scholarly journals A well-posed multiscale regularization scheme for digital image denoising

2011 ◽  
Vol 21 (4) ◽  
pp. 769-777 ◽  
Author(s):  
V. Prasath
Keyword(s):  
Image Denoising ◽  
Digital Image ◽  
Regularization Parameter ◽  
Input Image ◽  
Smooth Transition ◽  
Functions Of Bounded Variation ◽  
Edge Preserving ◽  
Regularization Scheme ◽  
Adaptive Parameter ◽  
Well Posed

A well-posed multiscale regularization scheme for digital image denoisingWe propose an edge adaptive digital image denoising and restoration scheme based on space dependent regularization. Traditional gradient based schemes use an edge map computed from gradients alone to drive the regularization. This may lead to the oversmoothing of the input image, and noise along edges can be amplified. To avoid these drawbacks, we make use of a multiscale descriptor given by a contextual edge detector obtained from local variances. Using a smooth transition from the computed edges, the proposed scheme removes noise in flat regions and preserves edges without oscillations. By incorporating a space dependent adaptive regularization parameter, image smoothing is driven along probable edges and not across them. The well-posedness of the corresponding minimization problem is proved in the space of functions of bounded variation. The corresponding gradient descent scheme is implemented and further numerical results illustrate the advantages of using the adaptive parameter in the regularization scheme. Compared with similar edge preserving regularization schemes, the proposed adaptive weight based scheme provides a better multiscale edge map, which in turn produces better restoration.

SPACE-FREQUENCY LOCALIZATION AS BIVARIATE MOTHER WAVELETS SELECTING CRITERION FOR HYPERANALYTIC BAYESIAN IMAGE DENOISING

2012 ◽  
Vol 11 (02) ◽  
pp. 1250009 ◽  
Author(s):  
ALEXANDRU ISAR
Keyword(s):  
Image Processing ◽  
Image Denoising ◽  
Digital Image Processing ◽  
Digital Image ◽  
Wavelet Transforms ◽  
Input Image ◽  
Space Frequency ◽  
Mother Wavelets ◽  
Selection Of

Throughout recent years, many wavelet transforms (WTs) were used in digital image processing: the discrete WT (DWT), the stationary WT (SWT) or the hyperanalytic WT (HWT). All these transforms have in common a feature, the mother wavelets (MW). A great number of MWs was already proposed in literature. The purpose of this paper is the selection of MW for hyperanalytic Bayesian image denoising on the basis of its space-frequency localization. The MW with the same space-frequency localization as the elements of the input image gives the better results. Some procedures for the evaluation of the space-frequency localization of MWs and input images are proposed and applied to optimize the results obtained by the simulations of denoising, indicating the most appropriate MW.

Joint Image Denoising with Gradient Direction and Edge-Preserving Regularization

2021 ◽  
pp. 108506
Author(s):  
Pengliang Li ◽  
Junli Liang ◽  
Miaohua Zhang ◽  
Wen Fan ◽  
Guoyang Yu
Keyword(s):  
Image Denoising ◽  
Edge Preserving ◽  
Gradient Direction

Digital image correlation involves an inverse problem: A regularization scheme based on subset size constraint

2016 ◽  
Vol 81 ◽  
pp. 54-62 ◽  
Author(s):  
Qin Zhan ◽  
Yuan Yuan ◽  
Xiangtao Fan ◽  
Jianyong Huang ◽  
Chunyang Xiong ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Digital Image Correlation ◽  
Digital Image ◽  
Image Correlation ◽  
Subset Size ◽  
Regularization Scheme

scholarly journals REGULARIZATION PARAMETER INDEPENDENT ANALYSIS IN NAMBU–JONA-LASINIO MODEL

2013 ◽  
Vol 28 (31) ◽  
pp. 1350164 ◽  
Author(s):  
T. INAGAKI ◽  
D. KIMURA ◽  
H. KOHYAMA ◽  
A. KVINIKHIDZE
Keyword(s):  
Regularization Parameter ◽  
Dimensional Regularization ◽  
Low Energy ◽  
Leading Order ◽  
Regularization Scheme ◽  
Independent Analysis

Nambu–Jona-Lasinio model used to investigate low energy phenomena is nonrenormalizable, therefore the results depend on the regularization parameter in general. A possibility of the finite in four-dimensional limit and even the in regularization parameter (this is dimension in the dimensional regularization scheme) independent analysis is shown in the leading order of the 1/Nc expansion.

Exponential linear unit dilated residual network for digital image denoising

2018 ◽  
Vol 27 (05) ◽  
pp. 1
Author(s):  
Aditi Panda ◽  
Ruchira Naskar ◽  
Snehanshu Pal
Keyword(s):  
Image Denoising ◽  
Digital Image ◽  
Residual Network

scholarly journals On the Taut String Interpretation and Other Properties of the Rudin–Osher–Fatemi Model in One Dimension

2019 ◽  
Vol 61 (9) ◽  
pp. 1276-1300
Author(s):  
Niels Chr Overgaard
Keyword(s):  
Regularization Parameter ◽  
Total Variation Regularization ◽  
Functions Of Bounded Variation ◽  
Signal Restoration ◽  
Uniqueness Of Solutions ◽  
Taut String ◽  
Fundamental Estimate ◽  
Dimensional Version ◽  
String Algorithm ◽  
The One

Abstract We study the one-dimensional version of the Rudin–Osher–Fatemi (ROF) denoising model and some related TV-minimization problems. A new proof of the equivalence between the ROF model and the so-called taut string algorithm is presented, and a fundamental estimate on the denoised signal in terms of the corrupted signal is derived. Based on duality and the projection theorem in Hilbert space, the proof of the taut string interpretation is strictly elementary with the existence and uniqueness of solutions (in the continuous setting) to both models following as by-products. The standard convergence properties of the denoised signal, as the regularizing parameter tends to zero, are recalled and efficient proofs provided. The taut string interpretation plays an essential role in the proof of the fundamental estimate. This estimate implies, among other things, the strong convergence (in the space of functions of bounded variation) of the denoised signal to the corrupted signal as the regularization parameter vanishes. It can also be used to prove semi-group properties of the denoising model. Finally, it is indicated how the methods developed can be applied to related problems such as the fused lasso model, isotonic regression and signal restoration with higher-order total variation regularization.

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