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...pace methods by employing the concept of Bregman distance regularization. The latter has been derived in [8] with a detailed analysis for Gaussian-type problems (5) and generalized to time-continuity =-=[9]-=- and Lp-norm data fitting terms [10]. Here, in the case of Poisson-type problems, the method consists in computing a minimizer u1 of (6) with R(u) :=|u|BV first. Updates are determined successively by...

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...lems, for examples [30, 29, 40, 39, 42, 43, 27, 9, 2, 7, 41] just to mention a few. In the literature, some authors also discuss other non-quadratic fidelity terms besides the L1 fidelity term, e.g., =-=[13, 33, 34]-=-. In this paper, we consider the case where the images are digital images so that their pixel values have to lie in a certain dynamic range [l, u]. For example, for 8-bit images, we have [l, u] = [0, ...

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...is paper we analyze iterative regularization with the Bregman distance of the total variation semi norm. Moreover, we prove existence of a solution of the corresponding flow equation as introduced in =-=[8]-=- in a functional analytical setting using methods from convex analysis. The results are generalized to variational denoising methods with Lp-norm fit-to-data terms and Bregman distance regularization ...

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...luding city terrain and cortical surfaces. 1. Introduction Variational and partial differential equations (PDEs) based image denoising models have had great success in the past twenty years (see e.g. =-=[18, 16, 3, 25]-=-). The goal is to remove noise (in the form of random high frequency oscillations) from an image, while keeping features, e.g. sharp edges and textures. Recently, some of the models used for image den...

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...hing time-delay parameter in either medium is included. The double-porosity limit of Richards’ equation with dynamic capillary pressure is obtained. Keywords: homogenization; pseudoparabolic equations; fractured porous media; dynamic capillary pressure AMS Subject Classifications: Primary 35B27; 35K70; Secondary 74Q10; 76S05 1. Introduction Pseudoparabolic equations arise in a range of applications from radiation with timedelay [1], degenerate double-diffusion and heat-conduction models [2,3] and resolution of ill-posed problems [4] through recently developed applications in level set methods [5] and models of lightning propagation [6]. They were first analysed in [7–9]; see [10] for an extensive review and bibliography. Here we are interested in a degenerate pseudoparabolic equation arising from modelling dynamic capillary pressure in unsaturated flow; specifically, we study the case of flow in heterogeneous media in which the coefficients are periodic on a fine scale. The classical Richards equation for flow through a partially saturated porous medium with porosity (x) and permeability K(x) takes the form ðxÞ @uðt, xÞ @t þ r KðxÞ kwðuðt, xÞÞ w r Pcðuðt, xÞÞ GDðxÞð Þ 0, ð1Þ...

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...iplicative noise, this assumption has been formalized using Markov random fields, under the Bayesian framework [14], [2] and, more recently, using total variation (TV) regularization [1], [12], [16], =-=[17]-=-. 1.3. Contribution In this paper, we adopt TV regularization. In comparison with the canonical additive Gaussian noise model, we face two difficulties: the noise is multiplicative; the noise is non-G...

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...rs, ranging from basic regularization properties (cf. e.g. [1, 28]) over error estimation (cf. [22, 23, 56, 57, 11, 43, 49]) to corrections of inherent bias by iterative and time-flow techniques (cf. =-=[60, 54, 19, 18, 71]-=-). Singular values and vectors did so far not play any role in the analysis of such methods and it is common belief that their use is restricted to linear regularization methods. This is not surprisin...

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...get the highest SNR value using less iterations than the classic PM diffusion. As comparisons, Figure 5 (right column) shows the results by a so-called inverse scale space method recently proposed in =-=[7]-=-, in which we use the PM diffusivity, step size 0.3 and 70 iterations. We 17 �s50 100 150 200 250 50 100 150 200 250 50 100 150 200 250 SNR = 9.98 dB 50 100 150 200 250 50 100 150 200 250 SNR = 12.22 ...