A5060778033- Sparse and Compressive Sensing Techniques
- Numerical methods in inverse problems
- Advanced MRI Techniques and Applications
- Medical Imaging Techniques and Applications
- Image and Signal Denoising Methods
- Medical Image Segmentation Techniques
- Photoacoustic and Ultrasonic Imaging
- Advanced Neuroimaging Techniques and Applications
- Optimization and Variational Analysis
- Advanced Optimization Algorithms Research
- Seismic Imaging and Inversion Techniques
- Advanced Mathematical Modeling in Engineering
- Elasticity and Material Modeling
- Atomic and Subatomic Physics Research
- Advanced Image Processing Techniques
- Advanced X-ray Imaging Techniques
- Matrix Theory and Algorithms
- Advanced Electron Microscopy Techniques and Applications
- Physics and Engineering Research Articles
- Advanced Numerical Analysis Techniques
- Electron Spin Resonance Studies
- Statistical and numerical algorithms
- Mathematical Approximation and Integration
- Nonlinear Partial Differential Equations
- Geometric Analysis and Curvature Flows
University of Graz
2015-2024
BioTechMed-Graz
2016-2024
Institute of Mathematics and Informatics
2015-2022
Czech Academy of Sciences, Institute of Mathematics
2015-2022
Nawi Graz
2017-2019
Helmholtz Zentrum München
2018
Darmstadt University of Applied Sciences
2018
Heidelberg University
2018
Institute of Group Analysis
2015-2017
Institute of Computer Vision and Applied Computer Sciences
2015
The novel concept of total generalized variation a function u is introduced, and some its essential properties are proved. Differently from the bounded seminorm, new involves higher-order derivatives u. Numerical examples illustrate high quality this functional as regularization term for mathematical imaging problems. In particular selectively regularizes on different regularity levels and, side effect, does not lead to staircasing effect.
Total variation was recently introduced in many different magnetic resonance imaging applications. The assumption of total is that images consist areas, which are piecewise constant. However, practical situations, this not valid due to the inhomogeneities exciting B1 field and receive coils. This work introduces new concept generalized for imaging, a mathematical framework, generalization theory eliminates these restrictions. Two important applications considered article, image denoising...
Purpose The aim of the 2016 quantitative susceptibility mapping (QSM) reconstruction challenge was to test ability various QSM algorithms recover underlying from phase data faithfully. Methods Gradient‐echo images a healthy volunteer acquired at 3T in single orientation with 1.06 mm isotropic resolution. A reference map provided, which computed using tensor imaging algorithm on 12 head orientations. Susceptibility maps calculated were compared against map. Deviations quantified following...
The ill-posed problem of solving linear equations in the space vector-valued finite Radon measures with Hilbert data is considered. Approximate solutions are obtained by minimizing Tikhonov functional a total variation penalty. well-posedness this regularization method and further properties mentioned. Furthermore, flexible numerical minimization algorithm proposed which converges subsequentially weak* sense rate 𝒪(n-1) terms values. Finally, results for sparse deconvolution demonstrate...
We study the extension of total variation (TV), deformation (TD), and (second-order) generalized ($\TGV^2$) to symmetric tensor fields. show that for a suitable choice finite-dimensional norm, these variational seminorms are rotation-invariant in sense natural well suited application diffusion imaging (DTI). Combined with positive definiteness constraint, we employ novel as regularizers Rudin--Osher--Fatemi (ROF) type denoising medical vivo brain images. For numerical realization,...
While current state of the art MR-PET scanners enable simultaneous MR and PET measurements, acquired data sets are still usually reconstructed separately. We propose a new multi-modality reconstruction framework using second order Total Generalized Variation (TGV) as dedicated multi-channel regularization functional that jointly reconstructs images from both modalities. In this way, information about underlying anatomy is shared during image process while unique differences preserved....
A new iterative algorithm for the solution of minimization problems in infinite-dimensional Hilbert spaces which involve sparsity constraints form $\ell^{p}$-penalties is proposed. In contrast to well-known considered by Daubechies, Defrise, and De Mol, it uses hard instead soft shrinkage. It shown that shrinkage a special case generalized conditional gradient method. Convergence properties method with quadratic discrepancy term are analyzed. This leads strong convergence iterates rates...
We consider regularization of nonlinear ill-posed problems with constraints which are non-convex. As a special case, we separable constraints, i.e. the takes place in sequence space and constraint acts on each element possibly non-convex function. derive conditions under such provides regularization. Moreover, estimates for error obtain convergence rates vanishing noise level. Our assumptions especially cover example sparsity pth power 0 < p ? 1 is used, present other examples as well. In...
Abstract A new approach based on nonlinear inversion for autocalibrated parallel imaging with arbitrary sampling patterns is presented. By extending the iteratively regularized Gauss–Newton method variational penalties, improved reconstruction quality obtained from joint estimation of image and coil sensitivities combined superior noise suppression total variation generalized regularization. In addition, proposed can lead to enhanced removal artifacts arising pseudorandom radial patterns....
Abstract The regularization properties of the total generalized variation (TGV) functional for solution linear inverse problems by means Tikhonov are studied. Considering associated minimization problem general symmetric tensor fields, well-posedness is established in space fields bounded deformation, a generalization functions variation. Convergence vanishing noise level shown multiple parameter framework terms naturally arising notion TGV-strict convergence. Finally, some basic properties,...
Abstract In this paper, the automated spatially dependent regularization parameter selection framework for multi-scale image restoration is applied to total generalized variation (TGV) of order 2. Well-posedness underlying continuous models discussed and an algorithm numerical solution developed. Experiments confirm that due adapted parameter, method allows a faithful simultaneous recovery fine structures smooth regions in images. Moreover, because TGV term, adverse staircasing effect, which...
A variational model for image reconstruction is introduced and analyzed in function space. Specific to the data fidelity, which realized via a basis transformation with respect Riesz followed by interval constraints. This setting particular covers task of reconstructing images constrained obtained from JPEG or 2000 compressed files. As prior, total generalized variation (TGV) functional arbitrary order employed. The present paper, first two works that deal both analytical numerical aspects...
In this paper we characterize sparse solutions for variational problems of the form $\min_{u\in X} \phi(u) + F(\mathcal{A} u)$, where $X$ is a locally convex space, $\mathcal{A}$ linear continuous operator that maps into finite dimensional Hilbert space and $\phi$ seminorm. More precisely, prove there exists minimizer `sparse' in sense it represented as combination extremal points unit ball associated with regularizer (possibly translated by an element null $\phi$). We apply result to...
Purpose To accelerate dynamic MR applications using infimal convolution of total generalized variation functionals (ICTGV) as spatio‐temporal regularization for image reconstruction. Theory and Methods ICTGV comprises a new prior tailored to data that achieves via optimal local balancing between spatial temporal regularity. Here it is applied the first time reconstruction MRI data. CINE perfusion scans were investigated study influence dependent morphology contrast changes. regularized from...
We propose a variational model for artifact-free JPEG decompression. It is based on the minimization of total variation over convex set U all possible source images associated with given data. The general case where represents pointwise restriction respect to an $L^2$-orthonormal basis considered. Analysis infinite dimensional presented, including derivation optimality conditions. A discretized version solved using primal-dual algorithm supplemented by gap-based stopping criterion....
We propose a preconditioned version of the Douglas--Rachford splitting method for solving convex-concave saddle-point problems associated with Fenchel--Rockafellar duality. Our approach makes it possible to use approximate solvers linear subproblem arising in this context. prove weak convergence Hilbert space under minimal assumptions. In particular, various efficient preconditioners are introduced framework which only few inner iterations needed instead computing an exact solution or...
Computational models of cardiac electromechanics (EM) are increasingly being applied to clinical problems, with patient-specific generated from high fidelity imaging and used simulate patient physiology, pathophysiology response treatment. Current structured meshes limited in their ability fully represent the detailed anatomical data available images capture complex varied anatomy geometric accuracy. In this paper, we review state art image-based personalization for biophysically detailed,...