Orthogonalization, Bernstein polynomials, and image restoration

A projection access order for speedy convergence of ART (algebraic reconstruction technique): a multilevel scheme for computed tomography

The practical performance of algebraic reconstruction techniques (ART) for computed tomography (CT) depends heavily on the order in which the projections are considered. Complete orthogonalization, notwithstanding its theoretical justification, is not feasible because the computational time is prohibitive. The authors report here a scheme that yields the most efficient reconstruction without orthogonalization: projections are organized and accessed in a nominally multilevel fashion. Each level makes the best use of the image information reconstructed in the preceding levels. If the number of projections is a power of two. Then the access orders are exactly that for the 1D FFT. The authors' scheme can be easily implemented. Using it, one iteration of ART yields a high-quality image. Experimental results of this algorithm are demonstrated and compared with the results from the conventional sequential method and also random ordering. Comparisons show that this scheme is superior. ART is better in image quality than the Fourier back-projection algorithm, at least for a smaller number of projections. Since the authors have made it much more efficient in computational speed, ART could now find widespread use in medical imaging.