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The co-sparse analysis model for signals assumes that the signal of interestcan be multiplied by an analysis dictionary \Omega, leading to a sparseoutcome. This model stands as an interesting alternative to the more classicalsynthesis based sparse representation model. In this work we propose atheoretical study of the performance guarantee of the thresholding algorithmfor the pursuit problem in the presence of noise. Our analysis reveals twosignificant properties of \Omega, which govern the pursuit performance: Thefirst is the degree of linear dependencies between sets of rows in \Omega,depicted by the co-sparsity level. The second property, termed the RestrictedOrthogonal Projection Property (ROPP), is the level of independence betweensuch dependent sets and other rows in \Omega. We show how these dictionaryproperties are meaningful and useful, both in the theoretical bounds derived,and in a series of experiments that are shown to align well with thetheoretical prediction.

Performance Guarantees of the Thresholding Algorithm for the Co-Sparse Analysis Model