Convolutional sparse representation of color images

Convolutional sparse representations differ from the standard form of sparse representations in their composition from coefficient maps convolved with dictionary filters instead of linear combinations of dictionary vectors. When applied to images, the standard form is usually independently computed over a set of overlapping image patches. The advantage of the convolutional form is that it provides a single-valued representation optimized over an entire signal, but this comes at a substantial computational cost. A recent algorithm for sparse coding via a convolutional form of Basis Pursuit DeNoising, however, has substantially reduced the computational cost of computing these representations. The present paper extends this algorithm to multi-channel signals such as color images, which has not previously been reported in the literature.