A generalization of analysis and synthesis sparsity

This paper introduces a generalized sparsity model that extends synthesis and analysis sparsity. The generalized model asserts that a signal has a sparse representation in a dictionary, which is at the same time orthogonal to a part of the dictionary´s null space. Alternatively, analyzing the signal with an analysis operator yields an output vector that can be represented as the sum between a sparse vector and a vector from a low-dimensional subspace. We show that the proposed model allows recovery of sparse signals from few incoherent measurements, with algorithms that are similar to the familiar algorithms of the synthesis and analysis sparsity models.