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Maximum Penalized-Likelihood Structured Covariance Estimation for Imaging Extended Objects, with Application to Radio Astronomy

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  • Aaron Lanterman

    (School of Electrical and Computer Engineering, Georgia Institute of Technology, 777 Atlantic Drive, Atlanta, GA 30332, USA)

Abstract

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.

Suggested Citation

  • Aaron Lanterman, 2024. "Maximum Penalized-Likelihood Structured Covariance Estimation for Imaging Extended Objects, with Application to Radio Astronomy," Stats, MDPI, vol. 7(4), pages 1-17, December.
  • Handle: RePEc:gam:jstats:v:7:y:2024:i:4:p:88-1512:d:1546069
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    References listed on IDEAS

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    1. Nychka, Douglas, 1990. "Some properties of adding a smoothing step to the EM algorithm," Statistics & Probability Letters, Elsevier, vol. 9(2), pages 187-193, February.
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