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Compressed Sensing Signal Reconstruction Method Based on Approximately Smooth l0 Norm

A signal reconstruction and compressed sensing technology, which is applied in the field of communication and wireless communication signal processing, can solve the problems of high complexity of reconstruction methods and low precision of reconstruction signal methods, and achieve low complexity, high precision, and realization of signal reconstruction. structure effect

Active Publication Date: 2018-11-16
XIDIAN UNIV
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Problems solved by technology

This method can realize signal reconstruction at a very fast speed in a noisy environment. However, the disadvantage of this method is that when the modified Newton method is used to solve the optimization problem, only an approximate estimated solution can be obtained, and the accuracy of the reconstructed signal method is too low
However, the disadvantage of this method is that only one atom in an overcomplete atomic set can be selected for each iteration, so multiple iterations are required to complete the reconstruction of the signal when processing massive data, and the complexity of the reconstruction method is high.

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  • Compressed Sensing Signal Reconstruction Method Based on Approximately Smooth l0 Norm

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[0044] The present invention will be further described below in conjunction with the accompanying drawings.

[0045] Refer to attached figure 1 , the concrete steps of the present invention are as follows.

[0046] Step 1, initialization.

[0047] Initialize the iteration number i of signal reconstruction to 1, and initialize the iteration number j of the modified Newton direction to 1;

[0048] Step 2, calculate the projection value of the reconstructed signal vector according to the following formula.

[0049] η=(Φ T Φ) -1 Φ T the y

[0050] Among them, η represents the projection value of the reconstructed signal vector, Φ represents the observation matrix required for M×N-dimensional compressed sensing processing, T represents the transpose operation, and y represents the M×1-dimensional observation signal obtained after compressive sensing processing Vector, M represents the number of rows of the observation matrix required for compressed sensing processing, N repres...

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Abstract

The invention discloses an approximate smoothed L0 norm-base compressed sensing signal reconstruction method. According to the method, the least square method is adopted to optimize reconstruction signal vectors obtained by using modified Newton method, so that the accurate values of the reconstruction signal vectors can be obtained, and therefore, accurate reconstruction of signals can be obtained. With the method of the invention adopted, the problem of low accuracy of a modified Newton method-based reconstruction method and the problem of high complexity of an orthogonal matching pursuit-based reconstruction method in massive data processing in the prior art can be solved. The method of the invention has the advantages of high reconstruction accuracy and low complexity in massive data processing.

Description

technical field [0001] The present invention belongs to the technical field of communication, and further relates to a compressed sensing signal reconstruction method based on approximately smooth L0 norm in the technical field of wireless communication signal processing. Under the condition of known observation signal and observation matrix, the present invention uses the least square method to optimize the reconstructed signal vector obtained by the modified Newton method, obtains the accurate value of the reconstructed signal vector, and realizes communication in the Gaussian white noise environment Accurate reconstruction of signals. Background technique [0002] Compressed Sensing (CS) can sample communication signals at a rate much lower than the Nyquist sampling rate, and at the same time, it can adopt low complexity, fast convergence and high reconstruction accuracy without loss of information. Therefore, it is of great significance to study the signal reconstructio...

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): H03M7/30
CPCH03M7/3062
Inventor 付卫红田德艳李聪韦娟黑永强刘乃安李晓辉
Owner XIDIAN UNIV
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