Inducing sparsity via the horseshoe prior in imaging problems

Yiqiu Dong, Monica Pragliola*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

A problem typically arising in imaging applications is the reconstruction task under sparsity constraints. A computationally efficient strategy to address this problem is to recast it in a hierarchical Bayesian framework coupled with a Maximum A Posteriori (MAP) estimation approach. More specifically, the original unknown is modeled as a conditionally Gaussian random variable with an unknown variance. Here, the expected behavior on the variance is encoded in a half-Cauchy hyperprior. The latter, coupled to the conditioned Gaussian prior, yields the horseshoe shrinkage prior, particularly popular within the statistics community and here introduced into the context of imaging problems. The arising non-convex MAP estimation problem is tackled via an alternating minimization scheme for which the global convergence to a stationary point is guaranteed. Experimental results prove that the derived hypermodel is competitive with classical variational methods as well as with other hierarchical Bayesian models typically employed for sparse recovery problems.
Original languageEnglish
Article number074001
JournalInverse Problems
Volume39
Issue number7
Number of pages28
ISSN0266-5611
DOIs
Publication statusPublished - 2023

Keywords

  • Sparse recovery
  • Hierarchical modeling
  • Horseshoe prior
  • Linear inverse problems

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