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Chase J Sakitis, D Andrew Brown, Daniel B Rowe, A Bayesian complex-valued latent variable model applied to functional magnetic resonance imaging, Journal of the Royal Statistical Society Series C: Applied Statistics, Volume 74, Issue 1, January 2025, Pages 100–125, https://doi.org/10.1093/jrsssc/qlae046
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Abstract
In linear regression, the coefficients are simple to estimate using the least squares method with a known design matrix for the observed measurements. However, real-world applications may encounter complications such as an unknown design matrix and complex-valued parameters. The design matrix can be estimated from prior information but can potentially cause an inverse problem when multiplying by the transpose as it is generally ill-conditioned. This can be combat by adding regularizers to the model but does not always mitigate the issues. Here, we propose our Bayesian approach to a complex-valued latent variable linear model with an application to functional magnetic resonance imaging (fMRI) image reconstruction. The complex-valued linear model and our Bayesian model are evaluated through extensive simulations and applied to experimental fMRI data.
