Total Variation Based Parameter-Free Model for Impulse Noise Removal

Federica Sciacchitano, Yiqiu Dong, Martin Skovgaard Andersen

Research output: Contribution to journalJournal articleResearchpeer-review


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.
Original languageEnglish
JournalNumerical Mathematics-theory Methods and Applications
Issue number1
Pages (from-to)186-204
Publication statusPublished - 2017

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