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We propose a new image restoration model based on the minimized surface regularization. The proposed model closely relates to the classical smoothing ROF model \cite{4}. We can reformulate the proposed model as a min-max problem and solve…

Optimization and Control · Mathematics 2016-05-31 Zhi-Feng Pang , Yuping Duan

Iterative image reconstruction algorithms for optoacoustic tomography (OAT), also known as photoacoustic tomography, have the ability to improve image quality over analytic algorithms due to their ability to incorporate accurate models of…

Analysis of PDEs · Mathematics 2015-06-05 Kun wang , Richard Su , Alexander A. Oraevsky , Mark A. Anastasio

A supervised learning approach is proposed for regularization of large inverse problems where the main operator is built from noisy data. This is germane to superresolution imaging via the sampling indicators of the inverse scattering…

Numerical Analysis · Mathematics 2025-08-22 Fatemeh Pourahmadian , Yang Xu

For image denoising problems, the structure tensor total variation (STV)-based models show good performances when compared with other competing regularization approaches. However, the STV regularizer does not couple the local information of…

Optimization and Control · Mathematics 2024-04-05 Xiuhan Sheng , Lijuan Yang , Jingya Chang

This paper addresses the solution of inverse problems in imaging given an additional reference image. We combine a modification of the discrete geodesic path model for image metamorphosis with a variational model,actually the $L^2$-$TV$…

Numerical Analysis · Mathematics 2019-05-22 Sebastian Neumayer , Johannes Persch , Gabriele Steidl

Recovering images corrupted by multiplicative noise is a well known challenging task. Motivated by the success of multiscale hierarchical decomposition methods (MHDM) in image processing, we adapt a variety of both classical and new…

Numerical Analysis · Mathematics 2023-10-11 Joel Barnett , Wen Li , Elena Resmerita , Luminita Vese

Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…

Numerical Analysis · Mathematics 2025-06-24 Chai Wah Wu , Mark S. Squillante , Vasileios Kalantzis , Lior Horesh

Most existing image denoising approaches assumed the noise to be homogeneous white Gaussian distributed with known intensity. However, in real noisy images, the noise models are usually unknown beforehand and can be much more complex. This…

Computer Vision and Pattern Recognition · Computer Science 2016-01-14 Fengyuan Zhu , Guangyong Chen , Jianye Hao , Pheng-Ann Heng

In this paper, we propose a novel locally statistical variational active contour model based on I-divergence-TV denoising model, which hybrides geodesic active contour (GAC) model with active contours without edges (ACWE) model, and can be…

Computer Vision and Pattern Recognition · Computer Science 2025-08-19 Guangming Liu

Dose reduction in computed tomography (CT) is essential for decreasing radiation risk in clinical applications. Iterative reconstruction is one of the most promising ways to compensate for the increased noise due to reduction of photon…

Image and Video Processing · Electrical Eng. & Systems 2021-03-24 Zhuonan He , Yikun Zhang , Yu Guan , Shanzhou Niu , Yi Zhang , Yang Chen , Qiegen Liu

Spectral domain optical coherence tomography (OCT) offers high resolution multidimensional imaging, but generally suffers from defocussing, intensity falloff and shot noise, causing artifacts and image degradation along the imaging depth.…

Image and Video Processing · Electrical Eng. & Systems 2021-08-04 Jonathan H. Mason , Yvonne Reinwald , Ying Yang , Sarah Waters , Alicia El Haj , Pierre O. Bagnaninchi

This paper presents several new algorithms for the regularized reconstruction of a surface from its measured gradient field. By taking a matrix-algebraic approach, we establish general framework for the regularized reconstruction problem…

Numerical Analysis · Mathematics 2013-08-21 Matthew Harker , Paul O'Leary

Ill-posed linear inverse problems (ILIP), such as restoration and reconstruction, are a core topic of signal/image processing. A standard approach to deal with ILIP uses a constrained optimization problem, where a regularization function is…

Optimization and Control · Mathematics 2016-11-15 Manya V. Afonso , Jose M. Bioucas-Dias , Mario A. T. Figueiredo

In this paper we present a new two-level iterative algorithm for tomographic image reconstruction. The algorithm uses a regularization technique, which we call edge-preserving Laplacian, that preserves sharp edges between objects while…

Computer Vision and Pattern Recognition · Computer Science 2015-09-17 Daniil Kazantsev , Evgueni Ovtchinnikov , William R. B. Lionheart , Philip J. Withers , Peter D. Lee

Color image denoising is frequently encountered in various image processing and computer vision tasks. One traditional strategy is to convert the RGB image to a less correlated color space and denoise each channel of the new space…

Computer Vision and Pattern Recognition · Computer Science 2022-09-20 Yiwen Shan , Dong Hu , Zhi Wang , Tao Jia

In this paper, we propose a regularization technique for noisy-image super-resolution and image denoising. Total variation (TV) regularization is adopted in many image processing applications to preserve the local smoothness. However, TV…

Image and Video Processing · Electrical Eng. & Systems 2022-02-23 Kaicong Sun , Sven Simon

This paper proposes a new two-step procedure for sparse-view tomographic image reconstruction. It is called RISING, since it combines an early-stopped Rapid Iterative Solver with a subsequent Iteration Network-based Gaining step. So far,…

Numerical Analysis · Mathematics 2022-01-25 Davide Evangelista , Elena Morotti , Elena Loli Piccolomini

This paper considers the problem of reconstructing sparse or compressible signals from one-bit quantized measurements. We study a new method that uses a log-sum penalty function, also referred to as the Gaussian entropy, for sparse signal…

Information Theory · Computer Science 2012-10-17 Jun Fang , Yanning Shen , Hongbin Li

In this paper we study the topic of signal restoration using complexity regularization, quantifying the compression bit-cost of the signal estimate. While complexity-regularized restoration is an established concept, solid practical methods…

Information Theory · Computer Science 2018-11-14 Yehuda Dar , Michael Elad , Alfred M. Bruckstein

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
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