l0-regularisation Signal Reconstruction Based on Fast Alternating Direction Method of Multipliers for Compressed Sensing
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摘要: 该文将压缩感知(CS)中信号的重构问题归结为求解l0-正则化问题，针对l0-正则化问题求解比较困难，提出了快速交替方向乘子法(FADMM)。该算法首先将信号的稀疏域的l0-正则化问题通过变量分裂技术转化为约束优化问题；然后引入乘子函数，采用一步Gauss-Seidel思想，对优化问题中的变量极小化；为了加快算法的收敛速度，对变量进行了二次更新，并更新了乘子；最后进行反正交变换，实现对原始信号的重构。将FADMM应用于含噪声图像的重构，进行了仿真实验及对实验结果进行了分析。实验结果表明：FADMM具有更高的峰值信噪比(Peak Signal to Noise Ratio, PSNR)和更快速的收敛速度。Abstract: Fast Alternating Direction Method of Multipliers (FADMM) is proposed to solve the l0-regularisation issue, which is a problem of signal compression and reconstruction for Compressed Sensing (CS). The first step of FADMM is to express the l0-regularisation issue of the sparse coefficient as a constrained optimization issue by using variable splitting technology. Then, by introducing the function of multipliers, the two variables are alternatively minimized by Gauss-Seidel method. And the two variables are updated once again to speed up the convergence rate, and then, the variable of multipliers is updated. Finally, the original signal is reconstructed by the orthogonal inverse transform. FADMM is better than other state-of-the-art algorithms on reconstructing image. And the experimental simulations demonstrate that the FADMM algorithm has a higher Peak Signal to Noise Ratio (PSNR) and a faster convergence rate.
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