For a PET scanner with circular array of detectors, the width of line-of-response (LOR) decreases as the distance between the LOR and the center increases. The decrease of width of the LOR leads to problem of non-uniform and under sampling of projections. The consequence of non-uniform sampling is the distortion of high frequency reconstructed images or loss of fine detail. Correcting this non-uniform sampling problem is known as arc-correction. The purpose of this study is to create the best estimate of non-uniformly sampled projections from uniformly spaced sets of LOR. Four polynomial type interpolating algorithms: Lagrange, iterative Neville, natural cubic spline and clamped cubic spline are used to get the best estimate of projections. A set of simulated projections are generated. The simulated projections are divided into two sets: the first set has 10 functions of pulses such that f11 has one pulse, f12 has two pulses and so on. In the second set f21 has one triangular pulse, f22 has two triangular pulses and so on. For each group interpolated data is compared to the original data. In addition, one projection of a 20cm FDG filled disk is used for comparison with simulated data. It is shown that clamped and natural cubic spline accuracy is superior to the other three algorithms in every case but Lagrange outperforms other algorithms for the speed of execution.
A new optimization method for image registration has been proposed. Registration using Simulated Annealing converges to global minima/maxima as opposed to the previously wildly used algorithms that get trapped in local minima. The performance of this algorithm is tested against two other well-known optimization algorithms, Powell and Down Hill Simplex using two different methods. First, the algorithms are tested against famous De jong Test Suites and second, they are tested against Two-Cube Phantom. Our data shows that simulated annealing is the only algorithm that will always converges to the global minima with the cost of more function evaluation.
A new model is proposed to reconstruct an image from its ray sum using Algebraic Reconstruction Techniques (ART). Assuming that the original image is band limited, an iterative algorithm is developed that evaluates the updated image and reduces the sampling error during each iteration. Depending on a weight factor, estimation of the updated images in each iteration is the contribution of correction to each sample of the ray sum. The weight factor is the fractional area intercepted by the ray sum and the sampling function. To model a 2D image, an optimal sampling function is used where the sampling function is a cylindrical pulse instead of the customary flat-top sample version of a 2D square pulse. Given energy concentration of the pulse, a class of such pulses are generated. A pulse with maximum concentration of energy is used for sampling of the 2D image. By determining the eigenfunctions of a homogeneous Fredholm equation of the second kind with a symmetric kernel such a pulse is generated. Moreover, it is shown that eigenfunctions of the above integral equation are those classes of pulses where the corresponding eigenvalue is the measure of the concentration of an eigenfunction. The desired pulse is an eigenfunction with the maximum eigenvalue.
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