论文标题
多项选择硬阈值追求（MCHTP），用于同时稀疏恢复和稀疏订单估算
Multiple Choice Hard Thresholding Pursuit (MCHTP) for Simultaneous Sparse Recovery and Sparsity Order Estimation
论文作者
论文摘要
我们使用贪婪的压缩感应恢复算法解决了稀疏恢复的问题，而无需明确了解稀疏性。在许多实际情况（例如，无线通信）中，估计稀疏顺序是一个至关重要的问题，其中未知通道的稀疏顺序的确切值可能是先验的。在本文中，我们提出了一种新的贪婪算法，称为多项选择硬阈值追击（MCHTP），该算法可修改流行的硬阈值追击（HTP），以适当地恢复未知的稀疏矢量以及未知矢量的稀疏顺序。我们提供可证明的性能保证，可确保MCHTP可以准确地估算稀疏顺序，同时恢复未知的稀疏矢量，并没有噪音的测量值。模拟结果证实了理论发现，表明即使没有确切的稀疏知识，MCHTP也只有稀疏性的宽松上限，也表现出出色的恢复性能，这几乎与具有精确稀疏性知识的常规HTP相同。此外，与其他最新技术（如MSP）相比，模拟结果表明，MCHTP的计算复杂性要低得多。
We address the problem of sparse recovery using greedy compressed sensing recovery algorithms, without explicit knowledge of the sparsity. Estimating the sparsity order is a crucial problem in many practical scenarios, e.g., wireless communications, where exact value of the sparsity order of the unknown channel may be unavailable a priori. In this paper we have proposed a new greedy algorithm, referred to as the Multiple Choice Hard Thresholding Pursuit (MCHTP), which modifies the popular hard thresholding pursuit (HTP) suitably to iteratively recover the unknown sparse vector along with the sparsity order of the unknown vector. We provide provable performance guarantees which ensures that MCHTP can estimate the sparsity order exactly, along with recovering the unknown sparse vector exactly with noiseless measurements. The simulation results corroborate the theoretical findings, demonstrating that even without exact sparsity knowledge, with only the knowledge of a loose upper bound of the sparsity, MCHTP exhibits outstanding recovery performance, which is almost identical to that of the conventional HTP with exact sparsity knowledge. Furthermore, simulation results demonstrate much lower computational complexity of MCHTP compared to other state-of-the-art techniques like MSP.
