鲁棒块稀疏信号恢复的广义全变分正则化稀疏贝叶斯学习
General Total Variation Regularized Sparse Bayesian Learning for Robust Block-Sparse Signal Recovery
摘要：
在不知道块大小和边界的情况下恢复块稀疏信号（例如在多天线毫米波信道模型中遇到的那些）是压缩感知（CS）算法的难题。我们提出了一种新的稀疏贝叶斯学习（SBL）方法的块稀疏恢复的基础上流行的CS为基础的正则化函数的输入变量与总变差（TV）。与对信号分量施加正则化的传统方法相反，我们正则化SBL超参数。这种迭代TV正则化SBL算法采用优化最小化方法，并将每次迭代减少为凸优化问题，从而可以灵活选择数值求解器。数值结果表明，TV正则化SBL算法对块结构的性质具有鲁棒性，能够恢复具有块模式分量和孤立分量的信号，适用于各种信号恢复系统。
英文摘要：
Block-sparse signal recovery without knowledge of block sizes and boundaries, such as those encountered in multi-antenna mmWave channel models, is a hard problem for compressed sensing (CS) algorithms. We propose a novel Sparse Bayesian Learning (SBL) method for block-sparse recovery based on popular CS based regularizers with the function input variable related to total variation (TV). Contrary to conventional approaches that impose the regularization on the signal components, we regularize the SBL hyperparameters. This iterative TV-regularized SBL algorithm employs a majorization-minimization approach and reduces each iteration to a convex optimization problem, enabling a flexible choice of numerical solvers. The numerical results illustrate that the TV-regularized SBL algorithm is robust to the nature of the block structure and able to recover signals with both block-patterned and isolated components, proving useful for various signal recovery systems.
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