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We compute the Fourier expansion of Hecke operators on vector-valued modular forms for the Weil representation associated to a lattice L. The Hecke operators considered in this paper include operators T(p^2l) where p is a prime dividing the level of the lattice L. Additionally, an explicit formula for a general type of Gauss sum associated to a lattice L drops out as a by-product.
EMDLAB: A toolbox for analysis of single-trial EEG dynamics using empirical mode decomposition
(2015)
Background:
Empirical mode decomposition (EMD) is an empirical data decomposition technique. Recently there is growing interest in applying EMD in the biomedical field.
New method:
EMDLAB is an extensible plug-in for the EEGLAB toolbox, which is an open software environment for electrophysiological data analysis.
Results:
EMDLAB can be used to perform, easily and effectively, four common types of EMD: plain EMD, ensemble EMD (EEMD), weighted sliding EMD (wSEMD) and multivariate EMD (MEMD) on EEG data. In addition, EMDLAB is a user-friendly toolbox and closely implemented in the EEGLAB toolbox.
Comparison with existing methods:
EMDLAB gains an advantage over other open-source toolboxes by exploiting the advantageous visualization capabilities of EEGLAB for extracted intrinsic mode functions (IMFs) and Event-Related Modes (ERMs) of the signal.
Conclusions:
EMDLAB is a reliable, efficient, and automated solution for extracting and visualizing the extracted IMFs and ERMs by EMD algorithms in EEG study.
Manual tasks in industrial production are often monotonous, leading to a decrease in concentration and motivation of the worker and thus to deficiencies in the products. With quality as well as performance requirements getting more and more stringent, workers need additional support by their work environment. We developed a novel approach providing worker assistance and inline quality assurance for manual workplaces. The prototypical system Smart Workbench (SWoB) uses a multimodal sensor interface consisting of a 3D depth sensor in combination with a 2D camera to control quality aspects of the product and track the work progress. The bidirectional flow of information is handled via an image processing driven gestural interface and the displaying of advice directly on the work surface. In this paper the developed system is introduced and the current state of evaluating its industrial usage with a manual quality control and packaging task reported.
PURPOSE
Reconstruction of x-ray computed tomography (CT) data remains a mathematically challenging problem in medical imaging. Complementing the standard analytical reconstruction methods, sparse regularization is growing in importance, as it allows inclusion of prior knowledge. The paper presents a method for sparse regularization based on the curvelet frame for the application to iterative reconstruction in x-ray computed tomography.
METHODS
In this work, the authors present an iterative reconstruction approach based on the alternating direction method of multipliers using curvelet sparse regularization.
RESULTS
Evaluation of the method is performed on a specifically crafted numerical phantom dataset to highlight the method's strengths. Additional evaluation is performed on two real datasets from commercial scanners with different noise characteristics, a clinical bone sample acquired in a micro-CT and a human abdomen scanned in a diagnostic CT. The results clearly illustrate that curvelet sparse regularization has characteristic strengths. In particular, it improves the restoration and resolution of highly directional, high contrast features with smooth contrast variations. The authors also compare this approach to the popular technique of total variation and to traditional filtered backprojection.
CONCLUSIONS
The authors conclude that curvelet sparse regularization is able to improve reconstruction quality by reducing noise while preserving highly directional features.
A Step Towards the Automated Diagnosis of Parkinson's Disease: Analyzing Handwriting Movements
(2015)
Parkinson’s disease (PD) has affected millions of people world-wide, being its major problem the loss of movements and, consequently, the ability of working and locomotion. Although we can find several works that attempt at dealing with this problem out there, most of them make use of datasets composed by a few subjects only. In this work, we present some results toward the automated diagnosis of PD by means of computer vision-based techniques in a dataset composed by dozens of patients, which is one of the main contributions of this work. The dataset is part of a joint research project that aims at extracting both visual and signal-based information from healthy and PD patients in order to go forward the early diagnosis of PD patients. The dataset is composed by handwriting clinical exams that are analyzed by means of image processing and machine learning techniques, being the preliminary results encouraging and promising. Additionally, a new quantitative feature to measure the amount of tremor of an individual’s handwritten trace called Mean Relative Tremor is also presented.
Steigende Fallzahlen von Menschen mit Demenz, der komplexe Bedarf und eine unzureichende Versorgungsrealität erfordern innovative und nachhaltige Lösungsansätze. Der Beitrag stellt ein Versorgungsmodell für Menschen mit Demenz vor, das infolge akuter Versorgungsprobleme entwickelt wurde und das eine umfassende, patientenorientierte Versorgung über Sektorengrenzen hinweg umsetzt. Beschrieben werden Struktur und Bedingungen gelingender Kooperation und umfassender Versorgung.
Artifacts in Incomplete Data Tomography with Applications to Photoacoustic Tomography and Sonar
(2015)
We develop a paradigm using microlocal analysis that allows one to characterize the visible and added singularities in a broad range of incomplete data tomography problems. We give precise characterizations for photoacoustic and thermoacoustic tomography and sonar, and provide artifact reduction strategies. In particular, our theorems show that it is better to arrange sonar detectors so that the boundary of the set of detectors does not have corners and is smooth. To illustrate our results, we provide reconstructions from synthetic spherical mean data as well as from experimental photoacoustic data.
We propose a new algorithmic approach to the non-smooth and non-convex Potts problem (also called piecewise-constant Mumford–Shah problem) for inverse imaging problems. We derive a suitable splitting into specific subproblems that can all be solved efficiently. Our method does not require a priori knowledge on the gray levels nor on the number of segments of the reconstruction. Further, it avoids anisotropic artifacts such as geometric staircasing. We demonstrate the suitability of our method for joint image reconstruction and segmentation. We focus on Radon data, where we in particular consider limited data situations. For instance, our method is able to recover all segments of the Shepp–Logan phantom from seven angular views only. We illustrate the practical applicability on a real positron emission tomography dataset. As further applications, we consider spherical Radon data as well as blurred data.
In-plant milk-run systems are transportation systems, where materials are delivered from a central storage area to several points of use on defined routes and in short intervals. Milk-run systems generally enable frequent deliveries in smaller lot sizes with short lead times and low inventory at the points of use. In real milk-run systems, the number of deliveries per interval varies due to, e.g., variations in the production program. To enable efficient and stable milk-run system operations, these systems therefore must be able to cope with peaks in the number of deliveries. We develop different strategies for handling these delivery peaks and evaluate them with respect to delivery cost, lead time and service level using real material consumption data from two large companies from the automotive industry.