Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Image denoising by a direct variational minimization | Janev et al. EURASIP Journal on Advances in Signal Processing 2011 2011 8 http content 2011 1 8 o EURASIP Journal on Advances in Signal Processing a SpringerOpen Journal RESEARCH Open Access Image denoising by a direct variational minimization 1 1 2 1 Marko Janev Teodor Atanackovic Stevan Pilipovic and Radovan Obradovic Abstract In this article we introduce a novel method for the image de-noising which combines a mathematically well-posdenes of the variational modeling with the efficiency of a patch-based approach in the field of image processing. It based on a direct minimization of an energy functional containing a minimal surface regularizer that uses fractional gradient. The minimization is obtained on every predefined patch of the image independently. By doing so we avoid the use of an artificial time PDE model with its inherent problems of finding optimal stopping time as well as the optimal time step. Moreover we control the level of image smoothing on each patch and thus on the whole image by adapting the Lagrange multiplier using the information on the level of discontinuities on a particular patch which we obtain by pre-processing. In order to reduce the average number of vectors in the approximation generator and still to obtain the minimal degradation we combine a Ritz variational method for the actual minimization on a patch and a complementary fractional variational principle. Thus the proposed method becomes computationally feasible and applicable for practical purposes. We confirm our claims with experimental results by comparing the proposed method with a couple of PDE-based methods where we get significantly better denoising results specially on the oscillatory regions. Keywords Image denoising Ritz method calculus of variations fractional gradient anisotropic diffusion Complementary Principle saddle point sparse frame approximation error bound 1. Introduction Since the work of Perona and Malik 1 PDE methods have been used
