State Estimation with Structural Priors in fMRI

Abstract

We propose a state estimation approach for functional magnetic resonance imaging (fMRI). In state estimation, time-dependent image reconstruction problem is modeled by separate state evolution and observation models, and the objective is to estimate the time series of system states, given the models and the time-dependent measurement data. Our method computes the state estimates by using the Kalman filter (KF) and Kalman smoother (KS) algorithms. We propose to complement the state estimation formulation with a structural prior which can be derived from the anatomical MRI, acquired as a part of the fMRI protocol. Two different constructions of the structural prior are considered. The first one is a structured smoothness prior where the state observation matrix is augmented with a spatially weighted regularization matrix which promotes structural similarity of the gradient of the unknown image with the gradient of the anatomical image. The second approach is based on applying structured total variation denoising to the KF estimate at each time step of the Kalman recursions. The proposed approaches are evaluated using simulated and experimental, radially sampled, small animal fMRI data from a rat brain. In our method, the state estimates are updated after each new spoke of radial data becomes available, leading to faster frame rate compared to the conventional image reconstruction approaches. The results are compared to a sliding window method and a conventional reconstruction which produces new image only after a full circle of k-space spokes becomes available. The results suggest that the state estimation approach with the structural prior can improve both spatial and temporal resolution of fMRI.