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Related papers: Total Variation Denoising via the Moreau Envelope

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Denoising has always been theoretically considered as removal of high frequency disturbances having Gaussian distribution. Here we relax this assumption and the method used here is completely different from traditional thresholding schemes.…

Information Theory · Computer Science 2016-01-19 Vibhor Kumar , Jukka Heikkonen

Removing noise from piecewise constant (PWC) signals, is a challenging signal processing problem arising in many practical contexts. For example, in exploration geosciences, noisy drill hole records need separating into stratigraphic zones,…

Data Analysis, Statistics and Probability · Physics 2019-10-23 Max A. Little , Nick S. Jones

This work studies the denoising of piecewise smooth graph signals that exhibit inhomogeneous levels of smoothness over a graph, where the value at each node can be vector-valued. We extend the graph trend filtering framework to denoising…

Signal Processing · Electrical Eng. & Systems 2020-01-16 Rohan Varma , Harlin Lee , Jelena Kovačević , Yuejie Chi

Variational methods have become an important kind of methods in signal and image restoration - a typical inverse problem. One important minimization model consists of the squared $\ell_2$ data fidelity (corresponding to Gaussian noise) and…

Numerical Analysis · Mathematics 2018-06-15 Chunlin Wu , Zhifang Liu , Shuang Wen

We present the continuous wavelet transform (WT) of white Gaussian noise and establish a connection to the theory of Gaussian analytic functions. Based on this connection, we propose a methodology that detects components of a signal in…

Numerical Analysis · Mathematics 2020-05-12 Luis Daniel Abreu , Antti Haimi , Günther Koliander , José Luis Romero

We consider the image denoising problem using total variation (TV) regularization. This problem can be computationally challenging to solve due to the non-differentiability and non-linearity of the regularization term. We propose an…

Optimization and Control · Mathematics 2014-08-26 Zhiwei Qin , Donald Goldfarb , Shiqian Ma

We revisit total variation denoising and study an augmented model where we assume that an estimate of the image gradient is available. We show that this increases the image reconstruction quality and derive that the resulting model…

Optimization and Control · Mathematics 2018-04-05 Birgit Komander , Dirk A. Lorenz , Lena Vestweber

The total variation (TV) regularization method is an effective method for image deblurring in preserving edges. However, the TV based solutions usually have some staircase effects. In this paper, in order to alleviate the staircase effect,…

Numerical Analysis · Mathematics 2015-05-20 Gang Liu , Ting-Zhu Huang , Jun Liu , Xiao-Guang Lv

We introduce a new approach for Gaussianity testing using the envelope of a signal and its coefficient of variation. The envelope of a Gaussian signal follows the Rayleigh distribution, and given that the coefficient of variation of the…

Signal Processing · Electrical Eng. & Systems 2022-10-12 Víctor Manuel Hidalgo , Juan-Carlos Letelier , Javier Díaz

In the paper, a new method of blind estimation of noise variance in a single highly textured image is proposed. An input image is divided into 8x8 blocks and discrete cosine transform (DCT) is performed for each block. A part of 64 DCT…

Computer Vision and Pattern Recognition · Computer Science 2017-11-30 Mykola Ponomarenko , Nikolay Gapon , Viacheslav Voronin , Karen Egiazarian

In this paper, a novel weighted nonlocal total variation (WNTV) method is proposed. Compared to the classical nonlocal total variation methods, our method modifies the energy functional to introduce a weight to balance between the labeled…

Computer Vision and Pattern Recognition · Computer Science 2018-02-01 Haohan Li , Zuoqiang Shi , Xiaoping Wang

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

We study a nonlocal version of the total variation-based model with $L^1-$fidelity for image denoising, where the regularizing term is replaced with the fractional $s$-total variation. We discuss regularity of the level sets and uniqueness…

Analysis of PDEs · Mathematics 2022-02-01 Konstantinos Bessas

We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transforms. Our key…

Applications · Statistics 2009-11-13 François-Xavier Dupé , Jalal Fadili , Jean Luc Starck

In this paper, we denoise a given noisy image by minimizing a smoothness promoting function over a set of local similarity measures which compare the mean of the given image and some candidate image on a large collection of subboxes. The…

Optimization and Control · Mathematics 2024-06-24 Christian Kanzow , Fabius Krämer , Patrick Mehlitz , Gerd Wachsmuth , Frank Werner

In this paper, we are interested in the classical problem of restoring data degraded by a convolution and the addition of a white Gaussian noise. The originality of the proposed approach is two-fold. Firstly, we formulate the restoration…

Methodology · Statistics 2015-05-13 Jean-Christophe Pesquet , Amel Benazza-Benyahia , Caroline Chaux

We analyse a new notion of total anisotropic higher-order variation which, differently from the Total Generalized Variation by Bredies et al., quantifies for possibly non-symmetric tensor fields their variations at arbitrary order weighted…

Numerical Analysis · Mathematics 2020-01-09 Simone Parisotto , Simon Masnou , Carola-Bibiane Schönlieb

We propose a fully-convolutional neural-network architecture for image denoising which is simple yet powerful. Its structure allows to exploit the gradual nature of the denoising process, in which shallow layers handle local noise…

Computer Vision and Pattern Recognition · Computer Science 2018-10-17 Tal Remez , Or Litany , Raja Giryes , Alex M. Bronstein

In this paper, a methodology is investigated for signal recovery in the presence of non-Gaussian noise. In contrast with regularized minimization approaches often adopted in the literature, in our algorithm the regularization parameter is…

Optimization and Control · Mathematics 2017-01-23 Yosra Marnissi , Yuling Zheng , Emilie Chouzenoux , Jean-Christophe Pesquet

Total variation has proved its effectiveness in solving inverse problems for compressive sensing. Besides, the nonlocal means filter used as regularization preserves texture better for recovered images, but it is quite complex to implement.…

Computer Vision and Pattern Recognition · Computer Science 2016-08-30 Trinh Van Chien , Khanh Quoc Dinh , Viet Anh Nguyen , Byeungwoo Jeon