Improvement of NSL0 algorithm based on compressed sensing theory

Abstract

Compressed sensing theory provides a new way of signal acquisition.The signal is sparse transformed, and a few observed values are used to reconstruct the signal with high precision.Among them, the signal reconstruction method is the core of compressed sensing. Among all kinds of signal reconstruction algorithms, the most direct and effective signal reconstruction method is to solve under L0 Norm.In order to solve the problem of poor reconstruction quality of NSL0(Newton Smooth L0 Norm) algorithm, this paper proposed a faster and more accurate signal reconstruction algorithm named ACNSL0(Arc Cosin Newton Smooth L0) Norm, based on NSL0 algorithm, adopting the arccosine function with greater steepness, and combining the modified Newton method and Newton damping method.Experiments on one-dimensional signal and two-dimensional image reconstruction show that the reconstruction rate and signal-to-noise ratio are greatly improved compared with similar algorithms under the same conditions.

Keywords

• compressed sensing
• reconstruction algorithm
• arccosine
• modified newton method
• newton damping method