Detecting Edges from Non-uniform Fourier Data via Sparse Bayesian Learning

Victor Churchill, Anne Gelb

Research output: Contribution to journalArticle

Abstract

In recent investigations, the problem of detecting edges given non-uniform Fourier data was reformulated as a sparse signal recovery problem with an ℓ 1 -regularized least squares cost function. This result can also be derived by employing a Bayesian formulation. Specifically, reconstruction of an edge map using ℓ 1 regularization corresponds to a so-called type-I (maximum a posteriori) Bayesian estimate. In this paper, we use the Bayesian framework to design an improved algorithm for detecting edges from non-uniform Fourier data. In particular, we employ what is known as type-II Bayesian estimation, specifically a method called sparse Bayesian learning. We also show that our new edge detection method can be used to improve downstream processes that rely on accurate edge information like image reconstruction, especially with regards to compressed sensing techniques.

Original languageEnglish (US)
JournalJournal of Scientific Computing
DOIs
StatePublished - Jan 1 2019
Externally publishedYes

Fingerprint

Bayesian Learning
Compressed sensing
Sparse Data
Edge detection
Image reconstruction
Cost functions
Recovery
Square Functions
Compressed Sensing
Maximum a Posteriori
Bayesian Estimation
Edge Detection
Image Reconstruction
Cost Function
Least Squares
Regularization
Formulation
Estimate

Keywords

  • Edge detection
  • Non-uniform Fourier data
  • Regularization
  • Signal reconstruction
  • Sparse Bayesian learning

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

Cite this

Detecting Edges from Non-uniform Fourier Data via Sparse Bayesian Learning. / Churchill, Victor; Gelb, Anne.

In: Journal of Scientific Computing, 01.01.2019.

Research output: Contribution to journalArticle

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