Self-adaptive regularized smoothed l<0> norm method

A self-adaptive and self-adaptive adjustment technology, applied in complex mathematical operations, electrical components, code conversion, etc., can solve the problems of weak anti-noise ability, low robustness, unable to effectively maintain signal sparsity and error tolerance, etc.

Inactive Publication Date: 2016-09-07
NANJING UNIV OF INFORMATION SCI & TECH
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In this algorithm, the regularization parameter is a fixed value in all iterative operations. However, in the actual iterative operation, the value of the error tolerance term will change greatly. Therefore, in differe

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  • Self-adaptive regularized smoothed l&lt;0&gt; norm method

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[0072] The present invention will be further described below in conjunction with the accompanying drawings. The following examples are only used to illustrate the technical solution of the present invention more clearly, but not to limit the protection scope of the present invention.

[0073] The present invention is similar to the SL0 algorithm and the regularized SL0 algorithm, and also uses two nested loop operations to obtain the sparsest representation solution of the signal x from formula (2). When σ is small, the function F σ (x) has a highly non-smooth phenomenon, which leads to the appearance of many local minima, which is not easy to optimize; and when σ is large, although the function F σ (x) is smoother, which is conducive to optimization, but the reconstruction error of the sparse signal x is larger. Therefore, a strategy of gradually reducing σ is adopted to avoid optimizing F σ (x) falls into a local maximum during the process, for each σ value, in the feasib...

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Abstract

The invention discloses a self-adaptive regularized smoothed l<0> norm method. A regularized SL0 algorithm is improved; in a steepest ascent method in an inner loop, a signal residual item estimated value iterative for the first time and a sparse signal estimated deviation value before and after the iteration are used as the selection basis of current regularization parameters; therefore, the signal sparse degree and the weight value of an error tolerance item in an outer loop every time can be adjusted self-adaptively; the balance of the two is kept in an optimization process; therefore, the reconstruction error of sparse signals can be effectively reduced; the anti-noise interference capability of the algorithm is improved; large-scale matrix inversion operation projected in operation of a feasible solution set in an iterative process can be avoided by introducing a SVD method; and the reconstruction speed to the sparse signals in the method disclosed by the invention is effectively increased.

Description

technical field [0001] The present invention relates to an adaptive regularization smoothing l 0 A norm method belongs to the technical field of compressed sensing restoration. Background technique [0002] As a new technology in the field of signal processing, compressed sensing has been widely used in the fields of biomedicine, image processing, wireless communication and radar signal processing. Compressive sensing theory solves l 0 The norm minimization problem can reconstruct sparse signals with high probability from a small number of non-adaptive projected measurements. However, l 0 The norm minimization problem is an NP-hard problem, which needs to be solved by combinatorial search, but it is difficult to solve the problem when the signal dimension is large. smooth l 0 Norm (Smoothed l 0 Norm, SL0) algorithm is to use a series of Gaussian functions to approximate l 0 norm, so that l 0 The NP-hard problem of norm minimization is transformed into an easy-to-solv...

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Application Information

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IPC IPC(8): G06F17/17H03M7/30
CPCG06F17/17H03M7/55H03M7/60H03M7/6041
Inventor 陈金立唐彬彬李家强高翔罗一凡
Owner NANJING UNIV OF INFORMATION SCI & TECH
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