Extending the Support Theorem to Infinite Dimensions
Jeremy J. Becnel
TL;DR
This paper extends the Radon transform and its Support Theorem to the white noise setting, broadening their applicability in infinite-dimensional functional analysis.
Contribution
It introduces a construction of the Radon transform in the white noise setting and develops a corresponding Support Theorem for this infinite-dimensional context.
Findings
Radon transform constructed in white noise setting
Support Theorem extended to infinite dimensions
Potential applications in functional analysis and stochastic processes
Abstract
The Radon transform is one of the most useful and applicable tools in functional analysis. First constructed by John Radon in 1917 it has now been adapted to several settings. One of the principle theorems involving the Radon transform is the Support Theorem. In this paper, we discuss how the Radon transform can be constructed in the white noise setting. We also develop a Support Theorem in this setting.
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Taxonomy
TopicsDigital Image Processing Techniques · Image and Object Detection Techniques · Mathematical Analysis and Transform Methods