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Variational Algorithms to Remove Stationary Noise: Applications to Microscopy Imaging

J. Fehrenbach, P. Weiss, C. Lorenzo
2012 IEEE Transactions on Image Processing  
In numerous denoising applications the white noise assumption fails: structured patterns (e.g. stripes) appear in the images. The model described here addresses these cases.  ...  A framework and an algorithm are presented in order to remove stationary noise from images. This algorithm is called VSNR (Variational Stationary Noise Remover).  ...  ACKNOWLEDGMENT The authors would like to thank Bernard Ducommun, Raphaël Jorand and Valérie Lobjois from the IP3D team in Toulouse cancéropole for their tireless support during this work and for all SPIM  ... 
doi:10.1109/tip.2012.2206037 pmid:22752131 fatcat:p3eeu3et75ez7abuou44tnwleq

Hyperspectral Image Denoising via Global Spatial-Spectral Total Variation Regularized Nonconvex Local Low-Rank Tensor Approximation [article]

Haijin Zeng, Xiaozhen Xie, Jifeng Ning
2020 arXiv   pre-print
According to this fact, we propose a novel tensor L_γ-norm to formulate the local LR prior. From another aspect, HSIs are assumed to be piecewisely smooth in the global spatial and spectral domains.  ...  In this paper, we propose a novel spatial-spectral total variation (SSTV) regularized nonconvex local low-rank (LR) tensor approximation method to remove mixed noise in HSIs.  ...  Unfortunately, since the nuclear norm may not be a perfect approximation to the rank function [24, 15] , the TNN based models may obtain suboptimal performance in real applications.  ... 
arXiv:2006.00235v1 fatcat:pybaxqwwwzdgdcfxm5rktj55py

Bilevel Image Denoising Using Gaussianity Tests [chapter]

Jérôme Fehrenbach, Mila Nikolova, Gabriele Steidl, Pierre Weiss
2015 Lecture Notes in Computer Science  
We propose a new methodology based on bilevel programming to remove additive white Gaussian noise from images. The lowerlevel problem consists of a parameterized variational model to denoise images.  ...  The parameters are optimized in order to minimize a specific cost function that measures the residual Gaussianity. This model is justified using a statistical analysis.  ...  The case p > 1 The idea proposed in the case of a single parameter can be generalized by defining a set of q Euclidean semi-norms ( · 2 Mi ) q i=1 .  ... 
doi:10.1007/978-3-319-18461-6_10 fatcat:w5zkwj35cfaydc5tuarrlqn2sy

Weighted Low-rank Tensor Recovery for Hyperspectral Image Restoration [article]

Yi Chang, Luxin Yan, Houzhang Fang, Sheng Zhong, Zhijun Zhang
2017 arXiv   pre-print
We also consider the exclusive stripe noise in HSI as the gross error by extending WLRTR to robust principal component analysis (WLRTR-RPCA).  ...  Extensive experiments demonstrate the proposed WLRTR models consistently outperform state-of-the-arts in typical low level vision HSI tasks, including denoising, destriping, deblurring and super-resolution  ...  The L 211 norm (defined in section III) is introduced to capture the directional and structural property of the stripe noise.  ... 
arXiv:1709.00192v1 fatcat:ueremc3lzvhlna42pgngpgb3ka

Processing stationary noise: model and parameter selection in variational methods [article]

Jérôme Fehrenbach, Pierre Weiss
2013 arXiv   pre-print
Relatively few works address the design of dedicated denoising methods compared to the usual white noise setting. We recently proposed a variational algorithm to tackle this issue.  ...  In the second part, we focus on the Gaussian setting and analyze denoising methods which consist of minimizing the sum of a total variation term and an l^2 data fidelity term.  ...  It was also shown to generalize the negative norm models [2, 14, 20, 26] in the discrete setting [9].  ... 
arXiv:1307.4592v1 fatcat:f3ya5yzdsnf7hcbpw3mhhgwggq

Hyperspectral Image Denoising Using Non-convex Local Low-rank and Sparse Separation with Spatial-Spectral Total Variation Regularization [article]

Chong Peng, Yang Liu, Yongyong Chen, Xinxin Wu, Andrew Cheng, Zhao Kang, Chenglizhao Chen, Qiang Cheng
2022 arXiv   pre-print
In particular, the new method adopts the log-determinant rank approximation and a novel ℓ_2,log norm, to restrict the local low-rank or column-wisely sparse properties for the component matrices, respectively  ...  Extensive experiments on both simulated and real HSIs demonstrate the effectiveness of the proposed method in denoising HSIs.  ...  and ZR2019BF011; Q.C. is partially supported by NIH R21AG070909, UH3 NS100606-03 and a grant from the University of Kentucky.  ... 
arXiv:2201.02812v1 fatcat:vblvx553wzahzcgjeho66nzr3q

Constrained and SNR-Based Solutions for TV-Hilbert Space Image Denoising

Jean-François Aujol, Guy Gilboa
2006 Journal of Mathematical Imaging and Vision  
This framework generalizes the Rudin-Osher-Fatemi and the Osher-Sole-Vese models and opens way for new denoising or decomposition methods with tunable norms, which are adapted to the nature of the noise  ...  Moreover, we generalize a recent study of Gilboa-Sochen-Zeevi where the weight parameter is selected such that the denoised result is close to optimal, in the SNR sense.  ...  Aujol was supported by Grants from the NSF under contracts DMS-9973341, ACI-0072112,  ... 
doi:10.1007/s10851-006-7801-6 fatcat:3vczoye5kjcvxbzojxdmlwm6cq

Nonlinear Power Method for Computing Eigenvectors of Proximal Operators and Neural Networks [article]

Leon Bungert, Ester Hait-Fraenkel, Nicolas Papadakis, Guy Gilboa
2021 arXiv   pre-print
However, a fundamental theory supporting the practical applications is still in the early stages of development.  ...  In order to take the non-homogeneity of neural networks into account we define a modified version of the power method.  ...  The Rayleigh quotient can be generalized in the nonlinear setting to a generalized Rayleigh quotient, (2.3) R(u) = u, T (u) u 2 .  ... 
arXiv:2003.04595v3 fatcat:y4my6einujatlo6avvoc5qot3q

Can Terrestrial Restoration Methodologies be Transferred to Planetary Hyperspectral Imagery? A Quantitative Intercomparison and Discussion

Shuheng Zhao, Jie Li, Qiangqiang Yuan, Huanfeng Shen, Liangpei Zhang
2020 IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing  
In this work, a comprehensive and systematic investigation on planetary noise categories is summarized initially, and an intercomparison among state-of-the-art terrestrial joint spatial-spectral restoration  ...  However, hyperspectral images (HSIs) usually suffer from various noises because of complicated environment and equipment limitations, which leads to inconvenience to subsequent applications.  ...  We thank all the authors of the aforementioned algorithms for providing their excellent work and useful codes to us (we have collected and uploaded these codes to https://github.com/photonmango).  ... 
doi:10.1109/jstars.2020.3024911 fatcat:6gvm7afjt5g4jjxbh3dyf74y5q

Infimal Convolution of Oscillation Total Generalized Variation for the Recovery of Images with Structured Texture

Yiming Gao, Kristian Bredies
2018 SIAM Journal of Imaging Sciences  
We give a detailed theoretical analysis of the infimal-convolution-type model with oscillation TGV in function spaces.  ...  Finally, numerical experiments are presented which show that our proposed models can recover textures well and are competitive in comparison to existing state-of-the-art methods.  ...  Acknowledgement The second author acknowledges support by the Austrian Science Fund (FWF): project number P-29192 "Regularization Graphs for Variational Imaging".  ... 
doi:10.1137/17m1153960 fatcat:yieewphxhvej3jwldlov57gkli

Bayesian Approach in a Learning-Based Hyperspectral Image Denoising Framework

Hazique Aetesam, Suman Kumar Maji, Hussein Yahia
2021 IEEE Access  
A generative mization problem into smaller units. A 3D modelling of noisy model to HSI denoising is employed in [28].  ...  As a result; loss functions derived in Bayesian setting and employed in neural network training boosts the denoising performance.  ... 
doi:10.1109/access.2021.3137656 fatcat:f32vzzaz4nb3jin7vnrazlmtp4

Total Deep Variation: A Stable Regularizer for Inverse Problems [article]

Erich Kobler, Alexander Effland, Karl Kunisch, Thomas Pock
2020 arXiv   pre-print
This combination allows for a rigorous mathematical analysis including an optimal control formulation of the training problem in a mean-field setting and a stability analysis with respect to the initial  ...  A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and a regularizer.  ...  A semi-implicit time discretization of the gradient flow results in a discretized optimal control problem in the mean-field setting, for which we also prove the existence of minimizers as well as a first  ... 
arXiv:2006.08789v1 fatcat:fynzyozxh5difavlqwnn2cq6qq

Regularized Non-local Total Variation and Application in Image Restoration

Zhi Li, François Malgouyres, Tieyong Zeng
2017 Journal of Mathematical Imaging and Vision  
We illustrate the ability of the model to restore relevant unknown edges from the neighboring edges on an image inpainting problem.  ...  In this paper, we impose some regularity to those weight values. More precisely, we minimize a function involving a regularization term, analogous to an H 1 term, on weights.  ...  Acknowledgement François Malgouyres would like to thank Julien Rabin for fruitful discussions on the subject and for teaching him how to efficiently perform the projection on the simplex, and also would  ... 
doi:10.1007/s10851-017-0732-6 fatcat:bnks3fxl7ffd5cifgfumlufy6m

Enhanced 3DTV Regularization and Its Applications on Hyper-spectral Image Denoising and Compressed Sensing [article]

Jiangjun Peng, Qi Xie, Qian Zhao, Yao Wang, Deyu Meng, Yee Leung
2018 arXiv   pre-print
The 3-D total variation (3DTV) is a powerful regularization term, which encodes the local smoothness prior structure underlying a hyper-spectral image (HSI), for general HSI processing tasks.  ...  The E-3DTV term can easily replace the previous 3DTV term and be em- bedded into an HSI processing model to ameliorate its performance.  ...  Therefore, we choose the 1 norm, a more robust loss function to general heavy noises [41, 7] , to model the noise and construct our denoising model as: min X,E τ X E-3DTV + E 1 s.t.  ... 
arXiv:1809.06591v1 fatcat:finhrqiugjg73j46sik3inauoi

Hierarchical Sparse Learning with Spectral-Spatial Information for Hyperspectral Imagery Denoising

Shuai Liu, Licheng Jiao, Shuyuan Yang
2016 Sensors  
To improve the denoising performance, a metric Q-weighted fusion algorithm is proposed to merge the denoising results of both spatial and spectral views [22] .  ...  These methods denoise the HSI band by band and destroy the latent high-dimensional structure of the HSI, which result in a great loss of spectral correlations.  ...  2016, 16 , 1718 8 of 26 The negative logarithm posterior density function of the above model (utilized jointly to all data X c = x c i i=1,...  ... 
doi:10.3390/s16101718 pmid:27763511 pmcid:PMC5087505 fatcat:u3fj3oxqoza57lq5zlv4twmy2a
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