Abstract: Compressed sensing is widely used in signal recovery, image reconstruction and denoising. Reconstruction algorithm is one of the key parts of compressed sensing. When the sample rate is very low, reconstructing the original signal is a difficult problem. In this regard, existing algorithms generally perform poor. The [p(0<p≤1)] norm regularized minimization model is adopted to recover the sparse signal, and the smoothing quasi-Newton algorithm is used to solve this problem. By updating the smoothing parameter and the regularization parameter simultaneously, this algorithm realizes the adaptive adjustment of the smoothing parameter and the regularization parameter, then avoids the selection of parameters for solving different problems, which makes the algorithm have a wide range of adaptability and robustness. A large number of simulations and real image reconstruction and denoising experiments verify the effectiveness of the proposed algorithm. Experiments show that the proposed algorithm is superior to the current popular algorithms for image denoising, high sparsity and low sampling rate.

Key words: compressed sensing;p norm regularization, smoothing method, quasi-Newton algorithm, signal recovery, image reconstruction, image denoising

摘要： 压缩感知被广泛应用于信号恢复和图像重构与去噪，重构算法是压缩感知的关键部分之一。当采样率很低时，重建原始信号是个困难的问题。对此，现有算法普遍表现不佳。采用[p(0<p≤1)]范数正则极小化模型恢复原始稀疏信号，并利用光滑化拟牛顿算法求解该模型。通过同步更新光滑化参数和正则化参数，该算法实现了光滑化参数和正则化参数的自适应调整，避免求解不同问题时参数的选取问题，使得该算法具有广泛的适应性和鲁棒性。通过大量仿真和真实图像重构与去噪数值实验验证该算法的有效性，实验表明，该算法对于图像去噪、高稀疏度和低采样率信号的处理能力优于当前流行的优秀算法。

关键词: 压缩感知, [p]范数正则, 光滑化方法, 拟牛顿算法, 信号恢复, 图像重构, 图像去噪