What are analysis sparse models?

The standard notion of sparse models is synthesis-based, and assumes that the signal of interest is a linear combination of few columns from a given matrix, the so-called 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)

Recovery Rate of Greedy Analysis Pursuit (left) and Analysis-L1 (right). Top: non-redundant case. Bottom: more redundant case. Source: Nam et al., 2011.

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