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Bayesian random Fourier filters for Gaussian noises

Shiyuan Wang, Wanli Wang, Shukai Duan, Lidan Wang, Chi K. Tse
2018 Science China Information Sciences  
SCIENCE CHINA Information Sciences Gaussian approximate filter for stochastic dynamic systems with randomly delayed measurements and colored measurement noises SCIENCE CHINA Information Sciences 59, 092207  ...  (2016); Improved fast model migration method for centrifugal compressor based on bayesian algorithm and Gaussian process model  ...  The responsibility for scientific accuracy and content remains entirely with the authors.  ... 
doi:10.1007/s11432-018-9634-7 fatcat:gckemknrvfbl7pv56aqkbmqtm4

Application of wavelets to filtering of noisy data

U.-L. Pen
1999 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences  
A generalization of Wiener filtering to Non-Gaussian distributions and wavelets is described, as well as an approach to measure the errors in the reconstructed images.  ...  I discuss approaches to optimally remove noise from images.  ...  For Gaussian random processes, Fourier modes are statistically independent.  ... 
doi:10.1098/rsta.1999.0448 fatcat:ajv25oil3rcl3doz7n2yqpn4a4

Nonlinear Multidimensional Bayesian Estimation with Fourier Densities

Dietrich Brunn, Felix Sawo, Uwe D. Hanebeck
2006 Proceedings of the 45th IEEE Conference on Decision and Control  
Efficiently implementing nonlinear Bayesian estimators is still an unsolved problem, especially for the multidimensional case.  ...  Using multidimensional Fourier series as representation for probability density functions, so called Fourier densities, is proposed.  ...  ., random vectors, and employ a Bayesian Estimator. For linear systems with Gaussian random variables, the problem can be fully solved using the Kalman Filter [1] , [2] .  ... 
doi:10.1109/cdc.2006.377378 dblp:conf/cdc/BrunnSH06 fatcat:puod55qva5fzbadd5ui4zqcbw4

A New Perspective of Wavelet Based Image Denoising Using Different Wavelet Thresholding

2016 International Journal of Science and Research (IJSR)  
Image denoising is a process of removing noise without affecting and distorting the image and produce a better quality of denoised image.  ...  I=S+(S*N) (5) Where, N = random noise having a zero mean Gaussian probability distributive function S=random signal Benefits of wavelet transform over Fourier transform  Fourier Transform works well  ...  Some incipient techniques, recommended for image denoising process, were based on spatial filter and FFT (fast Fourier transform) filter [1] .  ... 
doi:10.21275/art20161212 fatcat:tx6gbcgb6zauxl5q7rmtzbasgi

Spatiotemporal Learning via Infinite-Dimensional Bayesian Filtering and Smoothing: A Look at Gaussian Process Regression Through Kalman Filtering

Simo Sarkka, Arno Solin, Jouni Hartikainen
2013 IEEE Signal Processing Magazine  
This formulation allows for use of computationally efficient infinite-dimensional Kalman filtering and smoothing methods, or more general Bayesian filtering and smoothing methods, which reduces the problematic  ...  In this article, we discuss connections of Gaussian process regression with Kalman filtering and present methods for converting spatiotemporal Gaussian process regression problems into infinite-dimensional  ...  GAUssIAN PROCesses IN ReGRessION AND KAlmAN fIlTeRING Definition of a Gaussian Process A Gaussian process is a random function ( ) f p with d-dimensional input p such that any finite collection of random  ... 
doi:10.1109/msp.2013.2246292 fatcat:4sxpmbcndbezxiopzs733xicqe

Efficient Nonlinear Bayesian Estimation based on Fourier Densities

Dietrich Brunn, Felix Sawo, Uwe Hanebeck
2006 2006 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems  
For linear systems with Gaussian random variables, the problem can be fully solved using the Kalman Filter [1], [2] .  ...  In this paper, the use of nonnegative Fourier series, so-called Fourier densities, for Bayesian estimation is proposed.  ...  NONLINEAR FILTERING WITH FOURIER DENSITIES In this section we discuss how to perform Bayesian filtering with Fourier densities. We begin with the filtering step of (4).  ... 
doi:10.1109/mfi.2006.265642 dblp:conf/mfi/BrunnSH06 fatcat:vxordzth2jft5pg7nrsqikiniq

Bayesian pattern recognition in optically degraded noisy images

Rafael Navarro, Oscar Nestares, Jose J Valles
2003 Journal of Optics. A, Pure and applied optics  
We present a novel Bayesian method for pattern recognition in images affected by unknown optical degradations and additive noise.  ...  The images are degraded by different levels of both random (atmospheric turbulence) and deterministic (defocus) optical aberrations, as well as additive white Gaussian noise.  ...  The input object, is introduced as a 128x128 pixels image (see Fig. 2 ), and is filtered by the simulated OTF, and finally three different levels of random Gaussian noise are added to the filtered image  ... 
doi:10.1088/1464-4258/6/1/008 fatcat:sftaf72ui5c75blrv34bhwu7ku

One-sided recursive filters for two-dimensional random fields (Corresp.)

E. Wong, E. Tsui
1977 IEEE Transactions on Information Theory  
< tz < ba, (1.1) where [is the observed process, x is a Gaussian two-parameter random field representing the state to be estimated, and d(ti,tz) is a two-parameter white Gaussian noise with In this paper  ...  )12 1 states which are stationary Gaussian random fields with spectral ON INFORMATION THEORY, VOL.  ... 
doi:10.1109/tit.1977.1055765 fatcat:5p3yxbe2dzajvizynoqnwfc23m

Speech Enhancement Modeling Towards Robust Speech Recognition System [article]

Urmila Shrawankar, V. M. Thakare
2013 arXiv   pre-print
In this contribution, speech enhancement system is introduced for enhancing speech signals corrupted by additive noise and improving the performance of Automatic Speech Recognizers in noisy conditions.  ...  The amount of improvement varies with the type of the corrupting noise.  ...  Under a Gaussian assumption for speech and noise, the estimator is linear (Wiener filter).  ... 
arXiv:1305.1426v1 fatcat:g35jkfvxwjdjjnhn6uw77xx5uu

On the Linearity of Bayesian Interpolators for Non-Gaussian Continuous-Time AR(1) Processes

Arash Amini, Philippe Thevenaz, John Paul Ward, Michael Unser
2013 IEEE Transactions on Information Theory  
We redefine the Bayesian estimation problem in the Fourier domain with the help of characteristic forms.  ...  The two common strategies for non-Gaussian models are either finding the best linear estimator or numerically evaluating the Bayesian estimator by Monte Carlo methods.  ...  Pad for fruitful discussions.  ... 
doi:10.1109/tit.2013.2258371 fatcat:74hmnuj27rdjrhpq4wnbnena7q

The footprints of visual attention in the Posner cueing paradigm revealed by classification images

Miguel P. Eckstein, Steven S. Shimozaki, Craig K. Abbey
2002 Journal of Vision  
We did not find statistically significant differences between the shapes of the inferred perceptual filters across the two locations, nor did the observed differences account for the measured cueing effects  ...  This effect can be explained in terms of a Bayesian observer where visual attention simply weights the information differently at the cued (attended) and uncued (unattended) locations without a change  ...  The authors would like to thank Albert Ahumada Jr. for insight in the topic of classification images and Charlie Chubb for a careful review and insightful comments.  ... 
doi:10.1167/2.1.3 pmid:12678595 fatcat:e477same2be2bh4vmyryjnjmhi

Novel Bayesian multiscale method for speckle removal in medical ultrasound images

A. Achim, A. Bezerianos, P. Tsakalides
2001 IEEE Transactions on Medical Imaging  
Then, we design a Bayesian estimator that exploits these statistics. We use the alpha-stable model to develop a blind noise-removal processor that performs a nonlinear operation on the data.  ...  A novel speckle suppression method for medical ultrasound images is presented. First, the logarithmic transform of the original image is analyzed into the multiscale wavelet domain.  ...  Starmer and the IT Lab at the Medical University of South Carolina for providing the ultrasound images used in this paper.  ... 
doi:10.1109/42.938245 pmid:11513028 fatcat:ljlqciwtsvcv5mqucjfynolcc4

Survey in Existing Non-Local Means Algorithm for Noise Reduction

Arti Singh, Ram Singar
2017 International Journal of Computer Applications  
Image accommodates noise like Gaussian noise, salt & pepper noise, speckle noise, film grain etc.  ...  In this paper, only survey on the existing non-local means algorithm for noise reduction which is taken from many devices like camera or other digital gadgets.  ...  Gaussian noise is used as additive white noise. Each pixel in the noisy image is the sum of pixels value and random Gaussian distributed noise value.  ... 
doi:10.5120/ijca2017913751 fatcat:bfzl67xvl5gqnikkwk3kkblbxi

A Bayesian view on cryo-EM structure determination

Sjors H. W. Scheres
2012 2012 9th IEEE International Symposium on Biomedical Imaging (ISBI)  
I describe a Bayesian interpretation of cryo-EM structure determination, where smoothness in the reconstructed density is imposed through a Gaussian prior in the Fourier domain.  ...  The statistical framework dictates how data and prior knowledge should be combined, so that the optimal 3D linear filter is obtained without the need for arbitrariness and objective resolution estimates  ...  Acknowledgements I am grateful to colleagues from the Laboratory of Molecular Biology for stimulating discussions and to Tony Crowther, Richard Henderson, Nigel Unwin, and Niko Grigorieff for critical  ... 
doi:10.1109/isbi.2012.6235807 dblp:conf/isbi/Scheres12 fatcat:zqhrrdekcjhdxew54hdd3rtmv4

A Bayesian View on Cryo-EM Structure Determination

Sjors H.W. Scheres
2012 Journal of Molecular Biology  
I describe a Bayesian interpretation of cryo-EM structure determination, where smoothness in the reconstructed density is imposed through a Gaussian prior in the Fourier domain.  ...  The statistical framework dictates how data and prior knowledge should be combined, so that the optimal 3D linear filter is obtained without the need for arbitrariness and objective resolution estimates  ...  Acknowledgements I am grateful to colleagues from the Laboratory of Molecular Biology for stimulating discussions and to Tony Crowther, Richard Henderson, Nigel Unwin, and Niko Grigorieff for critical  ... 
doi:10.1016/j.jmb.2011.11.010 pmid:22100448 pmcid:PMC3314964 fatcat:wcyv2wen7jgxlgwavbnayynfma
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