2011/12/03 by Konstantinos Slavakis, Yannis Kopsinis, Slavakis, Konstantinos +5
Computer Science · Engineering · #Advanced Adaptive Filtering Techniques #FOS: Computer and information sciences #Image and Signal Denoising Methods #Information Theory (cs.IT) #PAPR reduction in OFDM #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1112.0665
openalex publication_date 2011/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies a sparse signal recovery task in time-varying\n(time-adaptive) environments. The contribution of the paper to sparsity-aware\nonline learning is threefold; first, a Generalized Thresholding (GT) operator,\nwhich relates to both convex and non-convex penalty functions, is introduced.\nThis operator embodies, in a unified way, the majority of well-known\nthresholding rules which promote sparsity. Second, a non-convexly constrained,\nsparsity-promoting, online learning scheme, namely the Adaptive\nProjection-based Generalized Thresholding (APGT), is developed that\nincorporates the GT operator with a computational complexity that scales\nlinearly to the number of unknowns. Third, the novel family of partially\nquasi-nonexpansive mappings is introduced as a functional analytic tool for\ntreating the GT operator. By building upon the rich fixed point theory, the\nprevious class of mappings helps us, also, to establish a link between the GT\noperator and a union of linear subspaces; a non-convex object which lies at the\nheart of any sparsity promoting technique, batch or online. Based on such a\nfunctional analytic framework, a convergence analysis of the APGT is provided.\nFurthermore, extensive experiments suggest that the APGT exhibits competitive\nperformance when compared to computationally more demanding alternatives, such\nas the sparsity-promoting Affine Projection Algorithm (APA)- and Recursive\nLeast Squares (RLS)-based techniques.\n