Related Experiment Video
Updated: Aug 2, 2025

Retrospective Cardiac Gating with A Prototype Small-Animal X-ray Computed Tomograph
Published on: February 21, 2025
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.
Abstract:
In Bayesian statistics, horseshoe prior has attracted increasing attention as an approach to compressed sensing. By considering compressed sensing as a randomly correlated many-body problem, statistical mechanics methods can be used to analyze the problem. In this paper, the estimation accuracy of compressed sensing with the horseshoe prior is evaluated by the statistical mechanical methods of random systems. It is found that there exists a phase transition in signal recoverability in the plane of the number of observations and the number of nonzero signals, and that the recoverable phase is more extended than that using the well-known l_{1} norm regularization.
Related Concept Videos
Upsampling
¹H NMR: Interpreting Distorted and Overlapping Signals
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
2D NMR: Heteronuclear Single-Quantum Correlation Spectroscopy (HSQC)
Reconstruction of Signal using Interpolation
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
Region of Convergence of Laplace Tarnsform
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This...

