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Rapid cardiovascular computed tomography (CT) requires image reconstruction from a limited set of projections. Deterministic methods using convolution back projection algorithms have not been suitable for these limited data cases. An alternative approach has been formulated to find the minimum mean squared error image estimate using a Kalman filter with polar pixels for two-dimensional reconstructions of both simulated phantoms and real objects from data obtained on a rotate only CT scanner. Computation time was minimized by limiting the number of pixels to 120 and using a rotationally symmetric (polar) pixel structure. The Kalman filter was compared with Algebraic Reconstruction Technique (ART) for full view, limited view, and missing view measurement sets. The Kalman filter performed with consistently lower mean squared error than ART for both real and simulated data and rapidly converged to the theoretical limit of resolution. Performance of the Kalman filter was optimized only if the system noise (error) was adequately characterized. When real objects were scanned it was necessary to include the measurement errors introduced by finite pixel width and finite beam width in addition to Poisson noise to achieve optimality. The use of polar rather than rectangular pixels provided a reduction in computation and storage requirements for the Kalman filter. This study demonstrates the potential utility of Kalman filtering methods using polar pixels for limited data CT image reconstruction. Common to the methods used to create cross-sectional images through various anatomic structures using x-rays, gamma rays or ultrasound is the mathematical reconstruction of a two-dimensional image using a series of projection measurements represented by line integrals. While considerable effort has been expended in the theory of image reconstruction from line integral measurements there are still many applications of cross-sectional imaging where the mathematical methods of computation are inadequate. Frequently used reconstruction algorithms assume that (1) projection data are symmetrically arranged; and (2) there are no sources of noise (i.e., all measurements are exact). In reality neither assumption is true, and for certain applications, e.g., rapid scanning of the heart, minimizing patient dose, etc., these assumptions are so flagrantly violated that these algorithms produce images with severe artifacts. In this paper we demonstrate the use of a new algorithm2 for image reconstruction which yields in the least squared sense optimal solutions in the presence of noisy and asymmetric measurement sets. Results indicate that this method could allow more accurate cross sectional imaging than is possible with conventional methods.
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