Compressed sensing and best 𝑘-term approximation

Compressed sensing is a new concept in signal processing where one seeks to minimize the number of measurements to be taken from signals while still retaining the information necessary to approximate them well. The ideas have their origins in certain abstract results from functional analysis and approximation theory by Kashin but were recently brought into the forefront by the work of Candès, Romberg, and Tao and of Donoho who constructed concrete algorithms and showed their promise in application. There remain several fundamental questions on both the theoretical and practical sides of compressed sensing. This paper is primarily concerned with one of these theoretical issues revolving around just how well…

• NS
  National Science Foundation

  Awards: 0221642, 0200187
• DA
  Deutscher Akademischer Austauschdienst

  Award: DAAD 19-02
• DA
  Defense Advanced Research Projects Agency
• UA
  U.S. Air Force
• OO
  Office of Naval Research

  Award: N00014
• AF
  Air Force Office of Scientific Research

  Awards: F49620, F49620-03-1-0381
• AR
  Army Research Office