A Denoising Method of the Complex Valued Images Based on Grouped Sparse Coding

The denoising of the complex valued images based on the sparse representation is a hot topic recently, and abundant of algorithms are proposed to solve this problem in the last decades. Unfortunately, the problem is not solved perfectly and there is still space for improvement to achieve better denoising results. We take this challenge to move the denoising method of the complex valued images forward. This paper proposes a grouped sparse coding method based denoising algorithm of the complex valued images, which handles the complex values as a unity rather than processing the real part and the imaginary part separately. By doing this, the whole complex values are processed and the relationship between the real part and the imaginary part is considered. The complex valued images are separated into overlapped patches firstly and then these patches are divided into several clusters by the distance function which is defined in the complexed domain. By the constraint to the patches in each cluster that they are represented by the similar items in the trained dictionary with different coefficients, we can suppress the coding noise in the patches. This paper researches on the algorithm to cluster the patches firstly and proposes a grouped sparse coding method. The coding of the patches in a cluster is modeled by an object function to be minimized. The object function contains two terms. The first term is the fitting error part while the second term is to measure the sparsity of the codes. There is also a regularized parameter between the two terms. In order to constrain the codes in each cluster to be similar, the regularization term which induces the sparse codes to have same non-zero positions is proposed to the object function to be minimized. Then the coding algorithm is researched. What is more, the proposal is applied to the denoising of the complex valued images. The reason that the grouped sparse coding method can suppress the noise is that the information in the images can be coded by the grouped sparse coding method since the dictionary is trained from the patches, on the contrary, the noise cannot be coded because it is very random. In the experiments section, the denoising results of the interferometric synthetic aperture radar (InSAR) images (both simulated and real data) and the magnetic resonance images (MRI) are illustrated to prove the efficiency of the proposed method. The results show that the proposed algorithm can achieve the lower root mean square error compared to the other denoising methods (e. g. WFT method and traditional sparse representation method). Especially, the proposed algorithm achieves a great improvement in the denoising results of the complex valued images with large smooth areas or high level of noise. The parameters in our method are also analyzed in this paper. The larger patch size leads to better denoising results but costs much more time and the improvement tends to be slow as the patch size increases. The regularized parameter in the proposed grouped spares coding balanced the fitted error and the sparsity of the codes. The best regularized parameter is determined by the noise level. If the noise is severe, the regularized parameter should be large to suppress the noise. © 2019, Science Press. All right reserved.