Covariance Matrix of a Probability Distribution for Image Dictionaries in Compressed Sensing

Sparse representation is one of the principles for the most effective signal processing, and makes it possible for us to infer from less data. The framework of signal processing based on it is called compressed sensing or compressive sensing, where dictionary matrices play an essential role of the basis for sparse representation. In our previous work, we successfully derived an analytical expression of the probability distribution followed by image dictionaries for the images generated by the Gaussian model [1]. However, we have found that the distribution has a difficulty of a divergent covariance matrix, which is needed for an analytical performance evaluation of image processing by compressed sensing. Therefore, it is the purpose of this paper to solve the difficulty and to open the way to the evaluation.