Linear spatial hypothesis tests for random fields

• Lineare räumliche Hypothesentests für Zufallsfelder

Sovetkin, Evgenii; Steland, Ansgar (Thesis advisor); Müller, Christine (Thesis advisor); Berkels, Benjamin (Thesis advisor)

Aachen (2019, 2020)
Dissertation / PhD Thesis

Dissertation, RWTH Aachen University, 2019

Abstract

We propose a statistical framework that tests a hypothesis about the functional properties of a random field. The framework is formulated for random fields with a compact d-dimensional Euclidean domain space, with a signal plus noise observation model. The test statistic has a linear form, and the hypothesis is formulated in terms of an integral operator applied to an unobserved signal. The test decision is performed using a single trajectory of a random field. Using the apparatus of Stieltjes integral, we prove functional limit theorems under the null and alternative hypotheses. To obtain those results we consider two different model assumptions on the noise random field. Our assumptions on the signal and test parameters feature the notion of the variation in the sense of Hardy and Krause. Extensive numerical simulations provide insights on various characteristics of the formulated tests. We present simulations under the null and alternative hypotheses, and compare power for different test parameters. This work is primarily motivated by an application in image processing in quality control of photovoltaic (PV) modules. Our framework allows identifying defects in such images. Furthermore, we propose a set of image preprocessing algorithms for such images.