# 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****Ω**

*in a transformed domain, using an overcomplete transform*

**y****Ω**called the analysis operator.

How can we learn such an operator from a collection **Y** = [**y**_{1} ... **y**_{N}] of training data ?

## Achievements

- Two new learning algorithms
- Constrained optimization: using a projected subgradient algorithm to solve the highly nonconvex problem min
_{Ω}||**Ω****Y**||_{1}s.t.**Ω**∈*C*; - Iterative detection of the rows of Ω, by a randomized algorithm combining ideas from RANSAC and K-SVD.

- Constrained optimization: using a projected subgradient algorithm to solve the highly nonconvex problem min

- 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