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.