论文标题
修改的硬阈值追击和正规化辅助支持识别
Modified Hard Thresholding Pursuit with Regularization Assisted Support Identification
论文作者
论文摘要
硬阈值追求（HTP）是最近提出的迭代稀疏恢复算法，是由迭代硬阈值（IHT）组合的结果组合的结果，以及从正交匹配的PURSIUT（OMP）的估计步骤。 HTP已被认为可以提高恢复保证，并提高收敛速度。由于IHT的支持选择步骤，HTP的大部分成功可以归因于其提高的支持选择能力。在本文中，我们提出了一种称为正规化HTP（RHTP）的广义HTP算法，其中HTP的支持选择步骤被IHT型支持选择取代，其中成本函数由正则化成本函数替换为正则化成本函数，而估计步骤则继续使用最小正方形的功能。使用可分解的正规剂，满足某些规律性条件，RHTP算法被证明会产生一个序列，该序列与根据HTP样进化的序列相等，在这种序列中，识别阶段的鉴定阶段具有梯度超级，具有时间变化的对角矩阵。在理论上和数字上，RHTP也经过证明，以享受与无嘈杂和嘈杂的测量向量相对于HTP更快的融合。
Hard thresholding pursuit (HTP) is a recently proposed iterative sparse recovery algorithm which is a result of combination of a support selection step from iterated hard thresholding (IHT) and an estimation step from the orthogonal matching pursuit (OMP). HTP has been seen to enjoy improved recovery guarantee along with enhanced speed of convergence. Much of the success of HTP can be attributed to its improved support selection capability due to the support selection step from IHT. In this paper, we propose a generalized HTP algorithm, called regularized HTP (RHTP), where the support selection step of HTP is replaced by a IHT-type support selection where the cost function is replaced by a regularized cost function, while the estimation step continues to use the least squares function. With decomposable regularizer, satisfying certain regularity conditions, the RHTP algorithm is shown to produce a sequence dynamically equivalent to a sequence evolving according to a HTP-like evolution, where the identification stage has a gradient premultiplied with a time-varying diagonal matrix. RHTP is also proven, both theoretically, and numerically, to enjoy faster convergence vis-a-vis HTP with both noiseless and noisy measurement vectors.
