Conference proceeding
Precise phase transition of total variation minimization
2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Vol.2016-, pp.4518-4522
03/2016
DOI: 10.1109/ICASSP.2016.7472532
Abstract
Characterizing the phase transitions of convex optimizations in recovering structured signals or data is of central importance in compressed sensing, machine learning and statistics. The phase transitions of many convex optimization signal recovery methods such as ℓ 1 minimization and nuclear norm minimization are well understood through recent years' research. However, rigorously characterizing the phase transition of total variation (TV) minimization in recovering sparse-gradient signal is still open. In this paper, we fully characterize the phase transition curve of the TV minimization. Our proof builds on Donoho, Johnstone and Montanari's conjectured phase transition curve for the TV approximate message passing algorithm (AMP), together with the linkage between the minmax Mean Square Error (MSE) of a denoising problem and the high-dimensional convex geometry for TV minimization.
Details
- Title: Subtitle
- Precise phase transition of total variation minimization
- Creators
- Bingwen Zhang - Dept. of Elec. and Comp. Engr., Worcester Poly. Inst., Worcester, MAWeiyu Xu - University of IowaJian-Feng Cai - Dept. of Math., Hong Kong U. of Sci. & Tech., Hong Kong, ChinaLifeng Lai - Dept. of Elec. and Comp. Engr., Worcester Poly. Inst., Worcester, MA
- Resource Type
- Conference proceeding
- Publication Details
- 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Vol.2016-, pp.4518-4522
- Publisher
- IEEE
- DOI
- 10.1109/ICASSP.2016.7472532
- ISSN
- 1520-6149
- eISSN
- 2379-190X
- Language
- English
- Date published
- 03/2016
- Academic Unit
- Electrical and Computer Engineering
- Record Identifier
- 9984196966702771
Metrics
1 Record Views