Fast Linearized Bregman Iteration for Compressive Sensing and Sparse Denoising

Abstract

We propose and analyze an extremely fast, efficient and simple method. This method was first described with more details and rigorous theory given. The motivation was compressive sensing, which now has a vast and exciting history, which seems to have started with Candes, Donoho, et.al. Our method introduces an improvement called "kicking" of the very efficient method and also applies it to the problem of denoising of undersampled signals. The use of Bregman iteration for denoising of images began and led to improved results for total variation based methods. Here we apply it to denoise signals, especially essentially sparse signals, which might even be undersampled.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2008
Accession Number
ADA497867

Entities

People

  • Bin Dong
  • Stanley Osher
  • Wotao Yin
  • Yu Mao

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Autonomy
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Compressed Sensing
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Electrical Engineering
  • Equations
  • Frequency
  • Frequency Domain
  • Inverse Problems
  • Iterations
  • Mathematical Analysis
  • Mathematics
  • Partial Differential Equations
  • Statistical Samples
  • Theorems

Readers

  • Educational Psychology
  • Image Processing and Computer Vision.