论文标题
部分可观测时空混沌系统的无模型预测
Recovery Conditions of Sparse Signals Using Orthogonal Least Squares-Type Algorithms
论文作者
论文摘要
正交最小二乘（OLS）型算法有效地重建稀疏信号，其中包括众所周知的OL，多个OLS（MOLS）和Block OLS（BOLS）。在本文中，我们首先研究了这些算法的无噪声精确恢复条件。具体而言，基于相互不一致的特性（MIP），我们提供了OLS和MOL的理论分析，以确保在迭代过程中可以选择正确的非零支持。然而，对BOL的理论分析利用块-MIP来应对块稀疏性。此外，无噪声基于MIP的分析将扩展到嘈杂的方案。我们的结果表明，对于K-SPARSE信号，当MIP或SNR满足某些条件时，OLS和MOL在最多的K迭代中获得可靠的重建，而BOLS最多可以成功（K/D）迭代，而D是块长度。结果表明，我们得出的理论结果改善了现有结果，这些结果已通过仿真测试验证。
Orthogonal least squares (OLS)-type algorithms are efficient in reconstructing sparse signals, which include the well-known OLS, multiple OLS (MOLS) and block OLS (BOLS). In this paper, we first investigate the noiseless exact recovery conditions of these algorithms. Specifically, based on mutual incoherence property (MIP), we provide theoretical analysis of OLS and MOLS to ensure that the correct nonzero support can be selected during the iterative procedure. Nevertheless, theoretical analysis for BOLS utilizes the block-MIP to deal with the block sparsity. Furthermore, the noiseless MIP-based analyses are extended to the noisy scenario. Our results indicate that for K-sparse signals, when MIP or SNR satisfies certain conditions, OLS and MOLS obtain reliable reconstruction in at most K iterations, while BOLS succeeds in at most (K/d) iterations where d is the block length. It is shown that our derived theoretical results improve the existing ones, which are verified by simulation tests.
