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EST is an iterative method that makes use of the pseudopolar Fourier transform (PPFT) [23]. It calculates the Fourier coefficients of an image directly on pseudopolar grids, which contain two types of samples: basically horizontal (BH) and basically vertical (BV), as can be seen in Figure 1. To reconstruct an N �� N image from its PPFT coefficients, 4N2 samples are needed (2N samples on 2N equally sloped radial lines). A fast algorithm has been proposed by Averbuch et al. [23] to calculate the PPFT http://www.selleckchem.com/products/AZD2281(Olaparib).html and its adjoint with complexity of O(N2logN). This algorithm can then be used to implement a fast and efficient 2D Radon transform on the equally sloped radial lines. The PPFT has three important properties which makes it a good alternative to conventional DFR methods: (1) it is closer to a polar (equiangular line) grid than to a Cartesian grid, which significantly decreases the gridding error, (2) it has both a fast forward and a fast selleck chemicals backward calculation algorithm [23], which enables our proposed algorithm to avoid the regridding step used in iterative non-Cartesian Fourier based reconstruction methods, and (3) it has an analytical adjoint function. As a result, it can efficiently be used in iterative algorithms, including compressed sensing [24, 25]. However, it should be noted that Fourier-based reconstruction algorithms, for example, ESR and DFR, are only valid for parallel X-ray projections. Figure 1 (a) Pseudopolar grids: red lines are Sitaxentan basically horizontal (BH) and the black lines are basically vertical (BV). (b) Polar grids (red dots) on the pseudopolar grids (gray dots). A major objective of this paper is to accelerate the CS-based CT reconstruction by decreasing the CS complexity using PPFT-based Radon transform proposed in [26]. The application of the proposed method is extended to equiangular parallel and nonparallel geometries using rebinning. 2.1.1. Rebinning Process To enable use of the PPFT-based Radon transform for nonparallel geometries, the projected rays must first be transformed to parallel beams [27]. This requires two interpolation steps. At first, projections are interpolated on equally sloped radial lines on the following angles: ��BH=tan?12mN,?N2��m