Non-parametric Bayesian Models of Response Function in Dynamic Image Sequences

TL;DR

This paper introduces non-parametric Bayesian priors for estimating complex response functions in dynamic medical imaging, improving accuracy over traditional parametric models through hierarchical priors that promote sparsity and smoothness.

Contribution

The paper proposes a novel non-parametric Bayesian framework for response function estimation, enhancing flexibility and performance in blind source separation and deconvolution tasks.

Findings

Non-parametric priors outperform parametric models in synthetic data.

Improved response function estimation in real renal scintigraphy data.

Hierarchical priors effectively incorporate sparsity and smoothness constraints.

Abstract

Estimation of response functions is an important task in dynamic medical imaging. This task arises for example in dynamic renal scintigraphy, where impulse response or retention functions are estimated, or in functional magnetic resonance imaging where hemodynamic response functions are required. These functions can not be observed directly and their estimation is complicated because the recorded images are subject to superposition of underlying signals. Therefore, the response functions are estimated via blind source separation and deconvolution. Performance of this algorithm heavily depends on the used models of the response functions. Response functions in real image sequences are rather complicated and finding a suitable parametric form is problematic. In this paper, we study estimation of the response functions using non-parametric Bayesian priors. These priors were designed to favor desirable properties of the functions, such as sparsity or smoothness. These assumptions are used within hierarchical priors of the blind source separation and deconvolution algorithm. Comparison of the resulting algorithms with these priors is performed on synthetic dataset as well as on real datasets from dynamic renal scintigraphy. It is shown that flexible non-parametric priors improve estimation of response functions in both cases. MATLAB implementation of the resulting algorithms is freely available for download.