An inertial forward-backward algorithm for monotone inclusions

In this paper, we propose an inertial forward backward splitting algorithm to compute a zero of the sum of two monotone operators, with one of the two operators being co-coercive. The algorithm is inspired by the accelerated gradient method of Nesterov, but can be applied to a much larger class of problems including convex-concave saddle point problems and general monotone inclusions. We prove convergence of the algorithm in a Hilbert space setting and show that several recently proposed first-order methods can be obtained as special cases of the general algorithm. Numerical results show that the proposed algorithm converges faster than existing methods, while keeping the computational cost of each iteration basically unchanged.Comment: The final publication is available at http://link.springer.co

Functional Liftings of Vectorial Variational Problems with Laplacian Regularization

We propose a functional lifting-based convex relaxation of variational problems with Laplacian-based second-order regularization. The approach rests on ideas from the calibration method as well as from sublabel-accurate continuous multilabeling approaches, and makes these approaches amenable for variational problems with vectorial data and higher-order regularization, as is common in image processing applications. We motivate the approach in the function space setting and prove that, in the special case of absolute Laplacian regularization, it encompasses the discretization-first sublabel-accurate continuous multilabeling approach as a special case. We present a mathematical connection between the lifted and original functional and discuss possible interpretations of minimizers in the lifted function space. Finally, we exemplarily apply the proposed approach to 2D image registration problems.Comment: 12 pages, 3 figures; accepted at the conference "Scale Space and Variational Methods" in Hofgeismar, Germany 201

Bilevel learning of regularization models and their discretization for image deblurring and super-resolution

Bilevel learning is a powerful optimization technique that has extensively been employed in recent years to bridge the world of model-driven variational approaches with data-driven methods. Upon suitable parametrization of the desired quantities of interest (e.g., regularization terms or discretization filters), such approach computes optimal parameter values by solving a nested optimization problem where the variational model acts as a constraint. In this work, we consider two different use cases of bilevel learning for the problem of image restoration. First, we focus on learning scalar weights and convolutional filters defining a Field of Experts regularizer to restore natural images degraded by blur and noise. For improving the practical performance, the lower-level problem is solved by means of a gradient descent scheme combined with a line-search strategy based on the Barzilai-Borwein rule. As a second application, the bilevel setup is employed for learning a discretization of the popular total variation regularizer for solving image restoration problems (in particular, deblurring and super-resolution). Numerical results show the effectiveness of the approach and their generalization to multiple tasks.Comment: Acknowledgments correcte

AMS radiocarbon dating of large za baobabs (Adansonia za) of Madagascar

© The Author(s), 2016. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in PLoS One 11 (2016): e0146977, doi:10.1371/journal.pone.0146977 .The article reports the radiocarbon investigation of Anzapalivoro, the largest za baobab (Adansonia za) specimen of Madagascar and of another za, namely the Big cistern baobab. Several wood samples collected from the large inner cavity and from the outer part/exterior of the tree were investigated by AMS (accelerator mass spectrometry) radiocarbon dating. For samples collected from the cavity walls, the age values increase with the distance into the wood up to a point of maximum age, after which the values decrease toward the outer part. This anomaly of age sequences indicates that the inner cavity of Anzapalivoro is a false cavity, practically an empty space between several fused stems disposed in a ring-shaped structure. The radiocarbon date of the oldest sample was 780 ± 30 bp, which corresponds to a calibrated age of around 735 yr. Dating results indicate that Anzapalivoro has a closed ring-shaped structure, which consists of 5 fused stems that close a false cavity. The oldest part of the biggest za baobab has a calculated age of 900 years. We also disclose results of the investigation of a second za baobab, the Big cistern baobab, which was hollowed out for water storage. This specimen, which consists of 4 fused stems, was found to be around 260 years old

PCA-based lung motion model

Organ motion induced by respiration may cause clinically significant targeting errors and greatly degrade the effectiveness of conformal radiotherapy. It is therefore crucial to be able to model respiratory motion accurately. A recently proposed lung motion model based on principal component analysis (PCA) has been shown to be promising on a few patients. However, there is still a need to understand the underlying reason why it works. In this paper, we present a much deeper and detailed analysis of the PCA-based lung motion model. We provide the theoretical justification of the effectiveness of PCA in modeling lung motion. We also prove that under certain conditions, the PCA motion model is equivalent to 5D motion model, which is based on physiology and anatomy of the lung. The modeling power of PCA model was tested on clinical data and the average 3D error was found to be below 1 mm.Comment: 4 pages, 1 figure. submitted to International Conference on the use of Computers in Radiation Therapy 201

Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle-Pock algorithm

The primal-dual optimization algorithm developed in Chambolle and Pock (CP), 2011 is applied to various convex optimization problems of interest in computed tomography (CT) image reconstruction. This algorithm allows for rapid prototyping of optimization problems for the purpose of designing iterative image reconstruction algorithms for CT. The primal-dual algorithm is briefly summarized in the article, and its potential for prototyping is demonstrated by explicitly deriving CP algorithm instances for many optimization problems relevant to CT. An example application modeling breast CT with low-intensity X-ray illumination is presented.Comment: Resubmitted to Physics in Medicine and Biology. Text has been modified according to referee comments, and typos in the equations have been correcte

Human polyomavirus 6 and 7 are associated with pruritic and dyskeratotic dermatoses

ABSTRACT Background: Human Polyomavirus 6 (HPyV6) and Human Polyomavirus 7 (HPyV7) are shed chronically from human skin. HPyV7, but not HPyV6, has been linked to a pruritic skin eruption of immunosuppression. Objective: We determined whether biopsies showing a characteristic pattern of dyskeratosis and parakeratosis might be associated with polyomavirus infection. Methods: We screened biopsies showing "peacock plumage" histology by PCR for human polyomaviruses. Cases positive for HPyV 6 or 7 were then analyzed by immunohistochemistry, electron microscopy (EM), immunofluorescence, quantitative PCR, and complete sequencing, including unbiased, next generation sequencing (NGS). Results: We identified three additional cases of HPyV6 or 7 skin infections. Expression of T antigen and viral capsid was abundant in lesional skin. Dual immunofluorescence staining experiments confirmed that HPyV7 primarily infects keratinocytes. High viral loads in lesional skin compared to normal skin and the identification of intact virions by both EM and NGS support a role for active viral infections in these skin diseases. Limitation: This was a small case-series of archived materials. Conclusion: We have found that HPyV6 and HPyV7 are associated with rare, pruritic skin eruptions with a unique histologic pattern and describe this entity as "HPyV6- and HPyV7-associated pruritic and dyskeratotic dermatosis (H6PD and H7PD).