Convolution kernel design and efficient algorithm for sampling density correction

Sampling density compensation is an important step in non‐cartesian image reconstruction. One of the common techniques to determine weights that compensate for differences in sampling density involves a convolution. A new convolution kernel is designed for sampling density attempting to minimize the error in a fully reconstructed image. The resulting weights obtained using this new kernel are compared with various previous methods, showing a reduction in reconstruction error. A computationally efficient algorithm is also presented that facilitates the calculation of the convolution of finite kernels. Both the kernel and the algorithm are extended to 3D. Magn Reson Med 61:439–447, 2009. © 2009 Wiley‐Liss, Inc.

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