The Jump Set under Geometric Regularization. Part 1: Basic Technique and First-Order Denoising
نویسندگان
چکیده
منابع مشابه
The Jump Set under Geometric Regularization. Part 1: Basic Technique and First-Order Denoising
Abstract. Let u ∈ BV(Ω) solve the total variation denoising problem with L2-squared fidelity and data f . Caselles et al. [Multiscale Model. Simul. 6 (2008), 879–894] have shown the containment Hm−1(Ju \ Jf ) = 0 of the jump set Ju of u in that of f . Their proof unfortunately depends heavily on the co-area formula, as do many results in this area, and as such is not directly extensible to high...
متن کاملThe jump set under geometric regularisation. Part 1: Basic technique and first-order denoising
Let u ∈ BV(Ω) solve the total variation denoising problem with L-squared fidelity and data f . Caselles et al. [Multiscale Model. Simul. 6 (2008), 879–894] have shown the containment H(Ju \Jf ) = 0 of the jump set Ju of u in that of f . Their proof unfortunately depends heavily on the co-area formula, as do many results in this area, and as such is not directly extensible to higher-order, curva...
متن کاملThe jump set under geometric regularisation. Part 2: Higher-order approaches
In Part 1, we developed a new technique based on Lipschitz pushforwards for proving the jump set containment property H(Ju \ Jf ) = 0 of solutions u to total variation denoising. We demonstrated that the technique also applies to Huber-regularised TV. Now, in this Part 2, we extend the technique to higher-order regularisers. We are not quite able to prove the property for total generalised vari...
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ژورنال
عنوان ژورنال: SIAM Journal on Mathematical Analysis
سال: 2015
ISSN: 0036-1410,1095-7154
DOI: 10.1137/140976248