Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Convex Optimization
Blind multiband signal reconstruction: compressed sensing for analog signals
IEEE Transactions on Signal Processing
Block-sparse signals: uncertainty relations and efficient recovery
IEEE Transactions on Signal Processing
Harmonic decomposition of audio signals with matching pursuit
IEEE Transactions on Signal Processing
On Polar Polytopes and the Recovery of Sparse Representations
IEEE Transactions on Information Theory
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Polytope Faces Pursuit is an algorithm that solves the standard sparse recovery problem. In this paper, we consider the case of block structured sparsity, and propose a novel algorithm based on the Polytope Faces Pursuit which incorporates this prior knowledge. The so-called Group Polytope Faces Pursuit is a greedy algorithm that adds one group of dictionary atoms at a time and adopts a path following approach based on the geometry of the polar polytope associated with the dual linear program. The complexity of the algorithm is of similar order to Group Orthogonal Matching Pursuit. Numerical experiments demonstrate the validity of the algorithm and illustrate that in certain cases the proposed algorithm outperforms the Group Orthogonal Matching Pursuit algorithm.