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 ?
Achievements
- Two new learning algorithms
- Constrained optimization: using a projected subgradient algorithm to solve the highly nonconvex problem minΩ ||ΩY||1 s.t. Ω∈C;
- 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