A parallel solution, fusion and reconstruction method for compressed sensing system

Abstract

A method for parallel solution fusion reconstruction of a compressed sensing system relates to the technical field of target signal reconstruction by a compressed sensing observation system, and solves the problem of how to achieve accurate, stable and high-precision target signal reconstruction by observing blind source signals with a compressed sensing system. The present invention is achieved by constructing a generalized dictionary set; analyzing the system response matrix and each dictionary in the dictionary set to implement a single screening of the dictionary; combining the system response matrix with the screened dictionary to carry out parallel sparse solution and signal reconstruction to obtain multiple reconstruction solutions; performing gross error elimination on the reconstructed signal corresponding to each dictionary in data segments to achieve a secondary screening; and performing maximum likelihood adaptive weighted fusion on multiple reconstruction results to obtain a final stable and high-precision reconstructed signal. While ensuring the reconstruction accuracy, the present invention makes the accuracy of the solution more stable, thereby achieving high-precision and stable reconstruction of the blind source target signal.

Description

Technical Field

[0001] The present invention relates to the technical field of target signal reconstruction by a compressed sensing observation system, and in particular to a parallel solution fusion reconstruction method for a compressed sensing system. In the absence of prior knowledge, a universal sparse transform system is used as a dictionary for blind source signals to achieve stable and high-precision reconstruction of the target signal. Background Art

[0002] Compressed sensing observation systems are designed to observe target signals in situations where the observation system is limited by practical factors such as time, space, and system integration, making it impossible to complete observation sampling at the Shannon-Nyquist rate. The output signal is not a direct sampling signal of the target signal. There is a linear or approximate linear relationship between the output signal and the target signal. In other words, the output signal is a dimensionality-reduced projection of the target signal after it passes through the observation system. Therefore, the reconstruction of the target signal from the output signal is an underdetermined linear system. Traditional linear algebra techniques believe that the solution obtained by solving underdetermined linear systems is non-unique, meaning that an exact solution cannot be obtained. Compressed sensing reconstruction is an effective means of finding an exact or approximate solution for this system.

[0003] Compressed sensing reconstruction demonstrates that when the target signal exhibits sparse characteristics, introducing a 1-norm constraint (sparse constraint) into the solution of the current observation system allows for direct, accurate or approximate computation of the target signal. If the target signal is not sparse, it is necessary to combine the underdetermined reconstruction system with a sparse transformation system (also known as a dictionary, hereinafter referred to as the dictionary) to add sparse constraints to the underdetermined solution system. The process of solving for sparse vectors involves selecting dictionary column vectors and calculating the corresponding coefficients. After solving for the sparse vectors, the dictionary is combined with the vector to reconstruct the target signal.

[0004] Currently, there are three common approaches to dictionary construction. The first is to select a complete orthogonal system as the dictionary, such as when the signal is sparse after discrete Fourier transform, discrete cosine transform, or wavelet transform. The second is dictionary learning based on a priori knowledge. By analyzing and learning a set of sparse transformation systems from traditional spectral remote sensing databases, a sparse transformation system can be constructed to guarantee sparse transformations for any object. The third is to build a richer transformation system by combining dictionaries based on the first two, meeting the reconstruction requirements of dictionary column vector selection from detailed to global perspectives. It is worth noting that the number of sparse transformation vectors selected is limited by the number of observations. To ensure the solution is non-singular during the sparse solution, the number of observations is generally required to be twice the sparsity k. Using a single complete orthogonal system as a dictionary has the problem of non-universality, namely, whether the target spectrum is sparse in the data domain. Dictionary learning can ensure that all target spectra in the database are sufficiently sparse under the transformation. However, considering the incompleteness of the database and the complexity of actual objects, dictionary incompleteness is inevitable, which leads to reduced accuracy in target spectrum reconstruction. However, the problem with the serial fusion of dictionaries is that they are too rich and there may be strong column vector correlation, which interferes with the selection of column vectors in the reconstruction process, resulting in sparse vector solution errors and reconstructed signal distortion. Summary of the Invention

[0005] The present invention provides a multi-dictionary set parallel solution and fusion reconstruction method to solve the problem of how to achieve accurate, stable and high-precision target signal reconstruction when observing blind source signals with a compressed sensing system.

[0006] A method for parallel solution, fusion and reconstruction of a compressed sensing system is implemented by the following steps:

[0007] Step 1: Construct a dictionary set, perform non-correlation and RIP restriction analysis on the compressed sensing observation system and each dictionary in the dictionary set, and implement a one-time screening of the dictionary;

[0008] Step 2: construct compressed sensing matrices for the dictionaries filtered in step 1, solve the sparse vectors corresponding to each dictionary, calculate the reconstructed signal, and construct a set of multiple target reconstructed signals;

[0009] Step 3: Perform gross error judgment on the multiple target reconstructed signals in step 2 based on the data points, and remove the reconstructed signals containing a data point with a gross error to achieve secondary screening;

[0010] Step 4: Calculate the unbiased estimated mean and variance of the multiple target reconstructed signals obtained by the secondary screening described in step 3 according to the data points, perform weighted mean calculation using maximum likelihood, and achieve segmented adaptive fusion of the multiple target reconstructed signals to obtain the final reconstructed signal.

[0011] The beneficial effects of the present invention are as follows: The method of the present invention, based on the parallel solution and fusion reconstruction of multiple dictionaries, uses an observation system to select some dictionaries from a generalized dictionary set, simultaneously reconstructs the selected dictionaries, performs statistical analysis on the reconstruction results, and uses confidence theory to achieve adaptive fusion of the reconstruction results, thereby improving the stability of the system's sparse reconstruction of multiple targets while ensuring accuracy. The method focuses on the impact of dictionaries as variables on the reconstruction results, and uses multi-dictionary reconstruction blind source statistical analysis to weaken the non-universal target signal reconstruction problem of a single dictionary. Adaptive fusion is used to achieve effective reconstruction accuracy assurance, while enriching compressed sensing reconstruction methods and further promoting the effective application of compressed sensing theory in practical systems.

[0012] The present invention overcomes the problem that the selection and solution of sparse variables are limited due to the number of observations of the compressed sensing system, and the non-universal problem that the compressed sensing system uses a single orthogonal system to reconstruct blind source target signals.

[0013] Without prior knowledge, this method uses a compressed sensing system to observe blind source signals, combines multiple general sparse transformation systems, and constructs a parallel reconstruction fusion solution architecture as the solution module of the compressed sensing system. This weakens the problems of insufficient sparsity and limited reconstruction accuracy caused by the single orthogonal system as the dictionary, while ensuring the reconstruction accuracy, making the solution accuracy more stable, and achieving high-precision and stable reconstruction of blind source target signals. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 This is a principle block diagram of a parallel solution, fusion and reconstruction method for a compressed sensing system according to the present invention;

[0015] Figure 2 Construct a flow chart of the principles for dictionary concatenation. DETAILED DESCRIPTION

[0016] Specific implementation method 1. Combination Figure 1 This embodiment describes a method for parallel solution, fusion and reconstruction of a compressed sensing system, which is implemented by the following steps:

[0017] A dictionary set based on independent complete orthogonal systems or a series of complete orthogonal systems is constructed. The non-correlation and restricted isometry property (RIP) analysis is performed on the compressed sensing observation system and each dictionary in the dictionary set to achieve a one-time screening of the dictionary to ensure that the dictionary can be used for sparse reconstruction.

[0018] The observation matrix is ​​combined with the dictionary after a screening to form a compressed sensing matrix. Sparse solutions are performed on multiple compressed sensing systems simultaneously. The multiple sparse solutions are combined with their corresponding dictionaries respectively to obtain reconstructed solutions of multiple target signals.

[0019] Judgment of gross error is performed on multiple target reconstruction signals based on data points, and the reconstruction signals containing a certain data point as gross error are eliminated to achieve secondary screening.

[0020] For multiple target reconstruction signals obtained through secondary screening, the unbiased estimated mean and variance are calculated separately for each data point, and the weighted mean is calculated with maximum likelihood to achieve the adaptive fusion of multiple target reconstruction signals in segmented data, and the final reconstruction signal is obtained.

[0021] Specific Embodiment 2. In combination with Figure 1 and Figure 2 This embodiment is described. This embodiment is an example of a parallel solution fusion reconstruction method for a compressive sensing system described in Specific Embodiment 1:

[0022] First, the observation of the target signal by the compressive sensing system can be expressed as

[0023] Ωφ = g (1)

[0024] where is the system response matrix obtained after calibration by the compressive sensing system, that is, the observation matrix, M is the number of observations of the compressive sensing system, N is the length of the discrete signal data, is the discretization result of the target signal, is the observation value output by the target signal after passing through the compressive sensing system. The solution by sparse representation can be expressed as

[0025] ΩDx = g subject to: Dx = φ (2)

[0026] where is the dictionary used to achieve sparse transformation, is the k-sparse vector (k<<L). After calculating x, the target signal φ can be calculated according to the selected dictionary D. Given that the target signal is unknown, a general transformation system with possible sparse transformation mapping for the target signal, such as the discrete cosine transform (DCT), discrete wavelet transform system (DWT), etc., is selected as the dictionary; and considering that there may be a problem that the number of observations does not match the corresponding sparsity of the dictionary for the target signal in a certain general transformation system (k≥M), multiple transformation systems are used in parallel to carry out the compressive sensing reconstruction of the target signal, and the reconstruction results are screened and fused.

[0027] Secondly, a generalized dictionary set is constructed. The dictionary set consists of two categories: one is an independent universal transformation system, and the other is a combination of multiple independent transformation systems. The column vectors of the first type of dictionary are normalized, and the column vectors are orthogonal, that is, they are independent of each other. Therefore, there is no problem of solving the matrix singularity during the column vector selection and solution process. The second type of dictionary is a selection and concatenation of the first type of dictionary. The concatenation process will cause the dictionary to lose its original orthogonality. Therefore, during the dictionary column vector selection and sparse vector calculation process, there may be problems with solving singularity, which will reduce the accuracy of the reconstructed signal. Therefore, after the dictionary is combined, the column vector correlation is judged and the correlation threshold th is set, with a value range of 0.5 to 0.8. The column vectors with correlation greater than or equal to the correlation threshold th are marked and recorded in the matrix p. If p has a mark, it proves that the current column vector has a strong correlation, and there is a risk of singularity in the solution of sparse vectors. Therefore, each column vector is marked and counted, and the column vector with the most marks is removed. The process is repeated until there are no column vectors with correlation greater than th in the current series dictionary. While ensuring the diversity of the series dictionary, the non-singularity and accuracy of the solution are guaranteed. Figure 2 As shown, the specific process is:

[0028] Step A: Set a dictionary combination as: DS = [D a ...D b ];

[0029] Step B: The calculation formula for column vector correlation η is: η=DS T DS-1;

[0030] Step C: Column vector correlation analysis: mark the column vectors whose correlation is greater than or equal to the correlation threshold th and record them in the matrix p: p = η ≥ th;

[0031] Step D: Determine whether the matrix P is empty. If so, concatenate the dictionary outputs and end. Otherwise, proceed to step E.

[0032] Step E: Perform column vector position mark statistics, maxp = max(col_sum(p)), and then selectively remove dictionary column vectors; that is, remove the column vector with the most marks, delete(DS(maxp)); return to step C.

[0033] Next, the feasibility analysis of the reconstruction of the system response matrix Ω and the dictionary D of the current compressed sensing system is carried out, including but not limited to non-correlation analysis. The non-correlation analysis method realizes the disproof of non-correlation by means of correlation calculation. The correlation calculation method of the two matrices is:

[0034]

[0035] where Ω m is the row vector of the observation matrix, D l is a column vector of the dictionary, if This proves that the system response is independent of the dictionary and that the solution for sparse vectors can be achieved.

[0036] The filtered dictionaries are then used to construct compressed sensing matrices, and the sparse vectors corresponding to each dictionary are solved. The reconstructed signals are then calculated and a set of reconstructed signals is constructed. Sparse solution methods include, but are not limited to, matching pursuit and convex optimization.

[0037] Then, the reconstructed signals corresponding to each dictionary are screened twice. When the reconstructed signals are accurate and stable, the reconstructed signals corresponding to multiple dictionaries will be similar. Therefore, the mean and variance are calculated for each data point, and the gross error is judged using the 3σ criterion. The reconstructed signal results containing gross errors are eliminated to achieve secondary screening of the reconstructed signals. This process is then repeated multiple times until all reconstructed signals meet the 3σ criterion. The screened reconstructed signal set is written in the form of a matrix:

[0038]

[0039] Where, It is the reconstructed estimated value of the nth data point of the sel_n1th dictionary obtained after screening.

[0040] Each type of dictionary causes different degrees of loss in the global and detailed aspects of the reconstructed signal, so a weighted method is used to perform weighted fusion on all reconstruction results.

[0041] Finally, based on the maximum likelihood, an unbiased estimate is made for the reconstructed signal after screening, and the weighted mean is calculated for each data point. That is, different data points of the same reconstructed signal have different weights. The weighting formula is:

[0042]

[0043] in and are the unbiased mean and variance estimates, is the row vector formed by the n-th signal data under multiple dictionary reconstructions. The n-th reconstruction result can be expressed as:

[0044]

[0045] Where w n,q is the weighted value of the nth signal data in the qth column; through adaptive parameter weighting, multiple reconstructed signals are adaptively fused according to the sub-data points, which realizes the correction of the reconstructed signal in the details while ensuring the stability of the reconstruction.

[0046] The technical features of the above-mentioned embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above-mentioned embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0047] The above-described embodiments merely illustrate several implementations of the present invention, and while their descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the spirit of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the patent for this invention shall be determined by the appended claims.

Claims

1. A method for parallel solution, fusion and reconstruction of a compressed sensing system, characterized by: The method is implemented by the following steps: Step 1: Construct a dictionary set, perform non-correlation and RIP restriction analysis on the compressed sensing observation system and each dictionary in the dictionary set, and implement a one-time screening of the dictionary; Step 2: construct compressed sensing matrices for the dictionaries filtered in step 1, solve the sparse vectors corresponding to each dictionary, calculate the reconstructed signal, and construct a set of multiple target reconstructed signals; Step 3: Perform gross error judgment on the multiple target reconstructed signals in step 2 based on the data points, and remove the reconstructed signals containing a data point with a gross error to achieve secondary screening; Step 4: Calculate the unbiased estimated mean and variance of the multiple target reconstructed signals obtained by the secondary screening described in step 3 according to the data points, perform weighted mean calculation using maximum likelihood, and achieve segmented adaptive fusion of the multiple target reconstructed signals to obtain the final reconstructed signal.

2. The method for parallel solution, fusion and reconstruction of a compressed sensing system according to claim 1, characterized in that: In step 1, an independent complete orthogonal system or a series of complete orthogonal systems is constructed as a dictionary set.

3. The method for parallel solution, fusion and reconstruction of a compressed sensing system according to claim 2, characterized in that: The complete orthogonal system series set includes: performing column vector analysis on multiple independent complete orthogonal systems; the specific process is: Conduct column vector correlation judgment, mark the column vectors whose correlation is greater than the correlation threshold th, and record them in the matrix p. If p has a mark, it proves that the current column vector has a strong correlation, and there is a risk of singularity in the sparse vector solution; perform mark statistics on each column vector, eliminate the column vector with the most marks, and repeat the process until there are no column vectors with a correlation greater than the correlation threshold th in the current series dictionary.

4. The method for parallel solution, fusion and reconstruction of a compressed sensing system according to claim 1, characterized in that: In step 2, the feasibility of reconstructing the system response matrix Ω and the dictionary D of the current compressed sensing system is analyzed. The correlation calculation method of the two matrices is: where Ω m is the row vector of the observation matrix, D l is a column vector of the dictionary, if This proves that the system response is independent of the dictionary and that the solution for sparse vectors can be achieved.

5. The method for parallel solution, fusion and reconstruction of a compressed sensing system according to claim 1, characterized in that: In step three, the 3σ criterion is used to judge the gross errors of multiple target reconstructed signals.

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