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!
|
| _version_ | 1846102636407816192 |
|---|---|
| author | Aaron Lanterman |
| author_facet | Aaron Lanterman |
| author_sort | Aaron Lanterman |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-51888018d7ee40b58d8f47aa8037ee64 |
| institution | Kabale University |
| issn | 2571-905X |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Stats |
| spelling | doaj-art-51888018d7ee40b58d8f47aa8037ee642024-12-27T14:54:45ZengMDPI AGStats2571-905X2024-12-01741496151210.3390/stats7040088Maximum Penalized-Likelihood Structured Covariance Estimation for Imaging Extended Objects, with Application to Radio AstronomyAaron Lanterman0School of Electrical and Computer Engineering, Georgia Institute of Technology, 777 Atlantic Drive, Atlanta, GA 30332, USAImage 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.https://www.mdpi.com/2571-905X/7/4/88astronomymaximum likelihoodregularization |
| spellingShingle | Aaron Lanterman Maximum Penalized-Likelihood Structured Covariance Estimation for Imaging Extended Objects, with Application to Radio Astronomy Stats astronomy maximum likelihood regularization |
| title | Maximum Penalized-Likelihood Structured Covariance Estimation for Imaging Extended Objects, with Application to Radio Astronomy |
| title_full | Maximum Penalized-Likelihood Structured Covariance Estimation for Imaging Extended Objects, with Application to Radio Astronomy |
| title_fullStr | Maximum Penalized-Likelihood Structured Covariance Estimation for Imaging Extended Objects, with Application to Radio Astronomy |
| title_full_unstemmed | Maximum Penalized-Likelihood Structured Covariance Estimation for Imaging Extended Objects, with Application to Radio Astronomy |
| title_short | Maximum Penalized-Likelihood Structured Covariance Estimation for Imaging Extended Objects, with Application to Radio Astronomy |
| title_sort | maximum penalized likelihood structured covariance estimation for imaging extended objects with application to radio astronomy |
| topic | astronomy maximum likelihood regularization |
| url | https://www.mdpi.com/2571-905X/7/4/88 |
| work_keys_str_mv | AT aaronlanterman maximumpenalizedlikelihoodstructuredcovarianceestimationforimagingextendedobjectswithapplicationtoradioastronomy |