Code and Data supplement to "Efficient Threshold Selection for Multivariate Total Variation Denoising"
Abstract/Contents
- Abstract
The data and code provided here are supplementary information for the paper “Efficient Threshold Selection for Multivariate Total Variation Denoising".
Abstract of the article:
Total variation (TV) denoising is a nonparametric smoothing method that has good properties for preserving sharp edges and contours in objects with spatial structures like natural images.The estimate is sparse in the sense that TV reconstruction leads to a piecewise constant function with a small number of jumps. A threshold parameter controls the number of jumps and the quality of the estimation. In practice, this threshold is often selected by minimizing a goodness-of-fit criterion like cross-validation, which can be costly as it requires solving the high-dimensional and non-differentiable TV optimization problem many times. We propose instead a two step adaptive procedure via a connection to large deviation of stochastic processes.
We also give conditions under which TV denoising achieves exact segmentation. We then apply our procedure to denoise a collection of 1D and 2D test signals verifying the effectiveness of our approach in practice.
Description
Type of resource | software, multimedia |
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Date created | [ca. 2014 - 2017] |
Creators/Contributors
Author | Sardy, Sylvain |
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Author | Monajemi, Hatef |
Subjects
Subject | Empirical processes |
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Subject | image processing |
Subject | segmentation |
Subject | smoothing |
Subject | Sup norm minimization. |
Genre | Dataset |
Bibliographic information
Related Publication | Sardy, Sylvain and Monajemi, Hatef. (2018). Efficient Threshold Selection for Multivariate Total Variation Denoising. Journal of Computational and Graphical Statistics. https://doi.org/10.1080/10618600.2018.1476251 |
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Location | https://purl.stanford.edu/sw114yc8625 |
Access conditions
- Use and reproduction
- User agrees that, where applicable, content will not be used to identify or to otherwise infringe the privacy or confidentiality rights of individuals. Content distributed via the Stanford Digital Repository may be subject to additional license and use restrictions applied by the depositor.
- License
- This work is licensed under an Open Data Commons Public Domain Dedication & License 1.0.
Preferred citation
- Preferred Citation
- Sardy, Sylvain and Monajemi, Hatef. (2016). Code and Data supplement to "Efficient Threshold Selection for Multivariate Total Variation Denoising". Stanford Digital Repository. Available at: http://purl.stanford.edu/sw114yc8625
Collection
Stanford Research Data
View other items in this collection in SearchWorksContact information
- Contact
- monajemi@stanford.edu
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