Recovery of Compressible Signals in Unions of Subspaces

Abstract

Compressive sensing (CS) is an alternative to Shannon/Nyquist sampling for acquisition of sparse or compressible signals; instead of taking periodic samples, we measure inner products with M < N random vectors and then recover the signal via a sparsity-seeking optimization or greedy algorithm. Initial research has shown that by leveraging stronger signal models than standard sparsity, the number of measurements required for recovery of a structured sparse signal can be much lower than that of standard recovery. In this paper, we introduce a new framework for structured compressible signals based on the unions of subspaces signal model, along with a new sufficient condition for their recovery that we dub the restricted amplification property (RAmP). The RAmP is the natural counterpart to the restricted isometry property (RIP) of conventional CS. Numerical simulations demonstrate the validity and applicability of our new framework using wavelet-tree compressible signals as an example.

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Document Details

Document Type
Technical Report
Publication Date
Dec 21, 2009
Accession Number
ADA520217

Entities

People

  • Chinmay Hegde
  • Marco F. Duarte
  • Richard G. Baraniuk
  • Volkan Cevher

Organizations

  • Rice University

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Acquisition
  • Algorithms
  • Amplification
  • Coefficients
  • Compressed Sensing
  • Compression
  • Data Acquisition
  • Detectors
  • Electrical Engineering
  • Guarantees
  • High Resolution
  • Measurement
  • Probability
  • Random Variables
  • Recovery
  • Residuals
  • Standards

Fields of Study

  • Engineering

Readers

  • Applied Combinatorial Optimization and Logic Circuit Design.
  • Graph Algorithms and Convex Optimization.
  • Image Processing and Computer Vision.