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Michael Sandbichler

Publications and source records attributed to Michael Sandbichler.

7 recordsLinked to original sources
arXiv2026

The data-driven extreme value distribution: non-parametric tail estimation with a derived stability criterion

Quantifying the likelihood of extreme events underpins risk assessment, yet classical Extreme Value Theory relies on asymptotic assumptions that fail in the data-sparse, non-stationary regimes practitioners increasingly face. We introduce the Data-Driven Extreme Value Distribution (DDEVD), a non-parametric estimator that aggregates all observations metastatistically and reconstructs the base distribution with a kernel, removing parametric tail assumptions. We derive its optimal bandwidth and prove a stability law $m < C\,n^{1+\gamma/2}$ relating reliable extrapolation to the extreme value index $\gamma$. In sub-hourly Alpine precipitation, DDEVD recovers stable 100-year return levels from single decades (calibration ratio $0.96$), departing from the full-record reference by over $50\,\%$ in fewer than one window in fifty -- versus one in five for a GEV fit. In metallurgical micrographs, it matches a generalised extreme-value fit on the safety-relevant grain-size tail, where the standard log-normal over-predicts by $58\,\%$ at $1\,\mathrm{cm}^{2}$.

stat.AP↗
arXiv2017

A New Sparsification and Reconstruction Strategy for Compressed Sensing Photoacoustic Tomography

Compressed sensing (CS) is a promising approach to reduce the number of measurements in photoacoustic tomography (PAT) while preserving high spatial resolution. This allows to increase the measurement speed and to reduce system costs. Instead of collecting point-wise measurements, in CS one uses various combinations of pressure values at different sensor locations. Sparsity is the main condition allowing to recover the photoacoustic (PA) source from compressive measurements. In this paper we introduce a new concept enabling sparse recovery in CS PAT. Our approach is based on the fact that the second time derivative applied to the measured pressure data corresponds to the application of the Laplacian to the original PA source. As typical PA sources consist of smooth parts and singularities along interfaces the Laplacian of the source is sparse (or at least compressible). To efficiently exploit the induced sparsity we develop a reconstruction framework to jointly recover the initial and the modified sparse source. Reconstruction results with simulated as well as experimental data are given.

math.NA↗
arXiv2017

Total Variation Minimization in Compressed Sensing

This chapter gives an overview over recovery guarantees for total variation minimization in compressed sensing for different measurement scenarios. In addition to summarizing the results in the area, we illustrate why an approach that is common for synthesis sparse signals fails and different techniques are necessary. Lastly, we discuss a generalizations of recent results for Gaussian measurements to the subgaussian case.

cs.IT↗
arXiv2017

Compressive Time-of-Flight 3D Imaging Using Block-Structured Sensing Matrices

Spatially and temporally highly resolved depth information enables numerous applications including human-machine interaction in gaming or safety functions in the automotive industry. In this paper, we address this issue using Time-of-flight (ToF) 3D cameras which are compact devices providing highly resolved depth information. Practical restrictions often require to reduce the amount of data to be read-out and transmitted. Using standard ToF cameras, this can only be achieved by lowering the spatial or temporal resolution. To overcome such a limitation, we propose a compressive ToF camera design using block-structured sensing matrices that allows to reduce the amount of data while keeping high spatial and temporal resolution. We propose the use of efficient reconstruction algorithms based on l^1-minimization and TV-regularization. The reconstruction methods are applied to data captured by a real ToF camera system and evaluated in terms of reconstruction quality and computational effort. For both, l^1-minimization and TV-regularization, we use a local as well as a global reconstruction strategy. For all considered instances, global TV-regularization turns out to clearly perform best in terms of evaluation metrics including the PSNR.

math.NA↗
arXiv2017

Online and Stable Learning of Analysis Operators

In this paper four iterative algorithms for learning analysis operators are presented. They are built upon the same optimisation principle underlying both Analysis K-SVD and Analysis SimCO. The Forward and Sequential Analysis Operator Learning (FAOL and SAOL) algorithms are based on projected gradient descent with optimally chosen step size. The Implicit AOL (IAOL) algorithm is inspired by the implicit Euler scheme for solving ordinary differential equations and does not require to choose a step size. The fourth algorithm, Singular Value AOL (SVAOL), uses a similar strategy as Analysis K-SVD while avoiding its high computational cost. All algorithms are proven to decrease or preserve the target function in each step and a characterisation of their stationary points is provided. Further they are tested on synthetic and image data, compared to Analysis SimCO and found to give better recovery rates and faster decay of the objective function respectively. In a final denoising experiment the presented algorithms are again shown to perform similar to or better than the state-of-the-art algorithm ASimCO.

cs.LG↗
arXiv2015

A Novel Compressed Sensing Scheme for Photoacoustic Tomography

Speeding up the data acquisition is one of the central aims to advance tomographic imaging. On the one hand, this reduces motion artifacts due to undesired movements, and on the other hand this decreases the examination time for the patient. In this article, we propose a new scheme for speeding up the data collection process in photoacoustic tomography. Our proposal is based on compressed sensing and reduces acquisition time and system costs while maintaining image quality. As measurement data we use random combinations of pressure values that we use to recover a complete set of pressure data prior to the actual image reconstruction. We obtain theoretical recovery guarantees for our compressed sensing scheme and support the theory by reconstruction results on simulated data as well as on experimental data.

math.NA↗