Peter Maass

Spatial segmentation of imaging mass spectrometry data with edge-preserving image denoising and clustering.

In recent years, matrix-assisted laser desorption/ionization (MALDI)-imaging mass spectrometry has become a mature technology, allowing for reproducible high-resolution measurements to localize proteins and smaller molecules. However, despite this impressive technological advance, only a few papers have been published concerned with computational methods for MALDI-imaging data. We address this issue proposing a new procedure for spatial segmentation of MALDI-imaging data sets. This procedure clusters all spectra into different groups based on their similarity. This partition is represented by a segmentation map, which helps to understand the spatial structure of the sample. The core of our segmentation procedure is the edge-preserving denoising of images corresponding to specific masses that reduces pixel-to-pixel variability and improves the segmentation map significantly. Moreover, before applying denoising, we reduce the data set selecting peaks appearing in at least 1% of spectra. High dimensional discriminant clustering completes the procedure. We analyzed two data sets using the proposed pipeline. First, for a rat brain coronal section the calculated segmentation maps highlight the anatomical and functional structure of the brain. Second, a section of a neuroendocrine tumor invading the small intestine was interpreted where the tumor area was discriminated and functionally similar regions were indicated.

A mollifier method for linear operator equations of the first kind

An inversion method for the solution of ill-posed linear problems is presented. It is based on the idea of computing a mollified version of the searched-for solution and the approximate inverse operator is computed with exactly given quantities. The method is compared with known methods such as the Tikhonov-Phillips and Backus-Gilbert methods. Numerical tests verify the advantages, which are: no additional or artificial discretisation of the solution is needed, locally varying point-spread functions are easily realised, a simple change of the regularisation parameter with regard of a posteriori parameter strategies is implemented and a straightforward interpretation of the regularised solution is possible. When the approximation inversion operator is computed the solution can be computed by parallel processing.

Fast CG-Based Methods for Tikhonov--Phillips Regularization

Tikhonov--Phillips regularization is one of the best-known regularization methods for inverse problems. A posteriori criteria for determining the regularization parameter

A Review of Some Modern Approaches to the Problem of Trend Extraction

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THE UNCERTAINTY PRINCIPLE ASSOCIATED WITH THE CONTINUOUS SHEARLET TRANSFORM

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Exploring Three-Dimensional Matrix-Assisted Laser Desorption/Ionization Imaging Mass Spectrometry Data: Three-Dimensional Spatial Segmentation of Mouse Kidney

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Adaptive wavelet methods and sparsity reconstruction for inverse heat conduction problems

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The interior Radon transform

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