reconstruction method based on block sparsity and binary tree search according to the present invention;

FIG. 5 is a flowchart illustrating a fourth embodiment of the compressed sensing signal reconstruction method based on block sparsity and binary tree search according to the present invention;

FIG. 6 is a schematic diagram of binary tree search according to an embodiment of the compressed sensing signal reconstruction method based on block sparsity and binary tree search of the present invention;

FIGS. 7(a) and 7(b) are graphs showing the comparison of the adaptive reconstruction capability of the present invention for Gaussian distributed block sparse signals with several existing algorithms;

FIGS. 8(a) and 8(b) are graphs showing adaptive reconstruction capability comparison of the present invention with several existing algorithms for 0-1 distributed block sparse signals;

FIG. 9 is a graph showing the robustness reconstruction capability of the present invention compared to several prior algorithms in AIC based CS receiver blind reception;

FIG. 10 is a block diagram illustrating a compressed sensing signal reconstruction system based on block sparseness and binary tree search according to an embodiment of the present invention;

FIG. 11 illustrates a schematic block diagram of a computer device suitable for use in implementing embodiments of the present invention.

Detailed Description

In order to more clearly illustrate the invention, the invention is further described below with reference to preferred embodiments and the accompanying drawings. Similar parts in the figures are denoted by the same reference numerals. It is to be understood by persons skilled in the art that the following detailed description is illustrative and not restrictive, and is not to be taken as limiting the scope of the invention.

According to one aspect of the invention, the embodiment discloses a compressed sensing signal reconstruction method based on block sparsity and binary tree search. As shown in fig. 1, in this embodiment, the method includes:

s100: and uniformly partitioning the received signals to construct a block sparse signal model.

S200: and carrying out block sparse signal reconstruction on the block sparse signal model to determine a support block with a signal and form a support block index set.

S300: and uniformly partitioning the supporting blocks of the supporting block index set again and constructing a block sparse signal model, reconstructing the reconstructed block sparse signal model to update the supporting block index set, repeatedly updating the supporting block index set until an iteration stop condition is met, and reconstructing signals according to the supporting blocks after iteration is stopped.

In blind signal receiving based on compressed sensing, aiming at signal reconstruction with block sparse characteristics, the invention provides a blind block orthogonal matching pursuit (BTSM-B) based on a binary tree search and supervision mechanism²OMP) algorithm. The invention is divided into an internal circulation part and an external circulation part. In the outer loop, the received signals are uniformly partitioned and then subjected to signal detection, and then the obtained supporting blocks are partitioned again, so that the block resolution of the signal detection is gradually increased (namely the partition length is gradually reduced), the interval where the signal supporting blocks exist is continuously reduced and refined, and the process is substantially a binary search tree downward search process. In the inner loop, a Block Orthogonal Matching Pursuit (BOMP) algorithm with a supervision condition is utilized to carry out signal support search on an original signal under the fixed block resolution (namely, the same-layer child nodes of the binary search tree), and the method is substantially transverse search of the binary search tree in the same-layer nodes. Experiments prove that the method has considerable accurate reconstruction probability in the same-class block self-adaptive greedy algorithm. Meanwhile, under the condition of blind receiving of the CS receiver, the experimental result shows that the invention has the advantages of self-adaptive reconstructionHas stronger robustness advantage.

In a preferred embodiment, as shown in fig. 2, the S100 may specifically include:

s110: and uniformly partitioning the received signals according to the preset block length.

S120: and forming a recovery sub-matrix and a sparse sub-vector corresponding to each sub-signal after uniform blocking to obtain an observation vector.

S130: and establishing a block sparse signal model according to the block sparse constraint of the mixed norm of each block of sub-signals after uniform blocking and the observation vector.

It can be understood that, during receiving, the signal is uniformly partitioned according to the characteristic that the signal has blocking appearance in a sparse domain, and a block sparse signal model is constructed.

In one specific example, Compressed Sensing (CS) is directed to how to recover an original signal x of dimension N × 1 from an observation vector y of dimension M × 1, where M is much smaller than N, and M and N are positive integers. The underlying CS model can be expressed as:

y＝Φx (1-1)

where Φ is an M × N dimensional observation matrix that is not correlated with signal x. Since the number of rows of the observation matrix Φ is much smaller than the number of columns, the process of reconstructing the original signal x from the observation vector y is an obvious underdetermined problem, with infinite solutions. For this reason, the CS theory needs to use the sparsity of the original signal x to constrain the reconstruction to ensure that the reconstruction process has a unique solution. The sparsity of the signal is expressed as follows:

x＝Ψs (1-2)

where s is an N × 1-dimensional sparse vector containing only k non-zero values. Ψ is the sparse transform basis matrix for signal x. This type of signal x, which can be represented by the sparse transform basis matrix Ψ and at most k non-zero valued sparse vectors s, is referred to as the k sparse signal at Ψ. Combining equations (1-1) and (1-2), the observation vector y can be rewritten as:

y＝ΦΨs＝Θs (1-3)

where Θ — Φ Ψ is an M × N-dimensional recovery matrix. Under the sparse constraint, the process of reconstructing the original signal x from the observation vector y can be represented as an optimization problem:

wherein the content of the first and second substances,

represents a reconstruction approximation of s | · | | non-woven phosphor₀Representing the zero norm of the vector, "s.t." is the constraint.

In a communication reconnaissance scenario, there are features that appear in blocks in the sparse domain for multiple narrowband features of the communication signal. Suppose a signal is represented by L in the sparse domain and has a length d_l(L ═ 1, 2.., L) the partitioned block components are represented as:

wherein s is_i,i∈[1,N]Is the ith element in the vector s, s [ i]Representing the ith sub-block.

i | · O in formula (1-6)₂The standard Euclidean norm, ξ, representing the vector is an indicator function as follows:

unlike K-sparse signals based on a random distribution of non-zero values, the non-zero values of the block K-sparse signal are distributed only within the range of K blocks, with the definition of Γ ═ d₁,d₂...,d_LIs the block distribution of the block sparse signal. When d is₁＝...＝d_LWhen d, the signal is referred to as a uniform block sparse signal:

for the uniform block K sparse signal, the actual sparsity has K less than or equal to Kd. The restoration matrix Θ can be expressed in terms of the distribution Γ as:

wherein phi is_i,i∈[1,N]Is the ith column vector in Θ, Θ [ i [ ]](i ═ 1, 2., L) is a submatrix of dimension M × d on Θ. Bringing formulae (1-8) and (1-9) into the CS process, then:

where T is the transpose operation.

Based on the above representation, the blocks are sparsely constrained with s_2,0The block sparse signal model with the K or less is as follows:

in a preferred embodiment, as shown in fig. 3, the S200 may specifically include:

s210: and carrying out block correlation detection on the block sparse signal model by using a block orthogonal matching pursuit algorithm (BOMP) to obtain a supporting block with a detected signal.

S220: adding the support blocks of the detected presence signal to a support block index set to update the support block index set.

S230: and repeating the process of updating the supporting block index set until the search residual of the current block signal meets a preset supervision condition.

It will be appreciated that after solving the problem of dual adaptive block search for unknown block distributions and block sparsity, it is necessary to make the search process reasonableAnd (4) reconstructing an algorithm. As shown in fig. 4, the present embodiment adopts a BOMP algorithm. In each outer loop of the binary tree search and supervision mechanism, there is an inner loop executed by the BOMP algorithm. The BOMP algorithm is responsible for reconstructing the block sparse signal under the resolution of the current block to obtain the occupation condition of the signal sparse block. The method has the advantages of simple implementation steps, excellent reconstruction performance, high reconstruction efficiency and the like. The BOMP algorithm is combined with a binary tree search supervision mechanism to obtain complete BTSM-B²And (4) an OMP algorithm.

Specifically, BTSM-B²The OMP algorithm may be implemented by algorithm 1 in table 1.

TABLE 1

Specifically, the outer loop performs sequentially decreasing block division on the original signal, and gives the search range of the inner loop in the next stage by referring to the search range and the residual result obtained by the inner loop. For the inner loop, in each loop, the BOMP algorithm is used to reconstruct the signal under the current block. When the supervision condition | | | r_k||₂/||r₀||₂When γ is satisfied ≦ γ, the supervision flag Use will assign a value of 1. This time, it means that the BOMP has successfully completed the reconstruction at this stage and found enough signal support blocks, and the support block information can be used for the iteration at the next block resolution. Conversely, if there is an inverse increase in residual after reconstruction, i.e. | | r_k||₂>||r₀||₂Or the total atomic number contained in the signal supporting block exceeds the undersampled number, the reconstruction failure under the resolution of the current block is judged, and the algorithm directly jumps into the next outer loop without using the information obtained by the reconstruction. The addition of a decision on reconstruction failure may reduce useless iterations of the algorithm in the inner loop. Due to mismatchThe block length will affect the reconstruction performance of the BOMP algorithm, so that not all reconstructions at block resolution can reach the supervision condition.

On the premise of the conventional sparsity of the unknown signal, the setting of the stopping condition takes the iteration residual as a main reference. In the algorithm, the residual-based stopping condition is given as | | | r | | non-woven phosphor₂≦ ε, i.e., stopping iteration when the residual energy is less than some threshold. The stop threshold epsilon here can be set to the average energy of the noise in a noisy environment, and can be set to be epsilon 0 in an ideal environment. In addition, the algorithm sets a stop condition h-1. When the block resolution level is reduced to 1, the block resolution is d-2¹2. If the block decomposition is continued, the reconstruction algorithm is degraded into a single-point iterative OMP algorithm, and the block sparse characteristic is not provided any more. From simulation experience, BTSM-B²The OMP algorithm usually achieves residual convergence within 2-6 decompositions.

In a preferred embodiment, as shown in fig. 5, the re-uniformly blocking the support blocks of the support block index set and constructing a block sparse signal model in S300 may specifically include:

s310: half of the block length of the current subsignal is taken as the decomposed block length.

S320: and uniformly partitioning the support blocks of the support block index set again according to the length of the decomposed block.

S330: and establishing a block sparse signal model for the sub-signals obtained by uniformly partitioning again according to the length of the decomposed block.

It can be understood that, in order to solve the problem of self-adaptation of the block size, the present invention gradually excludes the unoccupied sub-blocks in each outer loop according to the current block resolution through the search and supervision mechanism of the binary tree, and the search area is continuously reduced. And the resulting set of block supports at the current block resolution will be used as a priori information for the next block resolution iteration. The block resolution increases with the number of outer loops (i.e. the block length decreases with the number of outer loops), when the block length decreases to a given block length or 1, the reconstruction is performed and the whole binary tree search process does not require blocking or sparsity information of the signal.

In one specific example, as shown in FIG. 6, the binary tree search process may be summarized as:

(1) the signal is divided into 2 blocks with length d^h(h≤log₂(N/2)) are blocked and searched, and only the blocked portion of the detected signal is retained.

(2) The part to be retained is d-2^h-1And partitioning, searching again and continuously keeping the blocks with the detected signals.

(3) And (3) repeating the step (2) until d reaches the preset block resolution.

The basic operation of a binary search tree is proportional to the height of the tree, so if it is a complete binary tree, the worst running time is o (lgn), but if all the data is arranged in a column (i.e., a linear tree), the worst time for the search is o (n). Therefore, the introduction of binary tree search can speed up the search speed of the related block.

The binary tree searching scheme can effectively solve the self-adaption problem of the block sparsity and the block length at the same time. However, since there is a reconstruction error necessarily existing in the block support set searching process, the binary tree searching process also needs to take the factor of the searching error into consideration. In fact, binary tree search has considerable tolerance for reconstruction errors, and even if an erroneous original block is selected under the resolution of a current block, the erroneous block can be actively eliminated in the search process of the next block resolution. However, it should be noted that if there is a miss-selection of the signal support atomic block in the previous block resolution search, this support atomic block will be ignored continuously in the next smaller block resolution search due to the transfer of the prior information in different resolutions. Such an erroneous accumulation will result in the absence of a supporting set of reconstructed signals. In order to ensure that the missing selection phenomenon does not occur in the search of each resolution as much as possible, a supervision mechanism needs to be added to the binary tree search process. When the search of the c-th node satisfies the following inequality:

the searched set of block supports is used for search interval prior information for the next block resolution (i.e., the next node). Wherein, | | r₀||₂And r_c||₂Respectively, the original residual of the signal and the current node (d ═ 2)^c) Search for the standard Euclidean norm of the residual, where | | | r₀||₂＝||y||₂. In addition, gamma belongs to (0,1) and is a supervision threshold of binary tree search, and the threshold can ensure that the residual energy of the residual error is not more than 1/gamma of the original signal energy, so that the selection missing phenomenon of the original signal supporting atomic blocks can be effectively supervised and controlled. And if the residual after the search is finished under a certain resolution does not meet the supervision condition of the formula (2-1), determining that the reconstruction generates the omission of signal support, and directly adopting the search range of the previous node as prior information for the search of the next node by skipping the search of the current node.

The setting of the supervision threshold gamma is flexible relative to the other two parameters. The role of the supervision threshold is to supervise the search of each layer of nodes, making the search of the block support as complete as possible. Gamma is actually the ratio of the original residual (signal energy) to the standard Euclidean norm of the post-reconstruction residual (residual energy after removal of the chosen atomic block support), representing the ratio of the two energies. First, the supervision threshold γ can be directly set to be the same as the stop threshold ε, and at this time, the algorithm will directly satisfy the outer loop to obtain the reconstructed signal after finding the appropriate block length to satisfy the inner loop. Secondly, can be provided with 1>Gamma is more than or equal to epsilon. Since the effect of the inner loop is to find enough support blocks (many and not few) rather than accurately reconstruct the signal, it is not necessary to perform too many iterations to reduce the residual at each level of block resolution. According to simulation experience, the supervision threshold gamma can be set to be 1 to 3 orders of magnitude greater than the stop threshold (gamma is 10-³Epsilon), the number of redundant iterations under the unsuitable block resolution is reduced while the signal reconstruction precision is ensured, so that the reconstruction efficiency is improved, and the reconstruction calculation amount is reduced.

The decomposition level determines the maximum block length in the entire binary tree search process. The value range of decomposition is as follows

Wherein

Meaning rounding down the expression therein. First, to realize the advantage of block sparsity and avoid the degradation of the algorithm into a single-point iterative greedy algorithm, the block length needs to be greater than or equal to 2, i.e., h > 1. On the other hand, a larger block length may provide better reconstruction performance, and thus the signal needs to be successfully reconstructed at the larger block length as much as possible. Based on the above analysis, the present invention generally selects a larger value of h. According to the simulation experience, the general setting range of h is

Intermediate values of, i.e.

Or

The setting of the intermediate value can ensure the reconstruction performance and the reconstruction precision of the algorithm in the maximum range.

Fig. 7(a), 7(b), 8(a) and 8(b) depict simulation experiments of the prior BOMP algorithm, the SAMP algorithm and the BSAMP algorithm under block sparse signals as comparison algorithms in comparison with the adaptive reconstruction capability of the present invention. Wherein BOMP is BTSM-B²The basic algorithm of the OMP algorithm, SAMP algorithm can be regarded as BTSM-AB²Basic algorithm of MP. Furthermore, the BSAMP algorithm is also based on the SAMP algorithm as an improvement and has been shown to have better reconstruction effect than the BCoSaMP. In the simulation experiment, the block length of the block sparse signal is divided into two cases: (1) uniformly partitioning: all block lengths are uniformly set to d-4. (2) Non-uniform blocking: the block length is randomly divided into d 2, d 4 and d 6, and the number of blocks with d 2 is equal to that of blocks with d 6, so as to ensure that the total conventional sparsity of the signal is unchanged. The positions of all non-zero blocks satisfy a random distribution, and the amplitudes of the non-zero blocks are divided into two cases: (1) gaussian random distribution; (2)0-1 are randomly distributed. The block sparsity of the signal increases from 1 to 90 steps with an interval of 2. Signal length is set asN512, the undersampling number is set to M128, and the undersampling rate Q/N is approximately equal to 0.5. The parameter settings of each algorithm are shown in table 2.

TABLE 2

As can be seen from fig. 7(a), 7(b), 8(a) and 8(b), in the 4 block sparse signal scenarios, the block greedy algorithm has stronger reconstruction capability on a high-sparsity signal than the single-point matching reconstruction algorithm SAMP. In the existing single-point matching greedy algorithm, the SAMP algorithm has the most competitive reconstruction performance and self-adaptive capability. Thus, the result strongly verifies the block greedy algorithm's superiority in processing block sparse signals. In addition to this, an interesting phenomenon is reflected in the figure: BTSM-B²OMP Algorithm and BTSM-AB²The reconstruction performance of the MP algorithm under the uniform partitioning is respectively matched with the curves of the BOMP algorithm and the BSAMP algorithm and is slightly higher, however, in the non-uniform partitioning, the two proposed algorithms respectively show more obvious reconstruction advantages for large-sparsity signals on the basis of the curve trends of the respective basic algorithms. It should be noted that the simulation sets the correct block length and block sparsity for the BOMP algorithm and the BSAMP algorithm, so that both have the best reconstruction performance at this time. When the sizes of the blocks are not equal any more, the precision of the BOMP algorithm and the BSAMP algorithm is reduced inevitably due to the mismatch of the blocks, and the advantage of the self-adaptive processing capacity of the invention on the blocks is obviously reflected.

Fig. 9(a) -9 (d) show the adaptivity and robustness of the above algorithms in comparison to the present invention in Analog Information Converter (AIC) based CS receiver blind reception. The original signal adopts a multi-narrow-band signal model added with white Gaussian noise. For analog reception of unknown signals (unknown block distribution, unknown block sparsity), its carrier f_iSub bandwidth B_iAnd coefficient of energy E_iWill be randomly generated within a controllable range. We set the number of subbands to be L-4 and the time offset τ_i＝[7,3]. Coefficient of energy E_iAnd sub-band bandwidth B_iRespectively in the range (0, 10)]And (0, 2)]Randomly generated within MHz. Equivalent sampling rate of signal is f_s100MHz, signal length N2048^[112]. Carrier frequency f of each component_iIn (max (B)_i),(f_s/2)-max(B_i)]Randomly generated within the range. In addition, additive white gaussian noise is added to the received signal and controlled by the SNR. In the experiment, 4 different SNR scenarios were set, respectively: (1) ideal reception environment (no noise); (2) SNR is 30 dB; (3) SNR-20 dB; (4) SNR is 10 dB. The initialization parameters for all algorithms are shown in table 3.

TABLE 3

Under an ideal scenario without noise, as shown in fig. 9(a), two proposed blind reconstruction algorithm reconstructions based on binary tree search and supervision have the highest accurate reconstruction probability under the same under-sampling number. For the BOMP algorithm, due to the unmatched segmentation of the recovery matrix, the reconstruction probability curve obviously fluctuates along with the increase of the undersampled number. Similarly, similar curve fluctuations in exact reconstruction probability can also be observed with BSAMP algorithms with fixed block length settings. In addition, the BOMP algorithm and the BSAMP algorithm at this time are given correct block lengths, and if the block length is set incorrectly, the reconstruction probability curve will further decrease. The present invention effectively solves the above performance fluctuation problem in the sense of full self-adaptability of block distribution and block sparsity. On the other hand, in a noisy environment, the advantages of the invention remain evident. The results of FIG. 9 demonstrate BTSM-B²The reliability of the OMP algorithm in the context of handling complex blocks.

According to simulation experiments, the method utilizes the characteristic that the communication signals meet the block sparse signal model, fully exerts the advantages of the structural information in CS reconstruction, can greatly improve the undersampling efficiency, the reconstruction precision and the reconstruction speed of the signals compared with the existing non-block greedy reconstruction algorithm, and saves hardware and computing resources. Moreover, the search and supervision mechanism based on the binary tree is flexibleBy using the search method of the binary search tree for reference, the search speed of the related block is accelerated, and the search range can be adaptively and gradually reduced under the conditions of no signal blocking and sparsity. The method provides more excellent self-adaptive reconstruction performance for reconstruction on the basis of solving the problem of initialization sensitivity of the two parameters. The BOMP algorithm adopted by the inner loop has the advantages of simple implementation steps, excellent reconstruction performance, high reconstruction efficiency and the like, can be well matched with supervision measures, and solves the problem of BTSM-B²Error accumulation in the OMP algorithm.

In summary, in order to solve the problem that the block adaptive reconstruction algorithm in the CS blind receiving technology is sensitive to the initialization of block distribution, block sparsity and block length, the present invention adopts a binary tree search and supervision mechanism based on a binary search tree. The mechanism can search at different block resolutions from top to bottom and avoid error accumulation by proper supervision. Based on the mechanism, the invention provides a block greedy algorithm capable of carrying out double-adaptive reconstruction on the sparsity and the length of an unknown block at the same time, namely a blind block orthogonal matching pursuit (BTSM-B) based on a binary tree search and supervision mechanism²OMP) algorithm. The method can make full use of the advantages of the block sparse model, adaptively receive multi-narrowband communication signals with unknown block distribution, unknown block length and unknown block sparsity, is more suitable for the situation of non-uniform block sparse in practical situations, and provides higher reconstruction accuracy than the similar adaptive block greedy algorithm.

Based on the same principle, the embodiment also discloses a compressed sensing signal reconstruction system based on block sparsity and binary tree search. As shown in fig. 10, in the present embodiment, the system includes a model construction unit 11, a support block screening unit 12, and a signal reconstruction unit 13.

The model building unit 11 is configured to uniformly block the received signal to build a block sparse signal model.

The supporting block screening unit 12 is configured to perform block sparse signal reconstruction on the block sparse signal model to determine a supporting block with a signal and form a supporting block index set.

The signal reconstruction unit 13 is configured to re-uniformly partition the supporting blocks of the supporting block index set and construct a block sparse signal model, perform block sparse signal reconstruction on the reconstructed block sparse signal model to update the supporting block index set, repeatedly update the supporting block index set until an iteration stop condition is met, and perform signal reconstruction according to the supporting blocks after iteration is stopped.

In a preferred embodiment, the model building unit 11 is specifically configured to uniformly block the received signal according to a preset block length; forming a recovery sub-matrix and a sparse sub-vector corresponding to each sub-signal after uniform blocking to obtain an observation vector; and establishing a block sparse signal model according to the block sparse constraint of the mixed norm of each block of sub-signals after uniform blocking and the observation vector.

In a preferred embodiment, the supporting block screening unit 12 is specifically configured to perform block correlation detection on a block sparse signal model through a block orthogonal matching pursuit algorithm to obtain a supporting block with a detected signal; adding a support block of the detected presence signal to a support block index set to update the support block index set; and repeating the process of updating the supporting block index set until the search residual of the current block signal meets a preset supervision condition.

In a preferred embodiment, the signal reconstruction unit 13 is specifically configured to take half of the block length of the current sub-signal as the decomposed block length; uniformly partitioning the supporting blocks of the supporting block index set again according to the length of the decomposed block; and establishing a block sparse signal model for the sub-signals obtained by uniformly partitioning again according to the length of the decomposed block.

Since the principle of the system for solving the problem is similar to the above method, the implementation of the system can refer to the implementation of the method, and the detailed description is omitted here.

The systems, devices, modules or units illustrated in the above embodiments may be implemented by a computer chip or an entity, or by a product with certain functions. A typical implementation device is a computer device, which may be, for example, a personal computer, a laptop computer, a cellular telephone, a camera phone, a smart phone, a personal digital assistant, a media player, a navigation device, an email device, a game console, a tablet computer, a wearable device, or a combination of any of these devices.

In a typical example the computer arrangement comprises in particular a memory, a processor and a computer program stored on the memory and executable on the processor, the processor performing the method.

Referring now to FIG. 11, shown is a schematic diagram of a computer device 600 suitable for use in implementing embodiments of the present application.

As shown in fig. 11, the computer apparatus 600 includes a Central Processing Unit (CPU)601 which can perform various appropriate works and processes according to a program stored in a Read Only Memory (ROM)602 or a program loaded from a storage section 608 into a Random Access Memory (RAM)) 603. In the RAM603, various programs and data necessary for the operation of the system 600 are also stored. The CPU601, ROM602, and RAM603 are connected to each other via a bus 604. An input/output (I/O) interface 605 is also connected to bus 604.

The following components are connected to the I/O interface 605: an input portion 606 including a keyboard, a mouse, and the like; an output section 607 including a Cathode Ray Tube (CRT), a liquid crystal feedback (LCD), and the like, and a speaker and the like; a storage section 608 including a hard disk and the like; and a communication section 609 including a network interface card such as a LAN card, a modem, or the like. The communication section 609 performs communication processing via a network such as the internet. The driver 610 is also connected to the I/O interface 605 as needed. A removable medium 611 such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, or the like is mounted on the drive 610 as necessary, so that a computer program read out therefrom is mounted as necessary on the storage section 608.

In particular, according to an embodiment of the present invention, the processes described above with reference to the flowcharts may be implemented as computer software programs. For example, embodiments of the invention include a computer program product comprising a computer program tangibly embodied on a machine-readable medium, the computer program comprising program code for performing the method illustrated in the flow chart. In such an embodiment, the computer program may be downloaded and installed from a network through the communication section 609, and/or installed from the removable medium 611.

Computer-readable media, including both non-transitory and non-transitory, removable and non-removable media, may implement information storage by any method or technology. The information may be computer readable instructions, data structures, modules of a program, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), other types of Random Access Memory (RAM), Read Only Memory (ROM), Electrically Erasable Programmable Read Only Memory (EEPROM), flash memory or other memory technology, compact disc read only memory (CD-ROM), Digital Versatile Discs (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information that can be accessed by a computing device. As defined herein, a computer readable medium does not include a transitory computer readable medium such as a modulated data signal and a carrier wave.

For convenience of description, the above devices are described as being divided into various units by function, and are described separately. Of course, the functionality of the units may be implemented in one or more software and/or hardware when implementing the present application.

The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.

As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.

The application may be described in the general context of computer-executable instructions, such as program modules, being executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types. The application may also be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules may be located in both local and remote computer storage media including memory storage devices.

The embodiments in the present specification are described in a progressive manner, and the same and similar parts among the embodiments are referred to each other, and each embodiment focuses on the differences from the other embodiments. In particular, for the system embodiment, since it is substantially similar to the method embodiment, the description is simple, and for the relevant points, reference may be made to the partial description of the method embodiment.

The above description is only an example of the present application and is not intended to limit the present application. Various modifications and changes may occur to those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the scope of the claims of the present application.

Claims

1. A compressed sensing signal reconstruction method based on block sparsity and binary tree search is characterized by comprising the following steps:

2. The method according to claim 1, wherein the uniformly blocking the received signal and constructing the block sparse signal model specifically comprises:

uniformly partitioning the received signals according to a preset block length;

3. The method according to claim 1, wherein the block sparse signal reconstruction of the block sparse signal model to determine the support blocks where signals exist and form a support block index set specifically comprises:

4. The method according to claim 1, wherein the re-uniformly blocking the support blocks of the support block index set and constructing the block sparse signal model specifically comprises:

5. A compressed sensing signal reconstruction system based on block sparsity and binary tree search is characterized by comprising the following components:

6. The system according to claim 5, wherein the model construction unit is specifically configured to uniformly block the received signal according to a preset block length; forming a recovery sub-matrix and a sparse sub-vector corresponding to each sub-signal after uniform blocking to obtain an observation vector; and establishing a block sparse signal model according to the block sparse constraint of the mixed norm of each block of sub-signals after uniform blocking and the observation vector.

7. The system according to claim 5, wherein the support block filtering unit is specifically configured to perform block correlation detection on the block sparse signal model by using a block orthogonal matching pursuit algorithm to obtain a support block with a detected signal; adding a support block of the detected presence signal to a support block index set to update the support block index set; and repeating the process of updating the supporting block index set until the search residual of the current block signal meets a preset supervision condition.

8. The system according to claim 5, wherein the signal reconstruction unit is configured to take half the block length of the current sub-signal as the decomposed block length; uniformly partitioning the supporting blocks of the supporting block index set again according to the length of the decomposed block; and establishing a block sparse signal model for the sub-signals obtained by uniformly partitioning again according to the length of the decomposed block.

9. A computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor,

the processor, when executing the program, implements the method of any of claims 1-4.

10. A computer-readable medium, having stored thereon a computer program,

the program when executed by a processor implements the method of any one of claims 1 to 4.