Image Recovery Using Functions of Bounded Variation and Sobolev Spaces of Negative Differentiability
نویسندگان
چکیده
In this work we wish to recover an unknown image from a blurry, or noisy-blurry version. We solve this inverse problem by energy minimization and regularization. We seek a solution of the form u + v, where u is a function of bounded variation (cartoon component), while v is an oscillatory component (texture), modeled by a Sobolev function with negative degree of differentiability. We give several results of existence and characterization of minimizers of the proposed optimization problem. Experimental results show that this cartoon + texture model better recovers textured details in natural images, by comparison with the more standard models where the unknown is restricted only to the space of functions of bounded variation.
منابع مشابه
Image Restoration and Decomposition via Bounded Total Variation and Negative Hilbert-Sobolev Spaces
We propose a new class of models for image restoration and decomposition by functional minimization. Following ideas of Y. Meyer in a total variation minimization framework of L. Rudin, S. Osher, and E. Fatemi, our model decomposes a given (degraded or textured) image u0 into a sum u+ v. Here u ∈ BV is a function of bounded variation (a cartoon component), while the noisy (or textured) componen...
متن کاملOn Polar Cones and Differentiability in Reflexive Banach Spaces
Let $X$ be a Banach space, $Csubset X$ be a closed convex set included in a well-based cone $K$, and also let $sigma_C$ be the support function which is defined on $C$. In this note, we first study the existence of a bounded base for the cone $K$, then using the obtained results, we find some geometric conditions for the set $C$, so that ${mathop{rm int}}(mathrm{dom} sigma_C) neqem...
متن کاملC-interior regularity for minimizers of a class of variational problems with linear growth related to image inpainting in higher dimensions
We investigate a modification of the total variation image inpainting method in higher dimensions, i.e. we assume n ≥ 3 and discuss existence as well as smoothness of corresponding solutions to the underlying variational problem. Precisely, we are going to establish that our type of a linear growth regularization admits a unique solution in the Sobolev space W 1,1(Ω), i.e. we do not need to con...
متن کاملOn Poincaré-wirtinger Inequalities in Spaces of Functions of Bounded Variation
The goal of this paper is to extend Poincaré-Wirtinger inequalities from Sobolev spaces to spaces of functions of bounded variation of second order.
متن کاملLectures on Lipschitz Analysis
(1.1) |f(a)− f(b)| ≤ L |a− b| for every pair of points a, b ∈ A. We also say that a function is Lipschitz if it is L-Lipschitz for some L. The Lipschitz condition as given in (1.1) is a purely metric condition; it makes sense for functions from one metric space to another. In these lectures, we concentrate on the theory of Lipschitz functions in Euclidean spaces. In Section 2, we study extensio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010