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In sparse recovery, the unique sparsest solution to an under-determinedsystem of linear equations is of main interest. This scheme is commonlyproposed to be applied to signal acquisition. In most cases, the signals arenot sparse themselves, and therefore, they need to be sparsely represented withthe help of a so-called dictionary being specific to the corresponding signalfamily. The dictionaries cannot be used for optimization of the resultingunder-determined system because they are fixed by the given signal family.However, the measurement matrix is available for optimization and can beadapted to the dictionary. Multiple properties of the resulting linear systemhave been proposed which can be used as objective functions for optimization.This paper discusses two of them which are both related to the coherence ofvectors. One property aims for having incoherent measurements, while the otheraims for insuring the successful reconstruction. In the following, theinfluences of both criteria are compared with different reconstructionapproaches.

Dictionary Adaptation in Sparse Recovery Based on Different Types of Coherence