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: A Nonlinear Entropic Variational Model for Image Filtering | EURASIP Journal on Applied Signal Processing 2004 16 2408-2422 2004 Hindawi Publishing Corporation A Nonlinear Entropic Variational Model for Image Filtering A. Ben Hamza Concordia Institute for Information Systems Engineering Concordia University Montreal Quebec H3G 1T7 Canada Email hamza@ Hamid Krim Department of Electrical and Computer Engineering North Carolina State University Raleigh NC 27695-7911 USA Email ahk@ JosianeZerubia Ariana Research Group INRIA I3S BP 93 06902 Sophia Antipolis Cedex France Em ail bia@ Received 12 August 2003 Revised 8 June 2004 We propose an information-theoretic variational filter for image denoising. It is a result of minimizing a functional subject to some noise constraints and takes a hybrid form of a negentropy variational integral for small gradient magnitudes and a total variational integral for large gradient magnitudes. The core idea behind this approach is to use geometric insight in helping to construct regularizing functionals and avoiding a subjective choice of a prior in maximum a posteriori estimation. Illustrative experimental results demonstrate a much improved performance of the approach in the presence of Gaussian and heavy-tailed noise. Keywords and phrases MAP estimation variational methods robust statistics differential entropy gradient descent flows image denoising. 1. INTRODUCTION In recent years variational methods and partial differential equations- PDE based methods 1 2 3 4 5 6 have been introduced to explicitly account for intrinsic geometry to address a variety of problems including image segmentation mathematical morphology motion estimation image classification and image denoising 7 8 9 10 11 12 . The latter will be the focus of the present paper. The problem of sig-nal image denoising has been addressed using a number of different techniques including wavelets 13 order statisticsbased filters 14 PDE-based algorithms 9 15 and variational approaches 16 17 .
