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Mumford-Shah models and piecewise-constant Mumford-Shah models are frequently used for reconstruction and segmentation in imaging and inverse problems. Higher-order models have the property that they better preserve polynomial trends while still preserving sharp edges in the underlying signals and avoiding the so-called gradient limit effect. We first introduce the respective models and point out relevant literature. Then we focus on recent solution strategies of the authors based on dynamic programming as well as the alternating direction of multipliers for the numerical solution of such models and illustrate their potential use. [ABSTRACT FROM AUTHOR]

Magnetic Particle Imaging is a scanning modality that exploits the response of superparamagnetic nanoparticles to a dynamic magnetic field. In the multivariate case measurement-based reconstruction approaches are common and involve a system-matrix whose acquisition is time consuming and needs to be repeated whenever the scanning setup changes. Our approach uses a mathematical model, based on the MPI encoding of the signal, that is in particular independent of the scanning trajectories. We present basic ways of leveraging this independence property to enhance the quality of the reconstruction by using data from different scans. We demonstrate the potential of our approach with examples. [ABSTRACT FROM AUTHOR]

Magnetic Particle Imaging (MPI) is an emerging imaging modality and a very active field of research. In the multivariate MPI setup images are usually reconstructed using a system matrix which is obtained by a time-consuming measurement procedure. We approach the reconstruction problem by employing a mathematical model which is based on the MPI signal encoding and the properties of the MPI Core Operator. Here, we present a reconstruction algorithm which features two stages: in the first stage, we estimate components of the MPI Core Operator by using a variational formulation. In the second stage, the image is reconstructed by regularized deconvolution applied to the components of the MPI Core Operator robustly estimated in the first stage. We demonstrate the potential of our algorithm with examples. [ABSTRACT FROM AUTHOR]

Magnetic Particle Imaging (MPI) is an emerging imaging modality and is currently a very active field of research. In the multivariate MPI setup images are usually reconstructed using a system matrix which is obtained by a time-consuming measurement procedure. We approach the reconstruction problem by employing a mathematical model which we introduced in an earlier work and which is based on the MPI signal encoding. Here, we present an enhanced two-stage reconstruction algorithm derived from the decomposition of the imaging process provided by the model. In the first stage of the algorithm we propose a variational formulation together with adequate regularization which improves our reconstruction results. [ABSTRACT FROM AUTHOR]

Drone detection is an important yet challenging task in the context of object detection. The development of robust and reliable drone detection systems requires large amounts of labeled data, especially when using deep learning (DL) models. Unfortunately, acquiring real data is expensive, time-consuming, and often limited by external factors. This makes synthetic data a promising approach to addressing data deficiencies. In this paper, we present a data generation pipeline based on Unreal Engine4.25 and Microsoft AirSim, designed to create synthetic labeled data for drone detection using three-dimensional environments. As part of an ablation study, we investigate the potential use of synthetic data in drone detection by analyzing different training strategies, influencing factors, and data generation parameters, specifically related to the visual appearance of a drone. [ABSTRACT FROM AUTHOR]