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About 3,050 papers for “total variation regularization”
Kisung You · 2017
Provides tools for denoising noisy signal and images via Total Variation Regularization. Reducing the total variation of the given signal is known to remove spurious detail while preserving essential structural details. For the seminal work on the topic, see Rudin et al (1992) <<a href="https://doi.org/10.1016%2F0167-2789%2892%2990242-F" target="_top">doi:10.1016/0167-2789(92)90242-F</a>>.
Cited by 0Open access
Non-quadratic Fidelity, Lin He, Martin Burger et al. · 2015
Abstract. A generalized iterative regularization procedure based on the total variation penal-ization is introduced for image denoising models with non-quadratic convex fidelity terms. By using a suitable sequence of penalty parameters we solve the issue of solvability of minimization problems arising in each step of the iterative procedure, which has been encountered in a recently developed iterative total variation procedure Furthermore, we obtain rigorous convergence results for exact and noisy data. We test the behaviour of the algorithm on real images in several numerical experiments using L1 and L2 fitting terms. Moreover, we compare the results with other state-of-the art multiscale techniques for total variation based image restoration.
Cited by 0
Markus Grasmair · Lecture notes in computer science · 2009
Cited by 65
Xiyan He, Laurent Condat, Jocelyn Chanussot et al. · HAL (Le Centre pour la Communication Scientifique Directe) · 2012
In remote sensing, pansharpening refers to the technique that combines the complementary spectral and spatial resolution characteristics of a multispectral image and a panchromatic image, with the objective to generate a high-resolution color image. This paper presents a new pansharpening method based on the minimization of a variant of total variation. We consider the fusion problem as the colorization of each pixel in the panchromatic image. A new term concerning the gradient of the panchromatic image is introduced in the functional of total variation so as to preserve edges. Experimental results on IKONOS satellite images demonstrate the effectiveness of the proposed method.
Cited by 15Open access
Robin Rühlicke, Daniel Gervini · Communications in Statistics - Simulation and Computation · 2008
This article introduces a regularized logistic discrimination method that is especially suited for discretized stochastic processes (such as periodograms, spectrograms, EEG curves, etc.). The proposed method penalizes the total variation of the discriminant directions, giving smaller misclassification errors than alternative methods, and smoother and more easily interpretable discriminant directions. The properties of the new method are studied by simulation and by a real-data example involving classification of phonemes.
Cited by 1
Gazzola S, Sabaté Landman M · CINECA IRIS Institutial research information system (University of Pisa) · 2019
Cited by 0
Guofa Shou, Ling Xia, Mingfeng Jiang · Lecture notes in computer science · 2010
Cited by 14
Gengsheng L. Zeng · International Journal of Biomedical Research & Practice · 2024
The total variation (TV) regularization is popular in iterative image reconstruction when the piecewise-constant nature of the image is encouraged. As a matter of fact, the TV regularization is not strong enough to enforce the piecewise- constant appearance. This paper suggests a different regularization function that is able to discourage some smooth transitions in the image and to encourage the piecewise-constant behavior. This new regularization function involves a Gaussian function. We use the limited-angle tomography problem to illustrate the effectiveness of this new regularization function. The limited-angle tomography situation considered in this paper uses a scanning angular range of 40°. For two-dimensional parallel-beam imaging, the required angular range is supposed to be 180°.
Cited by 0Open access
Gengsheng L. Zeng, Ying Li · PubMed Central · 2024
The total variation (TV) regularization is popular in iterative image reconstruction when the piecewise-constant nature of the image is encouraged. As a matter of fact, the TV regularization is not strong enough to enforce the piecewise-constant appearance. This paper suggests a different regularization function that is able to discourage some smooth transitions in the image and to encourage the piecewise-constant behavior. This new regularization function involves a Gaussian function. We use the limited-angle tomography problem to illustrate the effectiveness of this new regularization function. The limited-angle tomography situation considered in this paper uses a scanning angular range of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>40</mml:mn></mml:mrow> <mml:mrow><mml:mo>°</mml:mo></mml:mrow> </mml:math> . For two-dimensional parallel-beam imaging, the required angular range is supposed to be <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>180</mml:mn></mml:mrow> <mml:mrow><mml:mo>°</mml:mo></mml:mrow> </mml:math> .
Cited by 0Open access
Karl–franzens Universität Graz, Technische Universität Graz, Medizinische Universität Graz et al. · 2008
Cited by 0
R. C. Aster, Brian Borchers, C. H. Thurber · Elsevier eBooks · 2018
Cited by 1
Sanyi Yuan, Junhong Liu, R. Zhang et al. · Proceedings · 2014
Summary The trace-by-trace seismic deconvolution methods for reducing band-limited wavelet interference often cause lateral instability of the estimated reflectivity or impedance, and yield some trails like noodles, corresponding to relatively high wave-number components, when the signal-to-noise ratio of data is low and/or the data include high wave-number noise (or error). In this paper, a modified total variation (TV) regularization by linearly combining the sparseness regularization of model difference along the temporal direction and that along the spatial direction, where spatial regularization can be described as L1 norm of difference model along the interpreted horizontal direction, is introduced to develop a seismic deconvolution method to reduce even overcome these problems. The TV regularization connects the reflectivity at a point with its adjacent points and implicitly with any other points, thus introduces some additional useful information, especially for spatial continuity. In theory, minimizing TV has the ability to preserve edges of model parameters. A synthetic data example and a field data example are adopted to illustrate the performances of the method especially for the inherent role of sparseness regularization of model difference along the temporal and spatial directions.
Cited by 5
Jonathan Fransson · KTH Publication Database DiVA (KTH Royal Institute of Technology) · 2013
Since a few years back, there has been a development boom of nano-scale imaging of cells and sub-cellular structures. In short, the technique consists of making the specimen under study self-luminous when radiated by a laser of a fixed wavelength. Now, higher radiation intensity results in a higher signal to noise ratio, which gives a higher quality image with finer details. The backside is the damaging of the object when radiated with high intensity laser. Especially for the case of imaging live cells, one is interested in doing as little damage as possible. As a consequence, the image result becomes noisy. Retrieving data information from a noisy signal is a mathematical problem (inverse problem).This thesis focuses on developing a software for reconstructing noisy confocal images, utilizing the mathematical theory of regularization. More specifically, the reconstruction is based on total variation regularization and its extension, Bregman iterations. The presentation will present some performance results of the applied software and also investigate how the regularization method depends on the choice of regularization parameter for different noise-levels dictated by the radiation intensity from the illuminating laser. The work has been carried out for the Department of Mathematics at KTH Royal Institute of Technology and the Advanced Light Microscopy facility at the Science for Life Laboratory in Stockholm.
Cited by 0Open access
Artyom Makovetskii, Сергей Воронин, Vitaly Kober · 2018
Images of outdoor scenes are often degraded by particles and water droplets in the atmosphere. Haze, fog, and smoke are such phenomena due to atmospheric absorption and scattering. Numerous image dehazing (haze removal) methods have been proposed in the last two decades, and the majority of them employ an image enhancing or restoration approach. Different variants of local adaptive algorithms for single image dehazing are also known. A haze-free image must have higher contrast compared with the input hazy image. It is possible to remove haze by maximizing the local contrast of the restored image. Some haze removal approaches estimate a dehazed image from an observed hazed scene by solving an objective function, whose parameters are adapted to local statistics of the hazed image inside a moving window. In the signal and image processing a common way to solve the denoising problem utilizes the total variation regularization. In this presentation we propose a new algorithm combining local estimates of depth maps toward a global map by regularization the total variation for piecewise-constant functions. Computer simulation results are provided to illustrate the performance of the proposed algorithm for restoration of hazed images.
Cited by 1
Maximilian Baust, Laurent Demaret, Martin Storath et al. · Infoscience (Ecole Polytechnique Fédérale de Lausanne) · 2015
This paper introduces the concept of shape signals, i.e., series of shapes which have a natural temporal or spatial ordering, as well as a variational formulation for the regularization of these signals. The proposed formulation can be seen as the shape-valued generalization of the Rudin-Osher-Fatemi (ROF) functional for intensity images. We derive a variant of the classical finite-dimensional representation of Kendall, but our framework is generic in the sense that it can be combined with any shape space. This representation allows for the explicit computation of geodesics and thus facilitates the efficient numerical treatment of the variational formulation by means of the cyclic proximal point algorithm. Similar to the ROF-functional, we demonstrate experimentally that ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> -type penalties both for data fidelity term and regularizer perform best in regularizing shape signals. Finally, we show applications of our method to shape signals obtained from synthetic, photometric, and medical data sets.
Cited by 11Open access
Tony F. Chan, Chiu-Kwong Wong · 1997
The total variational (TV) regularization method was first proposed for gray scale images and was extended for vector valued images. In this work, we apply the TV regularization method to solve the multichannel image deconvolution problem. The motivation for regularizing with the TV norm is that it is extremely effective for recovering edges of images. In this paper, a fast iterative method is developed to solve the deconvolution problem. Our method involves solving linear systems and the conjugate gradient method is applied in which Fourier transform type preconditioners are used to speed up the convergence rate. Numerical experiments demonstrate the effectiveness of the TV regularization method. In this paper, we present some preliminary results on multichannel blind deconvolution with TV regularization.
Cited by 0
Lizhen Deng, Hu Zhu, Guanming Lu · 2013
Deconvolution has become one of the most used methods for improving spectral resolution, and blind deconvolution as a typical method has been researched widely. However, the predefined point spread function (PSF) used in blind deconvolution method is not known exactly in practice. In general, the PSF is estimated simultaneously from the observed spectrum, but it becomes difficult when the spectroscopic data are polluted by strong noise. In this paper, we present a deconvolution method used to improve the resolution of THz spectrum. In the method, the energy function is constructed, which includes the likelihood term, Total variation of spectrum term and L2 norm of the PSF term. The PSF is modeled as a parametric function combination with the a priori knowledge about the characteristics of the instrumental response. The spectrum and the parameter of PSF are obtained by minimizing the energy functional using alternate minimization approach. Experimental results are shown to demonstrate the efficiency of the proposed method used for THz spectrum.
Cited by 7
Adesokan, Bolaji James, Jensen, Bjørn, Jin, Bangti et al. · arXiv (Cornell University) · 2018
We study the numerical reconstruction problem in acousto-electric tomography of recovering the conductivity distribution in a bounded domain from interior power density data. We propose a numerical method for recovering discontinuous conductivity distributions, by reformulating it as an optimization problem with $ L^1 $ fitting and total variation penalty subject to PDE constraints. We establish continuity and differentiability results for the forward map, the well-posedness of the optimization problem, and present an easy-to-implement and robust numerical method based on successive linearization, smoothing and iterative reweighing. Extensive numerical experiments are presented to illustrate the feasibility of the proposed approach.
Cited by 0Open access
Sun, Jiajia · Zenodo (CERN European Organization for Nuclear Research) · 2022
Recovering dipping structures in the interior of the Earth from geophysical data sets is often of scientific and/or economic interest. Different regularization strategies have been proposed to help recover dipping structures. One notable example is total variation (TV). However, there seems to be a lack of understanding within the geophysical community regarding why TV regularization allows dipping structures to be recovered, whereas L1 norm regularization does not. In Sun & Fournier (2023, Understanding total variation regularization: why can it recover dipping structures?), the authors compare these two regularization strategies from an optimization point of view. They also perform inversions using a synthetic example and a field data example involving gravity gradient data to demonstrate the resolving power of TV in potential field data inversion. All of their inversions were performed using an open source framework SimPEG. The codes and data sets in this repository allow interested readers to reproduce their inversion results.
Cited by 1Open access
Artyom Makovetskii, Сергей Воронин, Vitaly Kober · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2016
One of the most known techniques for signal denoising is based on total variation regularization (TV regularization). A better understanding of TV regularization is necessary to provide a stronger mathematical justification for using TV minimization in signal processing. In this work, we deal with an intermediate case between one- and two-dimensional cases; that is, a discrete function to be processed is two-dimensional radially symmetric piecewise constant. For this case, the exact solution to the problem can be obtained as follows: first, calculate the average values over rings of the noisy function; second, calculate the shift values and their directions using closed formulae depending on a regularization parameter and structure of rings. Despite the TV regularization is effective for noise removal; it often destroys fine details and thin structures of images. In order to overcome this drawback, we use the TV regularization for signal denoising subject to linear signal variations are bounded.
Cited by 8