2013/06/19 by Armin Eftekhari, Eftekhari, Armin, Michael B. Wakin +1 · 4 citations
Engineering · Mathematics · Medicine · #Advanced MRI Techniques and Applications #FOS: Computer and information sciences #Information Theory (cs.IT) #Mathematical Analysis and Transform Methods #Microwave Imaging and Scattering Analysis #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1306.4748
openalex publication_date 2013/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Compressive Sensing (CS) exploits the surprising fact that the information\ncontained in a sparse signal can be preserved in a small number of compressive,\noften random linear measurements of that signal. Strong theoretical guarantees\nhave been established concerning the embedding of a sparse signal family under\na random measurement operator and on the accuracy to which sparse signals can\nbe recovered from noisy compressive measurements. In this paper, we address\nsimilar questions in the context of a different modeling framework. Instead of\nsparse models, we focus on the broad class of manifold models, which can arise\nin both parametric and non-parametric signal families. Using tools from the\ntheory of empirical processes, we improve upon previous results concerning the\nembedding of low-dimensional manifolds under random measurement operators. We\nalso establish both deterministic and probabilistic instance-optimal bounds in\n\ℓ2 for manifold-based signal recovery and parameter estimation from noisy\ncompressive measurements. In line with analogous results for sparsity-based CS,\nwe conclude that much stronger bounds are possible in the probabilistic\nsetting. Our work supports the growing evidence that manifold-based models can\nbe used with high accuracy in compressive signal processing.\n