Denoising is the problem of removing noise from an image. The most commonly studied case is with additive white Gaussian noise (AWGN), where the observed noisy image f is related to the underlying true image u by a n d η is at each point in space independently and identically distributed as a zero-mean Gaussian random variable. Rudin, Osher, and Fatemi [9]. The TV regularization technique has since been applied to a multitude of other imaging problems, see for example Chan and Shen's book [20] . We focus here on the split Bregman algorithm of Goldstein and Osher [31] for TVregularized denoising. Total variation (TV) regularization is a technique that was originally developed for AWGN image denoising by Rudin, Osher, and Fatemi [9] proposed to estimate the denoised image u as the solution of a minimization problem, where λ is a positive parameter. This problem is referred to as the Rudin-Osher-Fatemi or ROF problem. Denoising is performed as an infinite-dimensional minimization problem, where the search space is all bounded variation (BV) images. A function u is in BV(Ω) if it is integrable and there exists a Radon measure Du such that This measure Du is the distributional gradient of u. When u is smooth, Du(x) = ∇u(x) dx. The total variation (TV) seminorm of u is published reference
The GFL is related to the technique known as total variation denoising in the signal processing literature REF .
Rudin-Osher-Fatemi Total Variation Denoising using Split Bregman
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