Total Variation Based Parameter-Free Model for Impulse Noise Removal

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.

Anℓp-ℓqminimization method with cross-validation for the restoration of impulse noise co

“…Similarly as the two-phase methods described in [3,6,7,30], it may be attractive to preprocess images that are contaminated by impulse noise by a median filter. This would result in a fully automatic two-phase method.…”

“…Several other methods have been developed for the restoration of images that are corrupted by blur and impulse noise. In particular, two-phase strategies have been shown to yield accurate restorations; see, e.g., [3,6,7,30]. These methods first identify pixels that are contaminated by impulse noise by means of a median-type filter.…”

“…In the current literature on two-phase methods, the functional to be minimized in the second phase is usually convex and little attention is given to the selection of the regularization parameter. In fact, only Sciacchitano et al [30] propose a two-phase method that does not require a user to specify a regularization parameter. None of the methods mentioned is designed to remove mixed noise, i.e., noise that is made up of both impulse noise and Gaussian noise.…”

Applications of the Bounded Total Variation Denoising Method to Urban Traffic Analysis

“…Refs. [1,2,4,7,9,10,13,17,21,24,26,27,34,35,40,42,43,46]. Some of them, such as wavelet method [37,47] and the compressive sensing method [39,48,49], are also used in traffic analysis.…”

Compound PDE-Based Additive Denoising Solution Combining an Improved Anisotropic Diffusion Model to a 2D Gaussian Filter Kernel

“…[5,23]. On the other hand the total variation (TV) denoising scheme proposed by Rudin et al [19], initiated the development of numerous PDE variational filtering techniques [1,3,7,8,11,15,20,22].…”