Variational Regularization for Multi-Channel Image Denoising
Abstract
Image restoration from noisy observations is an inverse problem. Total variation (TV) is widely used to regularize this problem. TV preserves object boundaries better than a quadratic regularizer; however, it performs poor in low-textured image regions because it generates undesirable staircase artefacts. Furthermore, TV can preserve sharp horizontal and vertical edges; however, it causes the unnecessary smoothing of edges at an angle other than 0o or 90o. This problem arises because TV minimizes the gradient magnitude. Therefore, to preserve sharp boundaries, the design of an efficient variational regularizer is crucial. This paper presents a novel regularizer for the denoising of multi-channel vector valued image. The proposed regularizer uses horizontal, vertical as well as diagonal derivatives, and imposes the intensity continuity of partial image derivatives at each pixel of the underlying image. Experiments reveal that the proposed regularizer preserves edges and object boundaries better than TV based regularizers. This regularizer is also able to reduce undesirable staircase artefacts produced by TV in flat image regions.
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