In this paper, a new method for the removal of Gaussian noise based on two types of prior information is described. The first type of prior information is internal, based on the similarities between the pixels in the noisy image, and the other is external, based on the index or pixel location in the image. The proposed method focuses on leveraging these two types of prior information to obtain tangible results. To this end, very similar patches are collected from the noisy image. This is done by sorting the image pixels in ascending order and then placing them in consecutive rows in a new two-dimensional image. Henceforth, a principal component analysis is applied on the patch matrix to help remove the small noisy components. Since the restored pixels are similar or close in values to those in the clean image, it is preferable to arrange them using indices similar to those of the clean pixels. Simulation experiments show that outstanding results are achieved, compared to other known methods, either in terms of image visual quality or peak signal to noise ratio. Specifically, once the proper indices are used, the proposed method achieves PSNR value better than the other well-known methods by >1.5 dB in all the simulation experiments.
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