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This paper presents a novel method on designing redundant dictionary from known orthogonal functions. The common way for discretization of continuous functions is obtained with uniform sampling. Our experiments show that dividing the function definition interval with nonuniform measure makes the redundant dictionary sparser, and the resulted dictionary is suitable for image denoising via sparse and redundant dictionary. In this case, the problem is to find an appropriate measure in order to construct each atom of dictionary. It has been shown that in sparse approximation context incoherent dictionary is suitable for sparse approximation method. According to this fact, we define some optimization problems to find the best parameters for distribution measure (in our study normal distribution). To obtain better convergence to optimum point, Genetic Algorithm (GA) with enough diversity on initial population is used. We show the effect of this type of dictionary design on exact sparse recovery support. Our results also show advantage of this design method on image denoising task.

This paper presented a novel method on designing redundant dictionary from known orthogonal functions. Usual way of discretization of continuous functions is uniform sampling. Our experiments show that dividing the function definition interval with non-uniform measure makes the redundant dictionary sparser and it is suitable for image denoising via sparse and redundant dictionary. In this case the problem is to find an appropriate measure in order to make each atom of dictionary. It has shown that in sparse approximation context, incoherent dictionary is suitable for sparse approximation method. According to this fact we define some optimization problems to find the best parameter of distribution measure (in our study normal distribution). For better convergence to optimum point we used Genetic Algorithm