Cramer-Rao lower bound and object reconstruction performance evaluation for intensity interferometry

Jean J. Dolne; David R. Gerwe; Peter N. Crabtree

doi:10.1117/12.2063418

29 July 2014 Cramer-Rao lower bound and object reconstruction performance evaluation for intensity interferometry

Jean J. Dolne, David R. Gerwe, Peter N. Crabtree

Proceedings Volume 9146, Optical and Infrared Interferometry IV; 914636 (2014) https://doi.org/10.1117/12.2063418
Event: SPIE Astronomical Telescopes + Instrumentation, 2014, Montréal, Quebec, Canada

Abstract

This paper addresses the fundamental performance limits of object reconstruction methods using intensity interferometry measurements. It shows examples of reconstructed objects obtained with the FIIRE (Forward-model Interferometry Image Reconstruction Estimator) code developed by Boeing for AFRL. It considers various issues when calculating the multidimensional Cramér-Rao lower bound (CRLB) when the Fisher information matrix (FIM) is singular. In particular, when comparing FIIRE performance, characterized as the root mean square difference between the estimated and pristine objects with the CRLB, we found that FIIRE performance improved as the singularity became worse, a result not expected. We found that for invertible FIM, FIIRE yielded lower root mean squared error than the square root of the CRLB (by a factor as large as 100). This may be due to various regularization constraints (positivity, support, sharpness, and smoothness) included in FIIRE, rendering it a biased estimator, as opposed to the unbiased CRLB framework used. Using the sieve technique to mitigate false high frequency content inherent in point-by-point object reconstruction methods, we also show further improved FIIRE performance on some generic objects. It is worth noting that since FIIRE is an iterative algorithm searching to arrive at an object estimate consistent with the collected data and various constraints, an initial object estimate is required. In our case, we used a completely random initial object guess consisting of a 2-D array of uniformly distributed random numbers, sometimes multiplied with a 2-D Gaussian function.

Citation Download Citation

Jean J. Dolne, David R. Gerwe, and Peter N. Crabtree "Cramer-Rao lower bound and object reconstruction performance evaluation for intensity interferometry", Proc. SPIE 9146, Optical and Infrared Interferometry IV, 914636 (29 July 2014); https://doi.org/10.1117/12.2063418

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