Novel Optimization Method for Projection Matrix in Compress Sensing Theory
Wu Guang-wen①② Zhang Ai-jun① Wang Chang-ming①
①(School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China) ②(Department of Electronic Engineering, East China Institute of Technology, Fuzhou 344000, China)
Considering the influence of the projection matrix on Compressed Censing (CS), a novel method is proposed to optimize the projection matrix. In order to improve the signal’s reconstruction precise and the stability of the optimization algorithm of the projection matrix, the proposed method adopts a differentiable threshold function to shrink the off-diagonal items of a Gram matrix corresponding to the mutual coherence between the projection matrix and sparse dictionary, and introduces a gradient descent approach based on the Wolf’s-conditions to solve the optimization projection matrix. The Basis-Pursuit (BP) algorithm and the Orthogonal Matching Pursuit (OMP) algorithm are applied to find the solution of the minimum l0-norm optimization issue and the compressed sensing are utilized to sense and reconstruct the random vectors, wavelet’s noise test signals and pictures. The results of the simulation show the proposed method based on the projection matrix optimization is able to improve the quality of the reconstruction performance.
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