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Learning analysis operators

See also: Cosparsity and Dictionary learning theory.

Learning Analysis Operators

In the cosparse model, a signal vector y is characterized by the sparsity of its analysis representation z = Ωy in a transformed domain, using an overcomplete transform Ω called the analysis operator.

How can we learn such an operator from a collection Y = [y1 ... yN] of training data ?


  • Two new learning algorithms
    • Constrained optimization: using a projected subgradient algorithm to solve the highly nonconvex problem minΩ ||ΩY||1 s.t. ΩC;
    • Iterative detection of the rows of Ω, by a randomized algorithm combining ideas from RANSAC and K-SVD.
  • Empirical results demonstrating the ability of the algorithms to recover the true underlying analysis operator.
  • Preliminary theoretical analysis of the success guarantees of the algorithms, showing the interest of the Uniform Normalized Tight Frame constraint C.

For more details, have a look to Michael Elad's presentation @EUSIPCO 2011 : Sequential Minimal Eigenvalues - An Approach to Analysis Dictionary Learning

More details


RĂ©mi Gribonval, coordinator
Equipe-Projet METISS
INRIA Rennes - Bretagne Atlantique
Campus de Beaulieu
F-35042 Rennes cedex, France.

Phone: (+33/0) 299 842 506
Fax: (+33/0) 299 847 171
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