scholarly journals Moderate deviations for a fractional stochastic heat equation with spatially correlated noise

2017 ◽  
Vol 17 (04) ◽  
pp. 1750025 ◽  
Author(s):  
Yumeng Li ◽  
Ran Wang ◽  
Nian Yao ◽  
Shuguang Zhang
Keyword(s):  
Heat Equation ◽  
Moderate Deviation ◽  
Stochastic Heat Equation ◽  
Correlated Noise ◽  
Derivative Operator ◽  
Spatially Correlated ◽  
Whole Space ◽  
Convergence Method ◽  
Spatially Correlated Noise ◽  
Weak Convergence Method

In this paper, we study the Moderate Deviation Principle for a perturbed stochastic heat equation in the whole space [Formula: see text]. This equation is driven by a Gaussian noise, white in time and correlated in space, and the differential operator is a fractional derivative operator. The weak convergence method plays an important role.

AUTOMATIC ESTIMATION OF SPATIALLY CORRELATED NOISE VARIANCE IN SPECTRAL DOMAIN FOR IMAGES

2014 ◽  
Vol 73 (6) ◽  
pp. 511-527 ◽  
Author(s):  
V.V. Abramova ◽  
S. K. Abramov ◽  
V. V. Lukin ◽  
A. A. Roenko ◽  
Benoit Vozel
Keyword(s):  
Spectral Domain ◽  
Correlated Noise ◽  
Noise Variance ◽  
Spatially Correlated ◽  
Automatic Estimation ◽  
Spatially Correlated Noise

Adaptive DCT-based filtering of images corrupted by spatially correlated noise

2008 ◽  
Author(s):  
Nikolay N. Ponomarenko ◽  
Vladimir V. Lukin ◽  
Aleksandr A. Zelensky ◽  
Jaakko T. Astola ◽  
Karen O. Egiazarian
Keyword(s):  
Correlated Noise ◽  
Spatially Correlated ◽  
Spatially Correlated Noise

scholarly journals Ring artifact reduction via multiscale nonlocal collaborative filtering of spatially correlated noise

2021 ◽  
Vol 28 (3) ◽  
Author(s):  
Ymir Mäkinen ◽  
Stefano Marchesini ◽  
Alessandro Foi
Keyword(s):  
Multiple Scales ◽  
Simulated Data ◽  
Block Matching ◽  
Artifact Reduction ◽  
Correlated Noise ◽  
Spatially Correlated ◽  
Ring Artifact ◽  
Fully Automatic ◽  
Micro Tomography ◽  
Spatially Correlated Noise

X-ray micro-tomography systems often suffer severe ring artifacts in reconstructed images. These artifacts are caused by defects in the detector, calibration errors, and fluctuations producing streak noise in the raw sinogram data. In this work, these streaks are modeled in the sinogram domain as additive stationary correlated noise upon logarithmic transformation. Based on this model, a streak removal procedure is proposed where the Block-Matching and 3-D (BM3D) filtering algorithm is applied across multiple scales, achieving state-of-the-art performance in both real and simulated data. Specifically, the proposed fully automatic procedure allows for attenuation of streak noise and the corresponding ring artifacts without creating major distortions common to other streak removal algorithms.

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