光滑lp范数压缩感知图像重构优化算法

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。

Smooth l_p Norm on Image Reconstruction Optimization Algorithm of Compressed Sensing

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.