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 (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 ADE-PCM is to express the l1-regularization problem of the sparse coefficient in the transform domain as an equivalent constrained opti-mization problem by using variable splitting (VS) technology .Then ,by introducing the penalty function ,the two variables are alter-natively minimized by Gauss-Seidel method ,and the penalty variable is updated by a continuation scheme ,and then the sparse coef-ficient 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 ) re-constructed image as well as a much faster convergence rate as compared to some existing reconstruction algorithms .
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