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! |
