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Compressive Sensing (CS) is a new paradigm for the efficient acquisition ofsignals that have sparse representation in a certain domain. Traditionally, CShas provided numerous methods for signal recovery over an orthonormal basis.However, modern applications have sparked the emergence of related methods forsignals not sparse in an orthonormal basis but in some arbitrary, perhapshighly overcomplete, dictionary, particularly due to their potential togenerate different kinds of sparse representation of signals. To this end, weapply a signal space greedy method, which relies on the ability to optimallyproject a signal onto a small number of dictionary atoms, to address signalrecovery in this setting. We describe a generalized variant of the iterativerecovery algorithm called Signal space Subspace Pursuit (SSSP) for this morechallenging setting. Here, using the Dictionary-Restricted Isometry Property(D-RIP) rather than classical RIP, we derive a low bound on the number ofmeasurements required and then provide the proof of convergence for thealgorithm. The algorithm in noisy and noise-free measurements has lowcomputational complexity and provides high recovery accuracy. Simulationresults show that the algorithm outperforms best compared with the existingrecovery algorithms.

Greedy Signal Space Recovery Algorithm with Overcomplete Dictionaries in Compressive Sensing