Regularized Hypothesis Testing in Random Fields with Applications to Neuroimaging

Oscar S.  Dalmau-Cedeño; Dora E.  Alvarado-Carrillo; José Luis Marroquín

doi:10.17488/RMIB.41.2.2

Authors

Oscar S. Dalmau-Cedeño Centro de Investigación en Matemáticas, CIMAT A. C., Mexico
Dora E. Alvarado-Carrillo Centro de Investigación en Matemáticas, CIMAT A. C., Mexico https://orcid.org/0000-0003-1984-7546
José Luis Marroquín Centro de Investigación en Matemáticas, CIMAT A. C. México

DOI:

https://doi.org/10.17488/RMIB.41.2.2

Keywords:

Regularized hypothesis test, Markovian random fields, Bayesian estimation, functional Magnetic resonance imaging

Abstract

The task of determining for which elements of a random field (e.g., pixels in an image) a certain null hypothesis may be rejected is a relevant problem in several scientific areas. In the current contribution, we introduce a new method for performing this task, the regularized hypothesis testing (RHT) method, focusing on its use in neuroimaging re- search. RHT is based on the formulation of the hypothesis testing task as a Bayesian estimation problem, with the previous application of a Markovian random field. The latter allows for the incorporation of local spatial informa- tion and considers different noise models, including spatially correlated noise. In tests on synthetic data showing regular activation levels on uncorrelated noise fields, RHT furnished a true positive rate (TPR) of 0.97, overcoming the state-of-the-art morphology-based hypothesis testing (MBHT) method and the traditional family-wise error rate (FWER) method, which afforded 0.93 and 0.58, respectively. For fields with highly correlated noise, the TPR provided by RHT was 0.65, and by MBHT and FWER was 0.35 and 0.29, respectively. For tests utilizing real func- tional magnetic resonance imaging (fMRI) data, RHT managed to locate the activation regions when 60% of the original signal were removed, while MBHT located only one region and FWER located none.

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