Maximum Penalized-Likelihood Structured Covariance Estimation for Imaging Extended Objects, with Application to Radio Astronomy
Image formation in radio astronomy is often posed as a problem of constructing a nonnegative function from sparse samples of its Fourier transform. We explore an alternative approach that reformulates the problem in terms of estimating the entries of a diagonal covariance matrix from Gaussian data....
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-12-01
|
| Series: | Stats |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2571-905X/7/4/88 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | Image formation in radio astronomy is often posed as a problem of constructing a nonnegative function from sparse samples of its Fourier transform. We explore an alternative approach that reformulates the problem in terms of estimating the entries of a diagonal covariance matrix from Gaussian data. Maximum-likelihood estimates of the covariance cannot be readily computed analytically; hence, we investigate an iterative algorithm originally proposed by Snyder, O’Sullivan, and Miller in the context of radar imaging. The resulting maximum-likelihood estimates tend to be unacceptably rough due to the ill-posed nature of the maximum-likelihood estimation of functions from limited data, so some kind of regularization is needed. We explore penalized likelihoods based on entropy functionals, a roughness penalty proposed by Silverman, and an information-theoretic formulation of Good’s roughness penalty crafted by O’Sullivan. We also investigate algorithm variations that perform a generic smoothing step at each iteration. The results illustrate that tuning parameters allow for a tradeoff between the noise and blurriness of the reconstruction. |
|---|---|
| ISSN: | 2571-905X |