### 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 language | English (US) |
---|---|

Journal | Journal of Scientific Computing |

DOIs | |

State | Published - Jan 1 2019 |

Externally published | Yes |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Detecting Edges from Non-uniform Fourier Data via Sparse Bayesian Learning

AU - Churchill, Victor

AU - Gelb, Anne

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Edge detection

KW - Non-uniform Fourier data

KW - Regularization

KW - Signal reconstruction

KW - Sparse Bayesian learning

UR - http://www.scopus.com/inward/record.url?scp=85064512134&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85064512134&partnerID=8YFLogxK

U2 - 10.1007/s10915-019-00955-w

DO - 10.1007/s10915-019-00955-w

M3 - Article

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

SN - 0885-7474

ER -