Objective.Magnetic particle imaging (MPI) is an emerging medical imaging modality which has gained increasing interest in recent years. Among the benefits of MPI are its high temporal resolution, and that the technique does not expose the specimen to any kind of ionizing radiation. It is based on the non-linear response of magnetic nanoparticles to an applied magnetic field. From the electric signal measured in receive coils, the particle concentration has to be reconstructed. Due to the ill-posedness of the reconstruction problem, various regularization methods have been proposed for reconstruction ranging from early stopping methods, via classical Tikhonov regularization and iterative methods to modern machine learning approaches. In this work, we contribute to the latter class: we propose a Plug-and-Play approach based on a generic zero-shot denoiser with anℓ1-prior.Approach.We validate the reconstruction parameters of the method on a hybrid dataset and compare it with the baseline Tikhonov, ART, DIP and the previous PP-MPI, which is a Plug-and-Play method with denoiser trained on MPI-friendly data.Main results.We derive a Plug-and-Play reconstruction method based on a generic zero-shot denoiser. Addressing (hyper)parameter selection, we perform an extended parameter search on a hybrid validation dataset we produced and apply the derived parameters for reconstruction on the 3D Open MPI Dataset. We offer a quantitative and qualitative evaluation of the zero-shot Plug-and-Play approach on the 3D Open MPI dataset with the validated parameters. Moreover, we show the quality of the approach with different levels of preprocessing of the data.Significance.The proposed method employs a zero-shot denoiser which has not been trained for the MPI reconstruction task and therefore saves the cost for training. Moreover, it offers a method that can be potentially applied in future MPI contexts.

Magnetic Particle Imaging (MPI) is a promising noninvasive in vivo imaging modality that makes it possible to map the spatial distribution of superparamagnetic nanoparticles by exposing them to dynamic magnetic fields. In the Field-Free Line (FFL) scanner topology, the spatial encoding of the particle distribution is performed by applying magnetic fields vanishing on straight lines. The voltage induced in the receiving coils by the particles when exposed to the magnetic fields constitute the signal from which the particle distribution is to be reconstructed. To avoid lengthy calibration, model-based reconstruction formulae have been developed for the 2D FFL scanning topology. In this work we develop reconstruction formulae for 3D FFL. Moreover, we provide a model-based reconstruction algorithm for 3D FFL and we validate it with a numerical experiment.

Computed tomography from a low radiation dose (LDCT) is challenging due to high noise in the projection data. Popular approaches for LDCT image reconstruction are two-stage methods, typically consisting of the filtered backprojection (FBP) algorithm followed by a neural network for LDCT image enhancement. Two-stage methods are attractive for their simplicity and potential for computational efficiency, typically requiring only a single FBP and a neural network forward pass for inference. However, the best reconstruction quality is currently achieved by unrolled iterative methods (Learned Primal-Dual and ItNet), which are more complex and thus have a higher computational cost for training and inference. We propose a method combining the simplicity and efficiency of two-stage methods with state-of-the-art reconstruction quality. Our strategy utilizes a neural network pretrained for Gaussian noise removal from natural grayscale images, fine-tuned for LDCT image enhancement. We call this method FBP-DTSGD (Domain and Task Shifted Gaussian Denoisers) as the fine-tuning is a task shift from Gaussian denoising to enhancing LDCT images and a domain shift from natural grayscale to LDCT images. An ablation study with three different pretrained Gaussian denoisers indicates that the performance of FBP-DTSGD does not depend on a specific denoising architecture, suggesting future advancements in Gaussian denoising could benefit the method. The study also shows that pretraining on natural images enhances LDCT reconstruction quality, especially with limited training data. Notably, pretraining involves no additional cost, as existing pretrained models are used. The proposed method currently holds the top mean position in the LoDoPaB-CT challenge.

Floods are an increasingly common global threat, causing emergencies and severe damage to infrastructure. During crises, organisations such as the World Food Programme use remotely sensed imagery, typically obtained through drones, for rapid situational analysis to plan life-saving actions. Computer Vision tools are needed to support task force experts on-site in the evaluation of the imagery to improve their efficiency and to allocate resources strategically. We introduce the BlessemFlood21 dataset to stimulate research on efficient flood detection tools. The imagery was acquired during the 2021 Erftstadt-Blessem flooding event and consists of high-resolution and georeferenced RGB-NIR images. In the resulting RGB dataset, the images are supplemented with detailed water masks, obtained via a semi-supervised human-in-the-loop technique, where in particular the NIR information is leveraged to classify pixels as either water or non-water. We evaluate our dataset by training and testing established Deep Learning models for semantic segmentation. With BlessemFlood21 we provide labeled high-resolution RGB data and a baseline for further development of algorithmic solutions tailored to flood detection in RGB imagery.

Flooding is one of the most common natural disasters, causing emergencies and significant damage to infrastructure. Amid crises, entities such as the World Food Program employ remotely sensed images, usually via drones, to analyze the situation quickly and plan life-saving interventions. Suitable Computer Vision (CV) tools are necessary to assist experts of first responder teams with the analysis of the image data, increasing their productivity and enabling strategic resource allocation. Many state-of-the-art CV-tools use supervised Deep Learning (DL) techniques, for which labeled training data is needed. In this paper, we present the BlessemFlood21 dataset to support the development of DL-based CV-tools for the task of advanced flood analysis in non-coastal river flood scenarios. In particular, we address the problem of segmenting water from RGB images. The presented resulting dataset consists of high-definition, georeferenced RGB images labeled with precise water masks. The water masks are derived using a proposed semi-automatic human-in-the-loop strategy based on the use of additionally imaged NIR data together with a classical Random Forest approach. We assess the resulting dataset and provide a baseline for future advancements in flood mapping by training and evaluating three different state-of-the-art segmentation models (UNet++, DeepLabV3+, SegFormer-B5). Further, we showcase the potential use of the dataset with several experiments. In particular, we compare with the Floodnet dataset and, we employ the segmentation models trained on our dataset together with a Digital Elevation Model to showcase the potential to estimate flood water levels.

We contribute to the mathematical modeling and analysis of magnetic particle imaging which is a promising new in-vivo imaging modality. Concerning modeling, we develop a structured decomposition of the imaging process and extract its core part which we reveal to be common to all previous contributions in this context. The central contribution of this paper is the development of reconstruction formulae for MPI in 2D and 3D. Until now, in the multivariate setup, only time consuming measurement-based approaches are available, whereas reconstruction formulae are only available in 1D. The 2D and the 3D (describing the real world) reconstruction formulae which we derive here are significantly different from the 1D situation-in particular there is no Dirac property in dimensions greater than one in the high resolution limit. As a further result of our analysis, we conclude that the reconstruction problem in MPI is severely ill-posed. Finally, we obtain a model-based reconstruction algorithm.

In this paper we construct a parametrization-free embedding technique for numerically evolving reaction-diffusion PDEs defined on algebraic curves that possess an isolated singularity. In our approach, we first desingularize the curve by appealing to techniques from algebraic geometry. We create a family of smooth curves in higher dimensional space that correspond to the original curve by projection. Following this, we pose the analogous reaction-diffusion PDE on each member of this family and show that the solutions (their projection onto the original domain) approximate the solution of the original problem. Finally, we compute these approximants numerically by applying the Closest Point Method which is an embedding technique for solving PDEs on smooth surfaces of arbitrary dimension or codimension, and is thus suitable for our situation. In addition, we discuss the potential to generalize the techniques presented for higher-dimensional surfaces with multiple singularities.

Image inpainting is the process of touching up damaged or unwanted portions of a picture and is an important task in image processing. For this purpose Bornemann and März (J Math Imaging Vision, 28:259–278, 2007) introduced a very efficient method, called image inpainting based on coherence transport, that fills the missing region by advecting the image information along integral curves of a coherence vector field from the boundary toward the interior of the hole. The mathematical model behind this method is a first-order functional advection partial differential equation posed on a compact domain with all inflow boundaries. We show that this problem is well posed under certain conditions.

We demonstrate a method for filtering images defined on curved surfaces embedded in 3D. Applications are noise removal and the creation of artistic effects. Our approach relies on in-surface diffusion: we formulate Weickert's edge/coherence enhancing diffusion models in a surface-intrinsic way. These diffusion processes are anisotropic and the equations depend non-linearly on the data. The surface-intrinsic equations are dealt with the closest point method, a technique for solving partial differential equations (PDEs) on general surfaces. The resulting algorithm has a very simple structure: we merely alternate a time step of a 3D analog of the in-surface PDE in a narrow 3D band containing the surface with a reconstruction of the surface function. Surfaces are represented by a closest point function. This representation is flexible and the method can treat very general surfaces. Experimental results include image filtering on smooth surfaces, open surfaces, and general triangulated surfaces.

We introduce a method-of-lines formulation of the closest point method, a numerical technique for solving partial differential equations (PDEs) defined on surfaces. This is an embedding method, which uses an implicit representation of the surface in a band containing the surface. We define a modified equation in the band, obtained in a straightforward way from the original evolution PDE, and show that the solutions of this equation are consistent with those of the surface equation. The resulting system can then be solved with standard implicit or explicit time-stepping schemes, and the solutions in the band can be restricted to the surface. Our derivation generalizes existing formulations of the closest point method and is amenable to standard convergence analysis.

We demonstrate a method for removing noise from images or other data on curved surfaces. Our approach relies on in-surface diffusion: we formulate both the Gaussian diffusion and Perona-Malik edge-preserving diffusion equations in a surface-intrinsic way. Using the Closest Point Method, a recent technique for solving partial differential equations (PDEs) on general surfaces, we obtain a very simple algorithm where we merely alternate a time step of the usual Gaussian diffusion (and similarly Perona-Malik) in a small 3D volume containing the surface with an interpolation step. The method uses a closest point function to represent the underlying surface and can treat very general surfaces. Experimental results include image filtering on smooth surfaces, open surfaces, and general triangulated surfaces.

The closest point method for solving partial differential equations (PDEs) posed on surfaces was recently introduced by Ruuth and Merriman [J. Comput. Phys., 227 (2008), pp. 1943-1961] and successfully applied to a variety of surface PDEs. In this paper we study the theoretical foundations of this method. The main idea is that surface differentials of a surface function can be replaced with Cartesian differentials of its closest point extension, i.e., its composition with a closest point function. We introduce a general class of these closest point functions (a subset of differentiable retractions), show that these are exactly the functions necessary to satisfy the above idea, and give a geometric characterization of this class. Finally, we construct some closest point functions and demonstrate their effectiveness numerically on surface PDEs.

We discuss an extension of our method image inpainting based on coherence transport. For the latter method the pixels of the inpainting domain have to be serialized into an ordered list. Until now, to induce the serialization we have used the distance to boundary map. But there are inpainting problems where the distance to boundary serialization causes unsatisfactory inpainting results. In the present work we demonstrate cases where we can resolve the difficulties by employing other distance functions which better suit the problem at hand.

We study the Dirichlet problem for first order hyperbolic quasi-linear functional PDEs on a simply connected bounded domain of $\R^2$, where the domain has an interior outflow set and a mere inflow boundary. While the question of existence of a solution has already been answered in its predecessor, the present paper discusses the uniqueness and continuous dependence on the coefficients of the PDE. Under the assumption that the functional dependence is causal, we are able to derive a contraction principle which is the key to proof uniqueness and continuous dependence. Such a causal functional dependence appears, e.g., in transport based image inpainting.