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Phase transition in compressed sensing with horseshoe prior
Yasushi Nagano1, Koji Hukushima1,2
1Graduate School of Arts and Sciences, The University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8902, Japan.
Physical Review. E
|April 19, 2023
Summary
The horseshoe prior improves compressed sensing accuracy by analyzing it as a many-body problem. This Bayesian statistics approach reveals a phase transition, extending signal recoverability beyond standard l1 norm methods.
Area of Science:
- Bayesian statistics
- Compressed sensing
- Statistical mechanics
Background:
- Horseshoe prior is gaining traction for compressed sensing applications.
- Compressed sensing can be modeled as a complex, randomly correlated many-body system.
Purpose of the Study:
- To evaluate the estimation accuracy of compressed sensing using the horseshoe prior.
- To analyze compressed sensing performance through statistical mechanics methods.
Main Methods:
- Applied statistical mechanics of random systems to analyze compressed sensing.
- Investigated the horseshoe prior within a many-body problem framework.
Main Results:
- Identified a phase transition in signal recoverability based on observation and signal counts.
- The horseshoe prior demonstrates a more extended recoverable phase compared to l1 norm regularization.
Conclusions:
- Statistical mechanics provides a powerful framework for understanding compressed sensing with horseshoe priors.
- The horseshoe prior offers enhanced signal recovery capabilities in compressed sensing.
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