Journal of Scientific Computing

, Volume 80, Issue 2, pp 762–783 | Cite as

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

  • Victor ChurchillEmail author
  • Anne Gelb


In recent investigations, the problem of detecting edges given non-uniform Fourier data was reformulated as a sparse signal recovery problem with an \(\ell _1\)-regularized least squares cost function. This result can also be derived by employing a Bayesian formulation. Specifically, reconstruction of an edge map using \(\ell _1\) 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.


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

Mathematics Subject Classification

94A12 62F15 62J05 65F22 



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Authors and Affiliations

  1. 1.Department of MathematicsDartmouth CollegeHanoverUSA

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