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| Author(s): |
Paulo Victor Camargo Rossi
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | São Paulo. |
| Institution: | Universidade de São Paulo (USP). Instituto de Física (IF/SBI) |
| Defense date: | 2018-03-02 |
| Examining board members: |
Renato Vicente;
Nestor Felipe Caticha Alfonso;
Adriano Polpo de Campos;
Tania Tome Martins de Castro;
Masayuki Oka Hase
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| Advisor: | Renato Vicente |
| Abstract | |
In this work, Compressed Sensing is introduced from a Statistical Physics point of view. Following a succinct introduction where the basic concepts of the framework are presented, including necessary measurement conditions and basic signal reconstruction methods, the typical performance of the Bayesian reconstruction scheme is analyzed through a replica calculation shown in pedagogical detail. Thereafter, the main original contribution of this work is introduced --- the Bayesian Online Compressed Sensing algorithm makes use of a mean-field approximation to simplify calculations and reduce memory and computation requirements, while maintaining the asymptotic reconstruction accuracy of the offline scheme in the presence of additive noise. The last part of this work are two extensions of the online algorithm that allow for optimized signal reconstruction in the more realistic scenarios where perfect knowledge of the generating distribution is unavailable. (AU) | |
| FAPESP's process: | 14/00792-7 - Statistical mechanics applied to compressed sensing |
| Grantee: | Paulo Victor Camargo Rossi |
| Support Opportunities: | Scholarships in Brazil - Doctorate |