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

摘要： 针对已有压缩感知重构算法重构精度不高、消耗时间长的问题，在研究[lp]范数和光滑[l0]范数压缩感知重构算法的基础上提出改进算法。通过极大熵函数构造一种光滑函数来逼近最小[lp] 范数，对解序列进行离散化来近似最小[lp]范数的最优解，结合图像分块压缩感知技术（BCS），在MATLAB中对测试图像进行仿真实验。结果表明，与传统的BOMP（Block Orthogonal Matching Pursuit）算法和IRLS（Iteratively Reweighted Least Squares）算法相比，改进后的算法不仅提高了重构精度，而且大大降低运行时间。

关键词: 压缩感知, 光滑函数, [lp]范数, 图像重构