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 (GA) with enough diversity on initial population. We show the effect of this type of dictionary design on exact sparse recovery support. Our results also show the advantage of this design method on image denoising task.
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