Stable Restoration and Separation of Approximately Sparse Signals

Abstract

This paper develops new theory and algorithms to recover signals that are approximately sparse in some general (i.e., basis, frame, over-complete, or incomplete) dictionary but corrupted by a combination of measurement noise and interference having a sparse representation in a second general dictionary. Particular applications covered by our framework include the restoration of signals impaired by impulse noise, narrowband interference, or saturation as well as image in-painting, super-resolution, and signal separation. We develop efficient recovery algorithms and deterministic conditions that guarantee stable restoration and separation. Two application examples demonstrate the efficacy of our approach.

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Document Details

Document Type
Technical Report
Publication Date
Jul 02, 2011
Accession Number
ADA549487

Entities

People

  • Christoph Studer
  • Richard G. Baraniuk

Organizations

  • Rice University

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Compressed Sensing
  • Computational Science
  • Computations
  • Dictionaries
  • Electrical Engineering
  • Frequency
  • Gaussian Noise
  • Guarantees
  • Impulse Noise
  • Measurement
  • Narrowband
  • Noise
  • Probability
  • Recovery
  • Saturation
  • Two Dimensional

Fields of Study

  • Engineering

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Image Processing and Computer Vision.
  • Neural Network Machine Learning.