The restoration of blurred images corrupted by Poisson noise is an important task in various applications such as astronomical imaging, electronic microscopy, single particle emission computed ...tomography (SPECT) and positron emission tomography (PET). In this paper, we focus on solving this task by minimizing an energy functional consisting of the I-divergence as similarity term and the TV regularization term. Our minimizing algorithm uses alternating split Bregman techniques (alternating direction method of multipliers) which can be reinterpreted as Douglas-Rachford splitting applied to the dual problem. In contrast to recently developed iterative algorithms, our algorithm contains no inner iterations and produces nonnegative images. The high efficiency of our algorithm in comparison to other recently developed algorithms to minimize the same functional is demonstrated by artificial and real-world numerical examples.
The problem of reconstructing a watertight surface from a finite set of oriented points has received much attention over the last decades. In this paper, we propose a general higher order framework ...for surface reconstruction. It is based on the idea that position and normal defined by each oriented point can be used to construct an implicit local description of the unknown surface. On the one hand, this allows us to systematically explain and relate several popular methods, for example implicit moving least squares, smooth signed distance surface reconstruction as well as (screened) Poisson surface reconstruction. On the other hand, it allows to derive and discuss a number of new approaches for reconstructing either the signed distance or the indicator function of the sought object. All of these approaches are able to achieve competitive results but one of them turns out to be especially promising. To improve reconstructions in difficult real world scenarios where point clouds have been estimated from colour images, we introduce a hull constraint that encourages the surface to stay within a given region. Our framework is implemented on the GPU using a recent cyclic scheme called Fast Jacobi, which combines low implementational effort with high efficiency.
On vector and matrix median computation Setzer, S.; Steidl, G.; Teuber, T.
Journal of computational and applied mathematics,
February 2012, 2012-02-00, 20120201, Letnik:
236, Številka:
8
Journal Article
Recenzirano
Odprti dostop
The aim of this paper is to gain more insight into vector and matrix medians and to investigate algorithms to compute them. We prove relations between vector and matrix means and medians, ...particularly regarding the classical structure tensor. Moreover, we examine matrix medians corresponding to different unitarily invariant matrix norms for the case of symmetric 2×2 matrices, which frequently arise in image processing. Our findings are explained and illustrated by numerical examples. To solve the corresponding minimization problems, we propose several algorithms. Existing approaches include Weiszfeld’s algorithm for the computation of ℓ2 vector medians and semi-definite programming, in particular, second order cone programming, which has been used for matrix median computation. In this paper, we adapt Weiszfeld’s algorithm for our setting and show that also two splitting methods, namely the alternating direction method of multipliers and the parallel proximal algorithm, can be applied for generalized vector and matrix median computations. Besides, we compare the performance of these algorithms numerically and apply them within local median filters.
Experimental results are presented from vacuum-ultraviolet free-electron laser (FEL) operating in the self-amplified spontaneous emission (SASE) mode. The generation of ultrashort radiation pulses ...became possible due to specific tailoring of the bunch charge distribution. A complete characterization of the linear and nonlinear modes of the SASE FEL operation was performed. At saturation the FEL produces ultrashort pulses (30-100 fs FWHM) with a peak radiation power in the GW level and with full transverse coherence. The wavelength was tuned in the range of 95-105 nm.
Many scientific disciplines ranging from physics, chemistry and biology to material sciences, geophysics and medical diagnostics need a powerful X-ray source with pulse lengths in the femtosecond ...range 1-4. This would allow, for example, time-resolved observation of chemical reactions with atomic resolution. Such radiation of extreme intensity, and tunable over a wide range of wavelengths, can be accomplished using high-gain free-electron lasers (FEL) 5-10. Here we present results of the first successful operation of an FEL at a wavelength of 32 nm, with ultra-short pulses (25 fs FWHM), a peak power at the Gigawatt level, and a high degree of transverse and longitudinal coherence. The experimental data are in full agreement with theory. This is the shortest wavelength achieved with an FEL to date and an important milestone towards a user facility designed for wavelengths down to 6 nm. With a peak brilliance exceeding the state-of-the-art of synchrotron radiation sources 4 by seven orders of magnitude, this device opens a new field of experiments, and it paves the way towards sources with even shorter wavelengths, such as the Linac Coherent Light Source 3 at Stanford, USA, and the European X-ray Free Electron Laser Facility 4 in Hamburg, Germany.
We present the first observation of self-amplified spontaneous emission (SASE) in a free-electron laser (FEL) in the vacuum ultraviolet regime at 109 nm wavelength (11 eV). The observed free-electron ...laser gain (approximately 3000) and the radiation characteristics, such as dependency on bunch charge, angular distribution, spectral width, and intensity fluctuations, are all consistent with the present models for SASE FELs.
Desmosomes are adhesive intercellular junctions prominent in the skin and heart. Loss of desmosome function is associated with severe congenital and acquired disorders characterized by tissue ...fragility. Pemphigus vulgaris (PV) is an autoimmune disorder in which antibodies are directed against the desmosomal adhesion molecule Dsg3, resulting in severe mucosal erosions and epidermal blistering. To define the mechanisms by which Dsg3 autoantibodies disrupt keratinocyte adhesion, the fate of PV IgG and various desmosomal components was monitored in primary human keratinocytes exposed to PV patient IgG. PV IgG initially bound to keratinocyte cell surfaces and colocalized with desmosomal markers. Within 6 h after PV IgG binding to Dsg3, electron microscopy revealed that desmosomes were dramatically disrupted and keratinocyte adhesion was severely compromised. Immunofluorescence analysis indicated that PV IgG and Dsg3 were rapidly internalized from the cell surface in a complex with plakoglobin but not desmoplakin. Dsg3 internalization was associated with retraction of keratin filaments from cell-cell borders. Furthermore, the internalized PV IgG-Dsg3 complex colocalized with markers for both endosomes and lysosomes, suggesting that Dsg3 was targeted for degradation. Consistent with this possibility, biotinylation experiments demonstrated that soluble Dsg3 cell surface pools were rapidly depleted followed by loss of detergent-insoluble Dsg3. These findings demonstrate that Dsg3 endocytosis, keratin filament retraction, and the loss of keratinocyte cell-cell adhesion are coordinated responses to PV IgG.
Methods for image restoration which respect edges and other important features are of fundamental importance in digital image processing. In this paper, we present a novel technique for the ...restoration of images containing rotated (linearly transformed) rectangular shapes which avoids the round-off effects at vertices produced by known edge-preserving denoising techniques. Following an idea of Berkels et al. our approach is also based on two steps: the determination of the angles related to the rotated shapes and a subsequent restoration step which incorporates the knowledge of the angles. However, in contrast to Berkels et al., we find the smoothed rotation angles of the shapes by minimizing a simple quadratic functional without constraints which involves only first order derivatives so that we finally have to solve only a linear system of equations. Moreover, we propose to perform the restoration step either by quadratic programming or by solving an anisotropic diffusion equation. We focus on a discrete approach which approximates derivatives by finite differences. Particular attention is paid to the choice of the difference filters. We prove some relations concerning the preservation of rectangular shapes for our discrete setting. Finally, we present numerical examples for the denoising of artificial images with rotated rectangles and parallelograms and for the denoising of a real-world image.
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