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

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