Image denoising algorithms using norm minimization techniques
No Thumbnail Available
Date
2021-05-25
Journal Title
Journal ISSN
Volume Title
Publisher
University of Oum El Bouaghi
Abstract
Image denoising is one of the fundamental image processing problems. Noise removal is an important step in the image restoration process. In this paper, firstly we develop and implement two different image denoising algorithms based on norm minimization, namely `1 and `2-regularization applied to images contaminated by gaussian noise. Then, after their discretization and implementation, we perform a comparison between the two methods using several test images.
Through this study, the algorithm which minimizes `2-norm of gradient of image has a unique solution and it’s easy to implement, but it doesn’t accept contour discontinuities, causing the obtained solution to be smooth. The `2-norm will blur the edges of the image. In order to preserve sharp edges, `1-norm is introduced.
There are different methods to solve the problem of energy minimization. In this work, we have chosen the discretization finite difference method before applying the gradient descent algorithm to optimize the signal (2D grayscale images) denoising functionality.
Experiments results, show that `1 regularization encourages image smoothness while allowing for presence of jumps and discontinuities, a key feature for image processing because of the importance of edges in human vision.
Description
Keywords
Denoising, `1-norm; `2-norm; finite difference discretization,