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In recent investigations, the problem of detecting edges given non-uniformFourier data was reformulated as a sparse signal recovery problem with anl1-regularized least squares cost function. This result can also be derived byemploying a Bayesian formulation. Specifically, reconstruction of an edge mapusing l1 regularization corresponds to a so-called type-I (maximum aposteriori) Bayesian estimate. In this paper, we use the Bayesian framework todesign 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 ournew edge detection method can be used to improve downstream processes that relyon accurate edge information like image reconstruction, especially with regardsto compressed sensing techniques.

Detecting edges from non-uniform Fourier data via sparse Bayesian learning