Dictionary-Sparse Recovery via Thresholding-Based Algorithms Academic Article

abstract

• 2015, Springer Science+Business Media New York. It is shown that the iterative hard thresholding and hard thresholding pursuit algorithms provide the same theoretical guarantees as 1-minimization for the recovery from imperfect compressive measurements of signals that have almost sparse analysis expansions in a fixed dictionary. Unlike other signal space algorithms targeting the recovery of signals with sparse synthesis expansions, the ability to compute (near) best approximations by synthesis-sparse signals is not necessary. The results are first established for tight frame dictionaries, before being extended to arbitrary dictionaries modulo an adjustment of the measurement process.

authors

• Foucart, Simon

published proceedings

• JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS

author list (cited authors)

• Foucart, S.

citation count

• 10

complete list of authors

• Foucart, Simon

publication date

• February 2016

publisher

• Springer Nature  Publisher

published in

• Journal of Fourier Analysis and Applications  Journal

keywords

• Compressive Sensing
• Hard Thresholding Pursuit
• Iterative Hard Thresholding
• Restricted Isometry Property Adapted To A Dictionary
• Sparse Recovery
• Tight Frames

Digital Object Identifier (DOI)

• 10.1007/s00041-015-9411-4

start page

• 6

end page

• 19

volume

• 22

issue

• 1

URL

• http://dx.doi.org/10.1007/s00041-015-9411-4