Peter Maaß

An adaptive discretization for Tikhonov-Phillips regularization with a posteriori parameter selection

Summary. The aim of this paper is to describe an efficient adaptive strategy for discretizing ill-posed linear operator equations of the first kind: we consider Tikhonov-Phillips regularization \[ x_{\alpha}^{\delta} = \left(A^{\ast}A+\alpha I\right)^{-1}A^{\ast}y^{\delta} \] with a finite dimensional approximation

Compressed sensing in imaging mass spectrometry

A_n

Nonlinear inverse unbalance reconstruction in rotor dynamics

instead of A. We propose a sparse matrix structure which still leads to optimal convergences rates but requires substantially less scalar products for computing

Integration of 3D multimodal imaging data of a head and neck cancer and advanced feature recognition

A_n

FPGA Acceleration for Simultaneous Image Reconstruction and Segmentation based on the Mumford-Shah Regularization (Abstract Only)

compared with standard methods.

Thermomechanical Deformation of Complex Workpieces in Milling and Drilling Processes

Imaging mass spectrometry (IMS) is a technique of analytical chemistry for spatially resolved, label-free and multipurpose analysis of biological samples that is able to detect the spatial distribution of hundreds of molecules in one experiment. The hyperspectral IMS data is typically generated by a mass spectrometer analyzing the surface of the sample. In this paper, we propose a compressed sensing approach to IMS which potentially allows for faster data?acquisition by collecting only a part of the pixels in the hyperspectral image and reconstructing the full image from this data. We present an integrative approach to perform both peak-picking spectra and denoising m/z-images simultaneously, whereas the state of the art data analysis methods solve these problems separately. We provide a proof of the robustness of the recovery of both the spectra and individual channels of the hyperspectral image and propose an algorithm to solve our optimization problem which is based on proximal mappings. The paper concludes with the numerical reconstruction results for an IMS dataset of a rat brain coronal section.

An iterative regularization method for nonlinear problems based on Bregman projections

This article is devoted to the identification and reconstruction of unbalance distributions in an aircraft engine rotor with a nonlinear damping element. We have developed a rotor model that takes into account the nonlinear behavior of a squeeze film damper between the engines shaft and casing for large oscillation amplitudes. Based on the Tikhonov regularization for nonlinear ill-posed problems, we provided a three-step algorithm that enables us to identify and reconstruct single and distributed unbalances from data measured at the casing of the engine. In view of practical capability, the algorithms were accelerated to meet the requirement of tolerable computation time for larger models, too.

Surface Generation Process with Consideration of the Balancing State in Diamond Machining

In the last years, matrix-assisted laser desorption/ionization mass spectrometry imaging (MALDI MSI) became an imaging technique which has the potential to characterize complex tumor tissue. The combination with other modalities and with standard histology techniques was achieved by the use of image registration methods and enhances analysis possibilities. We analyzed an oral squamous cell carcinoma with up to 162 consecutive sections with MALDI MSI, hematoxylin and eosin (H&E) staining and immunohistochemistry (IHC) against CD31. Spatial segmentation maps of the MALDI MSI data were generated by similarity-based clustering of spectra. Next, the maps were overlaid with the H&E microscopy images and the results were interpreted by an experienced pathologist. Image registration was used to fuse both modalities and to build a three-dimensional (3D) model. To visualize structures below resolution of MALDI MSI, IHC was carried out for CD31 and results were embedded additionally. The integration of 3D MALDI MSI data with H&E and IHC images allows a correlation between histological and molecular information leading to a better understanding of the functional heterogeneity of tumors. This article is part of a Special Issue entitled: MALDI Imaging, edited by Dr. Corinna Henkel and Prof. Peter Hoffmann.

Atmospheric Inverse Modeling via Sparse Reconstruction

X-ray computed tomography is an important technique for clinical diagnose and nondestructive testing. In many applications a number of image processing steps are needed before the image information becomes useful. Image segmentation is one of such processing steps and has important applications. The conventional flow is to first reconstruct the image and then obtain image segmentation afterwards. In contrast, an iterative method for simultaneous reconstruction and segmentation (SRS) with Mumford-Shah model has been proposed, which not only regularizes the ill-posedness of the tomographic reconstruction problem, but also produces the image segmentation at the same time. The Mumford-Shah model is both mathematically and computationally difficult. In this paper, we propose a data-decomposed algorithm of the SRS method, accelerate it using FPGA devices. The proposed algorithm has a structure that invokes a single kernel many times without involving other computational tasks. Though this structure seems best fit on GPU-like devices, experimental results show that a 73X, 11X, and 1.4X speedup can be achieved by the FPGA acceleration over the CPU implementation of the original SRS algorithm and ray-parallel SRS algorithm, and the GPU implementation of the ray-parallel SRS.

Wirkstoffe, Medikamente und Mathematische Bildverarbeitung

In this chapter the work of an interdisciplinary collaboration for modeling thermomechanical deformations in dry milling and drilling processes is presented. The simulation based approach allows the prediction of structural workpiece deformation due to thermal effects occurring during the machining process. Geometric changes of the workpiece volume and the current engagement of tool and workpiece are included in the developed model. The model is applied for the optimization of NC paths with respect to workpiece deformations. The combined model is assembled by individual sub-models, which are coupled to account for interactions with each other. A dexel model is applied for contact zone analysis of tool and workpiece and also allows efficient geometric modeling of the workpiece surface. Geometric process variables of the contact zone are passed to the process model which provides thermal and mechanical loads for the thermomechanics. The thermomechanical behaviour is numerically approximated using finite elements on the time depending co-domain of the dexel model together with thermal and mechanical loads provided by the process model. In all, a closed loop between Boolean material removal, process forces, heat flux and thermo-elastic deformation is established and allows an accurate prediction of workpiece deformation and shape deviations. Furthermore, the simulation operates as a forward model for an NC path optimization. A significant improvement of form deviation is achieved with the approach.