Abstract: Nonlinear compressive sensing reconstruction algorithm is one of three main studies. Based on the [?p]-norm detailed analysis of the existing iterative reweighted least squares optimization method, an improved iterative reweighted least square [?p]-norm minimization of nonconvex compressive sensing optimization algorithm is proposed. Experimental results show that the improved algorithm has a higher percentage of successful reconstruction and faster reconstruction speed, which can also greatly reduce the required number of measurements with the same sparsity and have great significance on reconstruction algorithms and practical application of compressive sensing.

Key words: compressive sensing, non-convex compressive sensing, [?p]minimization, iterative reweighted least squares

摘要： 非线性重构算法是压缩感知的三个主要研究内容之一。在详细分析了现有的迭代重加权最小二乘[?p]优化方法的基础上，提出改进的迭代重加权最小二乘[?p]范数最小化非凸压缩感知优化算法。实验结果表明，改进的算法拥有更高的成功重建百分比和重建速度，在同样稀疏度的情况下可以大大减少所需的测量次数，对于压缩感知的重建算法研究以及实际应用都具有重要的意义。

关键词: 压缩感知, 非凸压缩感知, [?p]最小化, 迭代重加权最小二乘法