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Image reconstruction in low-count PET is particularly challenging because gammas from natural radioactivity in Lu-based crystals cause high random fractions that lower the measurement signal-to-noise-ratio (SNR). In model-based image…

Image and Video Processing · Electrical Eng. & Systems 2020-05-27 Hongki Lim , Il Yong Chun , Yuni K. Dewaraja , Jeffrey A. Fessler

We study the problem of one-dimensional regression of data points with total-variation (TV) regularization (in the sense of measures) on the second derivative, which is known to promote piecewise-linear solutions with few knots. While there…

Optimization and Control · Mathematics 2021-12-22 Thomas Debarre , Quentin Denoyelle , Michael Unser , Julien Fageot

Multi-energy CT takes advantage of the non-linearly varying attenuation properties of elemental media with respect to energy, enabling more precise material identification than single-energy CT. The increased precision comes with the cost…

Medical Physics · Physics 2020-02-14 Jussi Toivanen , Alexander Meaney , Samuli Siltanen , Ville Kolehmainen

In this article, we study several reconstruction methods for the inverse source problem of photoacoustic tomography (PAT) with spatially variable sound speed and damping. The backbone of these methods is the adjoint operators, which we…

Analysis of PDEs · Mathematics 2018-08-21 Linh V. Nguyen , Markus Haltmeier

In this paper, we consider the efficient numerical minimization of Tikhonov functionals resulting from total-variation (TV) regularization of linear inverse problems. Since the TV penalty is non-smooth, this is typically done either via…

Numerical Analysis · Mathematics 2026-05-13 Helmut Gfrerer , Simon Hubmer , Stefan Kindermann , Jaakko Kultima , Ronny Ramlau , Tanja Tarvainen

This study presents the development of a spatially adaptive weighting strategy for Total Variation regularization, aimed at addressing under-determined linear inverse problems. The method leverages the rapid computation of an accurate…

Numerical Analysis · Mathematics 2025-01-20 Elena Morotti , Davide Evangelista , Andrea Sebastiani , Elena Loli Piccolomini

Learned iterative reconstruction algorithms for inverse problems offer the flexibility to combine analytical knowledge about the problem with modules learned from data. This way, they achieve high reconstruction performance while ensuring…

Image and Video Processing · Electrical Eng. & Systems 2022-10-24 Mareike Thies , Fabian Wagner , Mingxuan Gu , Lukas Folle , Lina Felsner , Andreas Maier

Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…

Computer Vision and Pattern Recognition · Computer Science 2020-06-17 Erich Kobler , Alexander Effland , Karl Kunisch , Thomas Pock

While Total Variation (TV) excels in noise reduction and edge preservation, its reliance on a scalar regularization parameter limits adaptivity. In this study, we present a Learnable Total Variation (LTV) framework coupling an unrolled TV…

Computer Vision and Pattern Recognition · Computer Science 2026-02-03 Yusuf Talha Basak , Mehmet Ozan Unal , Metin Ertas , Isa Yildirim

Diffuse Optical Tomography (DOT) is an emerging technology in medical imaging which employs light in the NIR spectrum to estimate the distribution of optical coefficients in biological tissues for diagnostic and monitoring purposes. DOT…

Numerical Analysis · Mathematics 2022-05-27 Alessandro Benfenati , Giuseppe Bisazza , Paola Causin

In many inverse problems it is essential to use regularization methods that preserve edges in the reconstructions, and many reconstruction models have been developed for this task, such as the Total Variation (TV) approach. The associated…

Numerical Analysis · Mathematics 2014-06-05 Donghui Chen , Misha E. Kilmer , Per Christian Hansen

This work considers using reduced basis techniques in connection to (smoothened) total variation regularization in electrical impedance tomography, but analogous ideas can also be used for other inverse elliptic boundary value problems. It…

Numerical Analysis · Mathematics 2026-02-18 A. Hannukainen , N. Hyvönen , V. Toresen

In Cone-Beam CT (CBCT) imaging systems, the scattering phenomenon has a significant impact on the reconstructed image and is a long-lasting research topic on CBCT. In this paper, we propose a simple, novel and fast approach for mitigating…

Medical Physics · Physics 2016-04-07 Shi-peng Xie , Rui-ju Yan

Over-fitting-based image compression requires weights compactness for compression and fast convergence for practical use, posing challenges for deep convolutional neural networks (CNNs) based methods. This paper presents a simple…

Image and Video Processing · Electrical Eng. & Systems 2023-10-13 Yun Ye , Yanjie Pan , Qually Jiang , Ming Lu , Xiaoran Fang , Beryl Xu

Recently, a number of approaches to low-dose computed tomography (CT) have been developed and deployed in commercialized CT scanners. Tube current reduction is perhaps the most actively explored technology with advanced image reconstruction…

Medical Physics · Physics 2018-09-05 Hoyeon Lee , Jongha Lee , Hyeongseok Kim , Byungchul Cho , Seungryong Cho

Novel sparse reconstruction algorithms are proposed for beamspace channel estimation in massive multiple-input multiple-output systems. The proposed algorithms minimize a least-squares objective having a nonconvex regularizer. This…

Information Theory · Computer Science 2021-12-02 Pengxia Wu , Julian Cheng

In dental cone-beam computed tomography (CBCT), compact and cost-effective system designs often use small detectors, resulting in a truncated field of view (FOV) that does not fully encompass the patient's head. In iterative reconstruction…

Computer Vision and Pattern Recognition · Computer Science 2025-08-12 Hyoung Suk Park , Kiwan Jeon

Medical imaging modalities have revolutionized health-care approaches by offering a better understanding of the human anatomy. Discovery of x-rays allowed the exploiting of the micro-scaled information of human anatomy. Computed tomography…

Medical Physics · Physics 2018-09-18 Sanam Assili

Low-dose CT imaging requires reconstruction from noisy indirect measurements which can be defined as an ill-posed linear inverse problem. In addition to conventional FBP method in CT imaging, recent compressed sensing based methods exploit…

Image and Video Processing · Electrical Eng. & Systems 2025-11-14 Mehmet Ozan Unal , Metin Ertas , Isa Yildirim

Proton computed tomography (pCT) is a novel medical imaging modality for mapping the distribution of proton relative stopping power (RSP) in medical objects of interest. Compared to conventional X-ray computed tomography, where range…

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