Compressed sensing signal reconstruction method

Abstract

The invention discloses a compressed sensing signal reconstruction method, which belongs to the technical field of signal processing. The compressed sensing signal reconstruction method aims to solve a regularization problem that is more difficult to solve; the regularization problem in a sparse domain of compressed sensing signals is converted to a constraint-regularization problem through a variable division technology, and the constraint-regularization problem is equivalent to the regularization problem and can better present the sparse characteristics of the signals compared with the regularization problem; and higher accuracy for reconstructing the signals can be achieved. The compressed sensing signal reconstruction method utilizes a rapid alternating direction multiplier method further so as to solve the constraint-regularization problem, updates variables in an algorithm of the alternating direction multiplier method for a second time, updates multipliers, and increases the convergence rate of optimization solution. Compared with the prior art, the compressed sensing signal reconstruction method has the advantages of higher reconstruction accuracy and higher convergence rate.

Description

technical field [0001] The invention relates to a compressed sensing (Compressed Sensing, CS for short) signal reconstruction method, which belongs to the technical field of signal processing. Background technique [0002] The theory of Compressed Sensing (CS) for signals with sparse characteristics was proposed by Donoho et al. in 2004. Under the condition of ensuring that the signal is not lost, it collects the signal at a rate far lower than that required by the Nyquist sampling theorem, and at the same time does not lose information, and can completely restore the signal. It is a revolutionary achievement in the field of signal processing. Under the framework of CS theory, the sampling rate no longer depends on the bandwidth of the signal, but on the structure and content of the information in the signal. [0003] The core problem in CS theory is the reconstruction of compressed signals. How to design a reconstruction algorithm with low complexity, fast convergence spee...

AI Technical Summary

Problems solved by technology

Different optimization objective functions are applied, resulting in different signal reconstruction effects

The original model of reconstructing the noisy signal in CS is l 0 -Regularization problem, but this problem is a non-convex problem, and it is very difficult to solve. Although the Iterative Hard Thresholding (IHT) algorithm can solve this problem by iterative method, the IHT algorithm solves the local minimum of the problem value, the reconstruction accuracy is low and the algorithm convergence speed is slow

For example, use ADMM to solve l 1 -Regularization problem, proposed SALSA (Split augmented Lagrangian Shrinkage Algorithm) and C-SALSA (Constrained-SALSA) algorithms, and applied them to image deblurring, deconvolution and other problems, and achieved good results, but When the observation matrix is ​​a random matrix, the computational complexity of these two algorithms is relatively high; for example, the steepest descent method is used to update the iterative variable instead of the inverse operation with a large amount of calculation, but the convergence of the algorithm cannot be guaranteed; ADMM can also be used to Solve the TV problem and apply it to the image deblurring and denoising problems; another example is to use ADMM to solve TV1 1 -l 2 problem, using part of the Fourier matrix as its observation matrix, but when the observation matrix is ​​a random matrix, the convergence speed is slow; another example is to use IADMM (Inexact ADMM) to solve the TV problem, which speeds up the convergence speed of the algorithm, but in the process of obtaining The solution is only an approximate solution to the original problem, resulting in low reconstruction accuracy

Most of them apply ADMM to image denoising, deblurring, deconvolution and other issues, and rarely apply ADMM to the signal reconstruction problem where the projection matrix is ​​a random matrix; in addition, there is no ADMM to solve the constraints l 0 - regularization problem

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