Paper Info
Title
New Analysis of Manifold Embeddings and Signal Recovery from Compressive Measurements.
Abstract
Compressive Sensing (CS) exploits the surprising fact that the information contained in a sparse signal can be preserved in a small number of compressive, often random linear measurements of that signal. Strong theoretical guarantees have been established concerning the embedding of a sparse signal family under a random measurement operator and on the accuracy to which sparse signals can be recovered from noisy compressive measurements. In this paper, we address similar questions in the context of a different modeling framework. Instead of sparse models, we focus on the broad class of manifold models, which can arise in both parametric and non-parametric signal families. Using tools from the theory of empirical processes, we improve upon previous results concerning the embedding of low-dimensional manifolds under random measurement operators. We also establish both deterministic and probabilistic instance-optimal bounds in ℓ2 for manifold-based signal recovery and parameter estimation from noisy compressive measurements. In line with analogous results for sparsity-based CS, we conclude that much stronger bounds are possible in the probabilistic setting. Our work supports the growing evidence that manifold-based models can be used with high accuracy in compressive signal processing.
Year
DOI
Venue
2013
10.1016/j.acha.2014.08.005
Applied and Computational Harmonic Analysis
Keywords
Field
DocType
53A07,57R40,62H12,68P30,94A12,94A29
Signal processing,Dimensionality reduction,Mathematical analysis,Artificial intelligence,Estimation theory,Probabilistic logic,Manifold,Compressed sensing,Embedding,Pattern recognition,Algorithm,Parametric statistics,Mathematics
Journal
Volume
Issue
ISSN
39
1
1063-5203
Citations 
PageRank 
References 
21
0.89
40
Authors
2
Name
Order
Citations
PageRank
Armin Eftekhari112912.42
Michael B. Wakin24299271.57