Conic Matching Pursuit

Expands data as sum of conic projections

This is a projection pursuit type algorithm that decomposes a signal by projecting the residual at each level onto a convex cone and the respective polar cone.

The set giving cone k is described by a vector w = W(:,k) and scalar rho:

C_k = { x : x'w >= rho*|| x || };

The polar cone is:

C*_k = { y: y'x <= 0, x element of C_k };

where w is the reference vector for the set C. The projector for this set is described in:

Henry Stark and Youngyi Yang, "Vector Space Projections: A Numerical Approach to Signal and Image Processing, Neural Nets, and Optics", Wiley Interscience Publications, 1998.

On pages 109-113, Section 3.5, in the discussion on similarity
constraints.

I have NOT yet published this algorithm, but it is my theory/development. Comments welcome!