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CT reconstruction method based on fractal and compression sensing

The invention provides a CT reconstruction method based on fractal and compression sensing. The method includes the steps that (1) CT projection data b, a corresponding projection angle theta and initialization parameters beta, lambda and lambda n are known, and a CT image u is equal to zero; (2) a corresponding projection matrix A is calculated according to the projection angle theta; (3) a CT image uART is calculated by means of a formula (5); (4) fractal encoding processing is carried out on uART, so that fai (u) is obtained, and alpha is obtained by means of a formula (12); (5) decoding processing is carried out on the fai (u), so that fai T(u) is obtained; (6) fai T(u), fai (u), fai T(u) alpha, ATA and ATb are solved; (7) a formula (15) is solved in a conjugate gradient method, and accordingly a CT image is obtained; (8) whether a condition of finishing iteration is met is detected, if the answer is positive, a step (9) is carried out and otherwise the step (3) is carried out; (9) operations are finished, and the CT image is output. According to the method, fractal serves as sparse transform so that a more sparse coefficient representation can be obtained, an alternating and continuity algorithm is used for obtaining solutions and the high-quality CT image is constructed on the condition that a little of projection exists.
Owner:CHONGQING UNIV
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