Study on Over-Complete Dictionaries for Sparse Representations of Signals

In recent years there has been a growing interest in the study of sparse representation of signals. The redundancy of over-complete dictionary can make it effectively capture the characteristics of the signals. Using an over-complete dictionary that contains prototype signal-atoms, signals are described as linear combinations of a few of these atoms. Applications that use sparse representation are many and include compression, regularization in inverse problems, Compressed Sensing (CS), and more. Recent activities in this field concentrate mainly on the study of sparse decomposition algorithm and dictionary design algorithm. In this paper, we discuss the advantages of sparse dictionaries, and present the implicit dictionaries for signal sparse presents. The overcomplete dictionaries which combined the different orthonormal transform bases can be used for the compressed sensing. Experimental results demonstrate the effectivity for sparse presents of signals.

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