Martin Holler

A Total Variation-Based JPEG Decompression Model

We propose a variational model for artifact-free JPEG decompression. It is based on the minimization of the total variation over the convex set

Regularization of linear inverse problems with total generalized variation

U

Joint MR-PET Reconstruction Using a Multi-Channel Image Regularizer

of all possible source images associated with given JPEG data. The general case where

Image-Based Personalization of Cardiac Anatomy for Coupled Electromechanical Modeling.

U

On Infimal Convolution of TV-Type Functionals and Applications to Video and Image Reconstruction ∗

represents a pointwise restriction with respect to an

A TGV Regularized Wavelet Based Zooming Model

L^2

Artifact-Free Decompression and Zooming of JPEG Compressed Images with Total Generalized Variation

-orthonormal basis is considered. Analysis of the infinite dimensional model is presented, including the derivation of optimality conditions. A discretized version is solved using a primal-dual algorithm supplemented by a primal-dual gap-based stopping criterion. Experiments illustrate the effect of the model. Good reconstruction quality is obtained even for highly compressed images, while a graphics processing unit (GPU) implementation is shown to significantly reduce computation time, making the model suitable for real-time applications.

Infimal convolution of total generalized variation functionals for dynamic MRI

Abstract The regularization properties of the total generalized variation (TGV) functional for the solution of linear inverse problems by means of Tikhonov regularization are studied. Considering the associated minimization problem for general symmetric tensor fields, the well-posedness is established in the space of symmetric tensor fields of bounded deformation, a generalization of the space of functions of bounded variation. Convergence for vanishing noise level is shown in a multiple regularization parameter framework in terms of the naturally arising notion of TGV-strict convergence. Finally, some basic properties, in particular non-equivalence for different parameters, are discussed for this notion.

Total Generalized Variation for Manifold-Valued Data

While current state of the art MR-PET scanners enable simultaneous MR and PET measurements, the acquired data sets are still usually reconstructed separately. We propose a new multi-modality reconstruction framework using second order Total Generalized Variation (TGV) as a dedicated multi-channel regularization functional that jointly reconstructs images from both modalities. In this way, information about the underlying anatomy is shared during the image reconstruction process while unique differences are preserved. Results from numerical simulations and in-vivo experiments using a range of accelerated MR acquisitions and different MR image contrasts demonstrate improved PET image quality, resolution, and quantitative accuracy.

A function space framework for structural total variation regularization with applications in inverse problems

Computational models of cardiac electromechanics (EM) are increasingly being applied to clinical problems, with patient-specific models being generated from high fidelity imaging and used to simulate patient physiology, pathophysiology and response to treatment. Current structured meshes are limited in their ability to fully represent the detailed anatomical data available from clinical images and capture complex and varied anatomy with limited geometric accuracy. In this paper, we review the state of the art in image-based personalization of cardiac anatomy for biophysically detailed, strongly coupled EM modeling, and present our own tools for the automatic building of anatomically and structurally accurate patient-specific models. Our method relies on using high resolution unstructured meshes for discretizing both physics, electrophysiology and mechanics, in combination with efficient, strongly scalable solvers necessary to deal with the computational load imposed by the large number of degrees of freedom of these meshes. These tools permit automated anatomical model generation and strongly coupled EM simulations at an unprecedented level of anatomical and biophysical detail.