Recursive tomographic image reconstruction using a Kalman filter approach in the time domain

摘要

The task of this work is to develop a technique for optimal linear recursive tomographic image reconstruction allowing the combination of the reconstruction process with projection data acquisition. The image supposes to be a discrete random field given by a set of linear stochastic difference equations with time as an independent variable. The proposed technique is applicable those tomographic modalities, scan geometries, and acquisition patterns that allow the introduction of a linear observation with an additive noise component. As a result the Kalman filter approach in the time domain is employed and the reconstruction process is represented as the optimal linear recursive estimation procedure with the optimal solution on each reconstruction step. The recursive properties of the proposed algorithm allow the parallelization of the data acquisition process and the reconstruction task. The main restrictions for the application of the Kalman filter approach are given by the huge dimension of the problem and the strong requirements to the amount of prior knowledge introduced. To overcome these restrictions a pseudo Kalman filter approach is investigated. This approach is based on replacing the prior covariance matrix with an empirical one. The reduction of the amount of prior knowledge decreases the dimensionality of the problem as well as the convergence velocity of the algorithm. Introducing an optimized scheme for the data acquisition procedure can partially compensate the degradation of the convergence process. [References: 16]