Joint Image Reconstruction and Segmentation Using the Potts Model

We propose a new algorithmic approach to the non-smooth and non-convex Potts problem (also called piecewise-constant Mumford-Shah problem) for inverse imaging problems. We derive a suitable splitting into specific subproblems that can all be solved efficiently. Our method does not require a priori knowledge on the gray levels nor on the number of segments of the reconstruction. Further, it avoids anisotropic artifacts such as geometric staircasing. We demonstrate the suitability of our method for joint image reconstruction and segmentation. We focus on Radon data, where we in particular consider limited data situations. For instance, our method is able to recover all segments of the Shepp-Logan phantom from $7$ angular views only. We illustrate the practical applicability on a real PET dataset. As further applications, we consider spherical Radon data as well as blurred data

Large Scale Inverse Problems

This book is thesecond volume of a three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation &amp Analysis in Energy and the Environment" that took placein Linz, Austria, October 3-7, 2011. This volume addresses the common ground in the mathematical and computational procedures required for large-scale inverse problems and data assimilation in forefront applications. The solution of inverse problems is fundamental to a wide variety of applications such as weather forecasting, medical tomography, and oil exploration. Regularisation techniques are needed to ensure solutions of sufficient quality to be useful, and soundly theoretically based. This book addresses the common techniques required for all the applications, and is thus truly interdisciplinary. This collection of survey articles focusses on the large inverse problems commonly arising in simulation and forecasting in the earth sciences

Dictionaries for fast and informative dynamic MRI acquisition

Magnetic resonance (MR) imaging is an invaluable tool for medical research and diagnosis but suffers from inefficiencies. The speed of its acquisition mechanism, based on sequentially probing the interactions between nuclear atom spins and a changing magnetic field, is limited by atomic properties and scanner physics. Modern sampling techniques termed compressed sensing have nevertheless demonstrated how near perfect reconstructions are possible from undersampled, accelerated acquisitions, showing promise for more efficient MR acquisition paradigms. At the same time, information extraction from MR images through image analysis implies a considerable dimensionality reduction, in which an image is processed for the extraction of a few clinically useful parameters. This signals an inefficient handling of information in the separated treatment of acquisition and analysis that could be tackled by joining these two essential stages of the imaging pipeline. In this thesis, we explore the use of adaptive sparse modelling for novel acquisition strategies of cardiac cine MR data. Conventional compressed sensing MR acquisition relies on fixed basis transforms for sparse modelling, which are only able to guarantee suboptimal sparse modelling. We introduce spatio-temporal dictionaries that are able to optimally adapt sparse modelling by absorbing salient features of cardiac cine data, and demonstrate how they can outperform sampling methods based on fixed basis transforms. Additionally, we extend the framework introduced to handle parallel data acquisition. Given the flexibility of the formulation, we show how it can be combined with a labelling model that provides a segmentation of the image as a by-product of the reconstruction, hence performing joint reconstruction and analysis.Open Acces