信号压缩与重构的交替方向外点持续法

针对压缩感知（Compressed Sensing，CS）中信号重构的l1-正则化问题中的l1-正则项非光滑，求解比较困难，提出了交替方向外点持续法（Alternating Direction Exterior Point Continuation Method，ADEPCM）.该算法首先将信号的稀疏域的l1-正则化问题通过变量分裂（Variable Splitting，VS）技术转化为与之等价的约束优化问题；然后采用一步Gauss-Seidel思想，对优化问题中的变量最小化，并采用持续的思想更新罚参数，重构出信号的稀疏系数；最后进行正交反变换，重构出原始信号.并将ADEPCM用于图像重构，进行了仿真实验及对实验结果进行了分析.实验结果表明：与现有的一些重构算法相比，ADEPCM具有稍高的峰值信噪比（Peak Signal to Noise Ratio，PSNR）和更快速的收敛速度.

Alternating Direction Exterior Point Continuation Method for Signal Compression and Reconstruction

Alternating direction exterior point continuation method (ADEPCM) is proposed to solve the l1-regularization problem,which is the classic problem of signal compression and reconstruction for compressed sensing (CS).The first step of ADEPCM is to express the l1-regularization problem of the sparse coefficient in the transform domain as an equivalent constrained optimization problem by using variable splitting (VS) technology.Then,by introducing the penalty function,the two variables are alternatively minimized by Gauss-Seidel method,and the penalty variable is updated by a continuation scheme,and then the sparse coefficient in the transform domain is reconstructed.Finally,the original signal is reconstructed by the orthogonal inverse transform.And the experimental simulations demonstrate that the ADEPCM algorithm yields a slightly higher peak signal to noise ratio (PSNR) reconstructed image as well as a much faster convergence rate as compared to some existing reconstruction algorithms.