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Abstract #2547

Sampling Density Compensation Function Estimation by Regularized Conjugate Gradient Iteration with a Reduced Oversampling Ratio

Sen Jia1, Ran Yang1

1School of Information Science and Technology, Sun Yat-Sen University, Guang Zhou, Guang Dong, China

The iterative convolution based estimation of non-Cartesian sampling density compensation function (DCF) typically employs an intermediate Cartesian grid oversampled by a ratio of two to achieve high convergence accuracy and this increases the memory and computational burden heavily when processing data of large size or of high dimension. And the iteration converges stably but saturates easily which limits the capacity to achieve higher estimation accuracy. In this work, an iterative procedure based on the Conjugate Gradient (CG) method is introduced to reduce the oversampled grid size while achieving higher DCF estimation accuracy without increasing computational and storage burden. Further the DCF estimated by the original method is employed as a regularization term to form a bi-criterion optimization problem to stabilize the CG iteration to achieve fast convergence with a reduced oversampling ratio.

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Keywords

accelerate accuracy accurately achieve achieving addition adopted although applied approximate arbitrary burden capacity china coefficient compensation computation computational compute condition conjugate constraint convergence convergences convolution convolve correction criterion crucial definiteness density depicted determined dimension dong easily efficiently else employed entries equation error errors estimation exit experiment faithful fast feasible final find form function gradient grid heavily ideal improve improved increasing indicated inherently intermediate introduced inverse inversing involves irrelevant iteration iterations iterative kaiser kernel kernels length linear listed load loop matrices matrix minimize much noted novel objectives offer operation optimization optimized original oversampled oversampling perfect pipe plotted positive powerful problem procedure process processing proportional proposed quality reconstruct reconstructed reduce reduced reducing regularization regularized relate reported representation required robust samples sampling satisfy saturates school separately significantly since smooth solution solve solved solving space speed spiral stabilize stably still storage synthesize system table term trades trajectory typically utilized various vector website whose worsen yang