Signal reestablishment method based on block compressed sensing

Abstract

The invention discloses a signal reestablishment method based on block compressed sensing and belongs to the field of signal processing. The method comprises the steps of uniformly dividing an original signal into L sub-signals; calculating a sparse signal x'[i], namely an expansion coefficient, of each sub-signal in a perfect base psi; filtering the L sparse signals, thereby obtaining reestablished signals; establishing a measuring matrix phi, and carrying out block compressed sensing processing on each reestablished signal, thereby obtaining an observation vector y[i] corresponding to each sub-signal; calculating a reestablished sub-signal of each signal x[i] by employing the expansion coefficient, the observation vector y [i] and the measuring matrix; and carrying out linear combination on the reestablished sub-signals, thereby obtaining the reestablished signal. According to the method, through full utilization of the characteristics of a characteristic base, the signal reestablishment method based on block compressed sensing is provided; the signal recovery performance is improved; a complicated matrix inversion process is avoided; and when the length of the signal is relatively long and the number of orders of the matrix is very high, the signal recovery operation complexity can be effectively reduced.

Description

technical field [0001] The invention belongs to the field of signal processing, and in particular relates to a signal reconstruction method based on block compressed sensing. Background technique [0002] The traditional sampling theory requires that the sampling rate of the signal is twice the highest frequency of the signal, that is, the sampling process must satisfy the Nyquist sampling theorem in order to accurately restore the original signal; in recent years, some people have proposed the theory of compressed sensing, which is aimed at sparse signals. Or a sparse signal in a transform domain, using linear transformation to project the signal into a low-dimensional space, and then recovering the original signal with high probability through nonlinear decoding; compressed sensing theory makes full use of the sparse characteristics of the signal to reduce the sampling rate; in practical applications , the compressed acquisition of the signal must be quantized, and the lim...

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Problems solved by technology

[0002] The traditional sampling theory requires that the sampling rate of the signal is twice the highest frequency of the signal, that is, the sampling process must satisfy the Nyquist sampling theorem in order to accurately restore the original signal; in recent years, some people have proposed the theory of compressed sensing, which is aimed at sparse signals. Or a sparse signal in a transform domain, using linear transformation to project the signal into a low-dimensional space, and then recovering the original signal with high probability through nonlinear decoding; compressed sensing theory makes full use of the sparse characteristics of the signal to reduce the sampling rate; in practical applications , the compressed acquisition of the signal must be quantized, and the limited quantization accuracy will introduce quantization errors; 1-Bit compressed sensing is to perform limit quantization on the compressed observations, and by retaining the symbol information of the observations, it relieves hardware pressure and improves storage efficiency. ; At present, the signal reconstruction methods of 1-Bit compressed sensing mainly include iterative signal reconstruction methods, greedy signal reconstruction methods and trust region signal reconstruction methods, etc.; among them, the binary iterative hard threshold signal reconstruction method in the iterative signal reconstruction method The reconstruction principle of the Binary Iterative HardThresholding (BIHT) method is simple, easy to understand, low in computational complexity and good in reconstruction effect; although the BIHT signal reconstruction method has excellent reconstruction effect, but the signal reconstruction method requires the signal The sparsity is known, which is difficult to achieve in actual measurement; in addition, the existing signal reconstruction methods have low recovery performance and high computational complexity

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