scholarly journals On the gap between the Gamma-limit and the pointwise limit for a nonlocal approximation of the total variation

2020 ◽  
Vol 13 (3) ◽  
pp. 627-649
Author(s):  
Clara Antonucci ◽  
Massimo Gobbino ◽  
Nicola Picenni
Keyword(s):  
Total Variation ◽  
Pointwise Limit

On Asymmetric Distances

2013 ◽  
Vol 1 ◽  
pp. 200-231 ◽  
Author(s):  
Andrea C.G. Mennucci
Keyword(s):  
Total Variation ◽  
Calculus Of Variations ◽  
Distance Function ◽  
Metric Space ◽  
Metric Spaces ◽  
Geodesic Segment ◽  
Intrinsic Metric ◽  
Typical Application ◽  
Variation Formula

Abstract In this paper we discuss asymmetric length structures and asymmetric metric spaces. A length structure induces a (semi)distance function; by using the total variation formula, a (semi)distance function induces a length. In the first part we identify a topology in the set of paths that best describes when the above operations are idempotent. As a typical application, we consider the length of paths defined by a Finslerian functional in Calculus of Variations. In the second part we generalize the setting of General metric spaces of Busemann, and discuss the newly found aspects of the theory: we identify three interesting classes of paths, and compare them; we note that a geodesic segment (as defined by Busemann) is not necessarily continuous in our setting; hence we present three different notions of intrinsic metric space.

DE-NOISING OF CT IMAGES USING COMBINED BIVARIATE SHRINKAGE AND ENHANCED TOTAL VARIATION TECHNIQUE

2018 ◽  
Vol 8 (4) ◽  
pp. 12
Author(s):  
DEVANAND BHONSLE ◽  
VIVEK KUMAR CHANDRA ◽  
SINHA G. R. ◽  
◽  
◽  
...  
Keyword(s):  
Total Variation ◽  
Ct Images ◽  
Bivariate Shrinkage ◽  
Variation Technique

Block wavelet threshold image denoising on total variation

2013 ◽  
Vol 32 (5) ◽  
pp. 1289-1292
Author(s):  
Yuan-yuan GAO ◽  
Yong-feng DIAO ◽  
Yun BIAN
Keyword(s):  
Image Denoising ◽  
Total Variation

scholarly journals Ant Colony-Based Hyperparameter Optimisation in Total Variation Reconstruction in X-ray Computed Tomography

Sensors ◽  
2021 ◽  
Vol 21 (2) ◽  
pp. 591
Author(s):  
Manasavee Lohvithee ◽  
Wenjuan Sun ◽  
Stephane Chretien ◽  
Manuchehr Soleimani
Keyword(s):  
Computed Tomography ◽  
Total Variation ◽  
Cross Validation ◽  
Ant Colony ◽  
Reference Image ◽  
X Ray ◽  
X Ray Computed ◽  
Hyperparameter Selection ◽  
The Cross ◽  
Optimal Set

In this paper, a computer-aided training method for hyperparameter selection of limited data X-ray computed tomography (XCT) reconstruction was proposed. The proposed method employed the ant colony optimisation (ACO) approach to assist in hyperparameter selection for the adaptive-weighted projection-controlled steepest descent (AwPCSD) algorithm, which is a total-variation (TV) based regularisation algorithm. During the implementation, there was a colony of artificial ants that swarm through the AwPCSD algorithm. Each ant chose a set of hyperparameters required for its iterative CT reconstruction and the correlation coefficient (CC) score was given for reconstructed images compared to the reference image. A colony of ants in one generation left a pheromone through its chosen path representing a choice of hyperparameters. Higher score means stronger pheromones/probabilities to attract more ants in the next generations. At the end of the implementation, the hyperparameter configuration with the highest score was chosen as an optimal set of hyperparameters. In the experimental results section, the reconstruction using hyperparameters from the proposed method was compared with results from three other cases: the conjugate gradient least square (CGLS), the AwPCSD algorithm using the set of arbitrary hyperparameters and the cross-validation method.The experiments showed that the results from the proposed method were superior to those of the CGLS algorithm and the AwPCSD algorithm using the set of arbitrary hyperparameters. Although the results of the ACO algorithm were slightly inferior to those of the cross-validation method as measured by the quantitative metrics, the ACO algorithm was over 10 times faster than cross—Validation. The optimal set of hyperparameters from the proposed method was also robust against an increase of noise in the data and can be applicable to different imaging samples with similar context. The ACO approach in the proposed method was able to identify optimal values of hyperparameters for a dataset and, as a result, produced a good quality reconstructed image from limited number of projection data. The proposed method in this work successfully solves a problem of hyperparameters selection, which is a major challenge in an implementation of TV based reconstruction algorithms.

scholarly journals The convergence of a numerical method for total variation flow

2021 ◽  
Vol 15 ◽  
pp. 174830262110113
Author(s):  
Qianying Hong ◽  
Ming-jun Lai ◽  
Jingyue Wang
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Numerical Method ◽  
Convergence Analysis ◽  
Total Variation ◽  
Iterative Algorithm ◽  
Finite Difference Scheme ◽  
Gradient Flow ◽  
Time Dependent ◽  
Total Variation Flow

We present a convergence analysis for a finite difference scheme for the time dependent partial different equation called gradient flow associated with the Rudin-Osher-Fetami model. We devise an iterative algorithm to compute the solution of the finite difference scheme and prove the convergence of the iterative algorithm. Finally computational experiments are shown to demonstrate the convergence of the finite difference scheme.

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