Abstract
Perfect radar pulse compression coding is a potential emerging field which aims at providing rigorous analysis and fundamental limit radar experiments. It is based on finding non-trivial pulse codes, which we can make statistically equivalent, to the radar experiments carried out with elementary pulses of some shape. Engineering-based radar experiment design, regarding pulse-compression, often omits rigorous theory and mathematical limitations. In this work, our aim is to develop a mathematical theory which coincides with understanding the radar experiment in terms of the theory of comparison of statistical experiments. We review and generalize some properties of the Itô measure. We estimate the unknown, i.e. the structure function in the context of Bayesian statistical inverse problems. We study the posterior for generalized d-dimensional inverse problems, where we consider both real-valued and complex-valued inputs for posteriori analysis. Finally, this is then extended to the infinite-dimensional setting, where our analysis suggests the underlying posterior is non-Gaussian.
| Original language | English |
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| Journal | Inverse Problems and Imaging |
| DOIs | |
| Publication status | Online published - Apr 2025 |
Bibliographical note
Research Unit(s) information for this publication is provided by the author(s) concerned.Funding
The authors thank Dr. Markku S. Lehtinen, for helpful discussions and directions for the paper. NKC is supported by an EPSRC-UKRI AI for Net Zero Grant: “Enabling CO2 Capture And Storage Projects Using AI”, (Grant EP/Y006143/1). NKC is also supported by a City University of Hong Kong Startup Grant, project number 7200809. This work of PP was also supported by the Finnish Ministry of Education and Culture’s Pilot for Doctoral Programmes (Pilot project Mathematics of Sensing, Imaging and Modeling).