Choice of Parameters in the Weighted Nuclear Norm Method for Image Denoising
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CHOICE OF PARAMETERS IN THE WEIGHTED NUCLEAR NORM METHOD FOR IMAGE DENOISING O. S. Volodina,1 A. V. Nasonov,2 and A. S. Krylov3
UDC 004.932
We consider the choice of image denoising parameters in an algorithm based on singular decomposition and minimization of the weighted nuclear norm. An automated parameter-choosing method is proposed that analyzes the structures on a difference image between the original noisy image and the denoised result and performs a quantitative assessment of the structures — computes the mutual information coefficient. We also analyze the choice of optimal parameters for different noise levels using a database of photographic images with normally distributed simulated noise. The denoising results are compared for the optimal choice of parameters and the choice of parameters by the mutual information coefficient, and also with denoising by a Peron–Malik diffusion algorithm. Keywords: image processing, denoising.
Introduction The noise removal, or denoising, problem is one of the open issues in image processing. The main difficulty in this problem is the separation of useful information from noise. Many studies have been carried out in this area. The simplest algorithms assume predominant localization of noise at high frequencies and apply frequency filtering, such as a Gauss filter [1], Winer filtering [2], or wavelet-transform filtering [3]. More complex algorithms use anisotropic diffusion [4] or total variation minimization [5]. All these filtering techniques, however, may lead to a loss of high-frequency detail and blurring of image textures, which in turn requires the development of algorithms with better separation of noise and useful information. The proposal in [6] is to find, not a single block in the image, but all similar blocks over the entire image. The proposal is based on the assumption that noise is random, while the fragments of details are similar. Averaging similar blocks, we can reduce noise while preserving the details, thus improving image reconstruction. This approach is the basis for methods such as BM3D [7], LSSC [8], and NCSR [9]. Block averaging is not always effective, for instance, if the input data are very noisy. One of the options is to decompose the blocks in some basis, for instance, by a discrete cosine transform [10]. Another approach is to assemble the image blocks into a matrix and apply singular decomposition [11]. By extracting the main characteristics from the matrix, we can better find the specific features of the blocks. The automatic choice of adequate denoising parameters constitutes an essential difficulty in image noise removal. One of the approaches is to collect statistical data on optimal parameters from image databases with simulated noise and find the dependences between noise level and optimal parameters. This approach requires preliminary noise level evaluation. An alternative approach is to evaluate the result of denoising. Methods [12, 13] assess global image quality from local statistics or frequency analysis [14]. In [15], structu
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