Photonic imaging with statistical guarantees: From multiscale testing to multiscale estimation

Axel Munk*, Katharina Proksch, Housen Li, Frank Werner

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

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Abstract

In this chapter we discuss how to obtain statistical guarantees in photonic imaging. We start with an introduction to hypothesis testing in the context of imaging, more precisely we describe how to test if there is signal in a specific region of interest (RoI) or just noise. Afterwards we extend this approach to a family of RoIs and examine the occurring problems such as inflation of type I error and dependency issues. We discuss how to control the family-wise error rate by different modifications, and provide a connection to extreme value theory. Afterwards we present possible extension to inverse problems. Moving from testing to estimation, we finally introduce a method which constructs an estimator of the desired quantity of interest with automatic smoothness guarantees.

Original languageEnglish
Title of host publicationTopics in Applied Physics
PublisherSpringer Singapore
Pages283-312
Number of pages30
ISBN (Electronic)978-3-030-34413-9
ISBN (Print)978-3-030-34412-2
DOIs
Publication statusPublished - 2020
Externally publishedYes

Publication series

NameTopics in Applied Physics
Volume134
ISSN (Print)0303-4216
ISSN (Electronic)1437-0859

Keywords

  • 62F17
  • 62G10
  • Primary 62-01
  • Secondary 62G20

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