Cosparsity
A new concept for structured sparsity in the challenging area of analysis sparse models
What are analysis sparse models?
The standard notion of sparse models is synthesisbased, and assumes that the signal of interest is a linear combination of few columns from a given matrix, the socalled dictionary. Analysis sparse models are an alternative, where an analysis operator multiplies the signal, the use of a (synthesis) dictionary being dropped.
Analysis vs Synthesis (click to enlarge the picture)

The new concept: cosparsity
The cosparse model is a new analysis sparse model. Structured sparsity in analysis sparse models is handled using a union of subspaces model.
See also: Learning Analysis Operators.
Achievements
 A better understanding of the recovery problem under the cosparse model.
 New uniqueness guarantees in the context of a generic missing data problem (e.g.,
compressed sensing, inpainting, source separation, etc.).  New recovery algorithms that are able to exploit the analysis structure, with performance guarantees.
For details, have a look on the poster presented at the SMALL Workshop on Cosparse Analysis Modeling.
More details