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Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…

Mathematical Physics · Physics 2020-09-03 Juuso Österman

The computation of 2-D optical flow by means of regularized pel-recursive algorithms raises a host of issues, which include the treatment of outliers, motion discontinuities and occlusion among other problems. We propose a new approach…

Computer Vision and Pattern Recognition · Computer Science 2016-11-07 Vania V. Estrela , Luis A. Rivera , Paulo C. Beggio , Ricardo T. Lopes

An extension of the Method of Regularized Stokeslets (MRS) in three dimensions is developed for triangulated surfaces with a piecewise linear force distribution. The method extends the regularized Stokeslet segment methodology used for…

Numerical Analysis · Mathematics 2024-11-05 Dana Ferranti , Ricardo Cortez

Purpose: To develop a synergistic image reconstruction framework that exploits multicontrast (MC), multicoil, and compressed sensing (CS) redundancies in magnetic resonance imaging (MRI). Approach: CS, MC acquisition, and parallel imaging…

Image and Video Processing · Electrical Eng. & Systems 2022-02-22 Erfan Ebrahim Esfahani

We address the optimization problem in a data-driven variational reconstruction framework, where the regularizer is parameterized by an input-convex neural network (ICNN). While gradient-based methods are commonly used to solve such…

Optimization and Control · Mathematics 2025-10-24 Matthias J. Ehrhardt , Subhadip Mukherjee , Hok Shing Wong

We propose a variational regularization approach based on a multiscale representation called cylindrical shearlets aimed at dynamic imaging problems, especially dynamic tomography. The intuitive idea of our approach is to integrate a…

Numerical Analysis · Mathematics 2025-08-05 Tatiana A. Bubba , Tommi Heikkilä , Demetrio Labate , Luca Ratti

Reconstructing high-quality magnetic resonance images (MRI) from undersampled raw data is of great interest from both technical and clinical point of views. To this date, however, it is still a mathematically and computationally challenging…

Numerical Analysis · Mathematics 2021-09-01 T. Schmoderer , A. I Aviles-Rivero , V. Corona , N. Debroux , C-B. Schönlieb

Motion degradation is a central problem in Magnetic Resonance Imaging (MRI). This work addresses the problem of how to obtain higher quality, super-resolved motion-free, reconstructions from highly undersampled MRI data. In this work, we…

Image and Video Processing · Electrical Eng. & Systems 2019-08-19 Veronica Corona , Angelica I. Aviles-Rivero , Noémie Debroux , Carole Le Guyader , Carola-Bibiane Schönlieb

In many imaging applications where segmented features (e.g. blood vessels) are further used for other numerical simulations (e.g. finite element analysis), the obtained surfaces do not have fine resolutions suitable for the task. Increasing…

Analysis of PDEs · Mathematics 2023-09-19 Yiyao Zhang , Ke Chen , Shang-Hua Yang

In this paper, we presented an efficient algorithm to implement the regularization reconstruction of SPECT. Image reconstruction with priori assumptions is usually modeled as a constrained optimization problem. However, there is no…

Optimization and Control · Mathematics 2013-06-07 Shousheng Luo , Tie Zhou

Polynomial and rational functions are the number one choice when it comes to modeling of radial distortion of lenses. However, several extrapolation and numerical issues may arise while using these functions that have not been covered by…

Optimization and Control · Mathematics 2014-09-22 Jan Heller , Didier Henrion , Tomas Pajdla

We consider the problem of reconstructing signals and images from periodic nonlinearities. For such problems, we design a measurement scheme that supports efficient reconstruction; moreover, our method can be adapted to extend to…

Machine Learning · Statistics 2017-10-03 Viraj Shah , Mohammadreza Soltani , Chinmay Hegde

We propose an adaptive regularization scheme in a variational framework where a convex composite energy functional is optimized. We consider a number of imaging problems including denoising, segmentation and motion estimation, which are…

Computer Vision and Pattern Recognition · Computer Science 2017-03-01 Byung-Woo Hong , Ja-Keoung Koo , Hendrik Dirks , Martin Burger

In Magnetic Resonance Imaging (MRI) data samples are collected in the spatial frequency domain (k-space), typically by time-consuming line-by-line scanning on a Cartesian grid. Scans can be accelerated by simultaneous acquisition of data…

Medical Physics · Physics 2015-03-24 Vivek Athalye , Michael Lustig , Martin Uecker

Magnetic Resonance Imaging (MRI) acquisitions require extensive scan times, limiting patient throughput and increasing susceptibility to motion artifacts. Accelerated parallel MRI techniques reduce acquisition time by undersampling k-space…

Computer Vision and Pattern Recognition · Computer Science 2025-11-25 Mingi Kang

Natural images tend to mostly consist of smooth regions with individual pixels having highly correlated spectra. This information can be exploited to recover hyperspectral images of natural scenes from their incomplete and noisy…

Computer Vision and Pattern Recognition · Computer Science 2016-11-03 Reza Arablouei , Frank de Hoog

We propose a new fast algorithm for simultaneous recovery of the coil sensitivities and of the magnetization image from incomplete Fourier measurements in parallel MRI. Our approach is based on a parameter model for the coil sensitivities…

Numerical Analysis · Mathematics 2024-10-30 Gerlind Plonka , Yannick Riebe

Parallel imaging is a widely-used technique to accelerate magnetic resonance imaging (MRI). However, current methods still perform poorly in reconstructing artifact-free MRI images from highly undersampled k-space data. Recently, implicit…

Image and Video Processing · Electrical Eng. & Systems 2022-10-20 Ruimin Feng , Qing Wu , Yuyao Zhang , Hongjiang Wei

Conventional Magnetic Resonance Imaging (MRI) is hampered by long scan times and only qualitative image contrasts that prohibit a direct comparison between different systems. To address these limitations, model-based reconstructions…

Image and Video Processing · Electrical Eng. & Systems 2022-10-24 Xiaoqing Wang , Zhengguo Tan , Nick Scholand , Volkert Roeloffs , Martin Uecker

Diffusion models have recently shown remarkable results in magnetic resonance imaging reconstruction. However, the employed networks typically are black-box estimators of the (smoothed) prior score with tens of millions of parameters,…

Image and Video Processing · Electrical Eng. & Systems 2025-01-16 Laurenz Nagler , Martin Zach , Thomas Pock