A sampling density compensation function denoted "same-image (SI) weight" is proposed to reconstruct MR images from the data acquired on an arbitrary k-space trajectory. An equation for the SI weight is established on the SI criterion and an iterative scheme is developed to find the weight. The SI weight is then used to reconstruct images from the data calculated on a random trajectory in a numerical phantom case and from the data acquired on interleaved spirals in an in vivo experiment, respectively. In addition, Pipe and Menon's weight (MRM 1999;41:179-186) is also used in the reconstructions to make a comparison. The images obtained with the SI weight were found to be slightly more accurate than those obtained with Pipe's weight.
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