Regularized Kalman filtering for dynamic SPECT

Abstract

We introduce a novel Bregman projection approach applied to Kalman filter to ensure nonnegativity and spatial regularization. While we do not postulate a precise anterior information about the underlying dynamics of the physical process, we put our method into practice for the case of image reconstruction in time-dependent single photon emission computed tomography (SPECT). Classical SPECT reconstruction algorithms assume that the activity does not vary in time; this is not always the case in practice. Thus arises the need of exploring time-varying SPECT which is an ill-posed and an ill-conditioned reconstruction problem. In this paper, we will explore a Kalman reconstruction approach to estimate the dynamic activity. We formulate a linear state-space model of the problem which we solve using the optimal Kalman filter (KF) and smoother. However, Kalman output image is unidentifiable because of the presence of nonnegative activity. In addition, KF does a temporal smoothing but not a spatial regularization. We thus incorporate a projection method to ensure nonnegativity and to enforce a spatial regularization using Tikhonov and median approaches. Numerical results are provided to corroborate the effectiveness of our reconstruction method. © 2008 IOP Publishing Ltd.