A Novel Image Denoising Method Based on Incoherent Dictionary Learning and Domain Adaptation Technique

In this paper, a new method for image denoising based on incoherent dictionary learning and domain transfer technique is proposed. The idea of using sparse representation concept is one of the most interesting areas for researchers. The goal of sparse coding is to approximately model the input data as a weighted linear combination of a small number of basis vectors. Two characteristics should be considered in the dictionary learning process: Atom-data coherence and mutual coherence between dictionary atoms. The first one determines the dependency between the dictionary atoms and training data frames. This criterion value should be high. Another parameter expresses the dependency between atoms defined as the maximum absolute value of the cross-correlations between them. Higher coherence to the data class and lower mutual coherence between atoms result in a small approximation error in sparse coding procedure. In the proposed dictionary learning process, a coherence criterion is employed to yield over complete dictionaries with the incoherent atoms. The purpose of learning dictionary with low mutual coherence value is to reduce the approximation error of sparse representation in the denoising process and also decrease the computing time. We utilize the least angle regression with coherence criterion (LARC) algorithm for sparse representation based on atom-data coherence in the first step of dictionary learning process. LARC sparse coding is an optimized generalization of the least angle regression algorithm with stopping condition based on a residual coherence. This approach is based on setting a variable cardinality value. Using atom-data coherence measure as stopping criteria in the sparse coding process yields the capability of balancing between source confusion and source distortion. A high value for the cardinality parameter or too dense coding results in the source confusion since the number of dictionary atoms is more than what is required for a proper representation. Source degradation occurs when the sparse coding is done with low cardinality parameter or too sparse coding. Therefore, the number of required atoms will not be enough and data cannot be coded exactly over these atoms. Therefore, the setting procedure of cardinality parameter must be performed precisely. The problem of finding a dictionary with low mutual coherence between its normalized atoms can be obtained by considering the Gram matrix. The mutual coherence is described by the maximum absolute value of the off-diagonal elements of this matrix. If all off-diagonal elements are the same, a dictionary with minimum self-coherence value is obtained. Also, we take advantage of domain adaptation technique to transfer a learned dictionary to an adapted dictionary in the denoising process. The initial atoms set randomly and are updated based on the selected patches of input noisy image using the proposed alternating optimization algorithm. According to these issues, the fitness function in dictionary learning problem includes three main sections: The first term is related to the minimization of approximation error. The next items are the incoherence criterion of dictionary atoms. The last one includes a transformation of initial atoms according to some patches of the noisy input data in the test step. We use limited-memory BFGS algorithm as an iterative solution for regular minimization of our objective function involved different terms. The simulation results show that the proposed method leads to significantly better results in comparison with the earlier methods in this context and the traditional procedures.