Radon inversion and Kalman reconstructions: A comparison

Some of the recent applications of computerized tomography (CT) such as gated cardiac scanning and dynamic scanning are challenging the capabilities of the convolution/backprojection reconstruction algorithm. Increased attention is being directed toward techniques which take advantage of apriori information (e.g., measurement noise statistics, average pixel (picture element) correlations, shape of scanning beam). Such algorithms (e.g., Kalman filter) are generally characterized (and controlled) by a pixel error-covariance matrix. It is important to be able to compare these algorithms with convolution/ backprojection techniques. This paper provides that capability by deriving a convenient expression for the pixel error-covariance for algorithms based on the Radon inversion formula. The expression is than adapted to a specific fan-beam data acquisition scheme. Using this expression, the convolution/backprojection algorithm is compared with two algorithms based on the Kalman filter for a variety of scanning configurations.