标题： ADMM在线性收敛性下的各向同性TV范数压缩感知 显示英文标题

标题： Asymptotic Linear Convergence of ADMM for Isotropic TV Norm Compressed Sensing

摘要： 我们证明了ADMM在一个多维问题中求解各向同性全变分（TV）范数压缩感知问题时的显式局部线性速率，通过分析对偶问题上等价Douglas-Rachford分裂中的辅助变量。将在大型三维问题和真实MRI数据上展示数值验证。虽然证明的速率不是最优的，但它接近于数值测试中观察到的结果。 显示英文摘要

摘要： We prove an explicit local linear rate for ADMM solving the isotropic Total Variation (TV) norm compressed sensing problem in multiple dimensions, by analyzing the auxiliary variable in the equivalent Douglas-Rachford splitting on a dual problem. Numerical verification on large 3D problems and real MRI data will be shown. Though the proven rate is not sharp, it is close to the observed ones in numerical tests.