Total Variation Based Parameter-Free Model for Impulse Noise Removal. Issue 1 (20th February 2017)

• Record Type: Journal Article
• Authors: Sciacchitano, Federica; Dong, Yiqiu; Andersen, Martin S.
• Is Part Of: Numerical mathematics. Volume 10:Issue 1(2017)
• Page Start: 186
• Page End: 204
• Publication Date: 2017-02-20
• Subjects: 68U10, -- 94A08, -- 49J40, -- 52A41, -- 65K10, -- 90C47, -- 49M15; Image deblurring, -- image denoising, -- impulse noise, -- noise detector, -- primal-dual first-order algorithm, -- semismooth Newton method, -- total variation regularization; Numerical analysis -- Periodicals; Numerical analysis; Periodicals; 518.05
• DOI: 10.4208/nmtma.2017.m1613
• Languages: English
• ISSNs: 1004-8979

Abstract

Abstract: We propose a new two-phase method for reconstruction of blurred images corrupted by impulse noise. In the first phase, we use a noise detector to identify the pixels that are contaminated by noise, and then, in the second phase, we reconstruct the noisy pixels by solving an equality constrained total variation minimization problem that preserves the exact values of the noise-free pixels. For images that are only corrupted by impulse noise (i.e., not blurred) we apply the semismooth Newton's method to a reduced problem, and if the images are also blurred, we solve the equality constrained reconstruction problem using a first-order primal-dual algorithm. The proposed model improves the computational efficiency (in the denoising case) and has the advantage of being regularization parameter-free. Our numerical results suggest that the method is competitive in terms of its restoration capabilities with respect to the other two-phase methods.