关键词: 压缩感知, 光滑函数, [lp]范数, 图像重构

Abstract: Aiming at the problem of low precision and long time consuming of the existing compressed sensing reconstruction algorithms, an improved algorithm is proposed based on the research of [lp] norm and smooth [l0] norm reconstruction algorithm. A smooth function is constructed with a maximum entropy function to approximate the minimum [lp] norm, then the solution sequence is discretized to approximate the optimal solution of the minimum [lp] norm. Combined with image block compressed sensing technology. The test images are simulated in MATLAB. The results show that the proposed algorithm not only improves the reconstruction accuracy, but also greatly reduces the running time, compared to the traditional block orthogonal matching pursuit algorithm and the Iteratively Reweighted Least Squares（IRLS） algorithm.

Key words: compressed sensing, smooth function, [lp] norm, image reconstruction