A minimum-norm least-squares image-reconstruction method for the reconstruction of magnetic resonance images from non-Cartesian sampled data is proposed. The method is based on a general formalism for continuous-to-discrete mapping and pseudoinverse calculation. It does not involve any regridding or interpolation of the data and therefore the methodology differs fundamentally from existing regridding-based methods. Moreover, the method uses a continuous representation of objects in the image domain instead of a discretized representation. Simulations and experiments show the possibilities of the method in both radial and spiral imaging. Simulations revealed that minimum-norm least-squares image reconstruction can result in a drastic decrease of artifacts compared with regridding-based reconstruction. Besides, both in vivo and phantom experiments showed that minimum-norm least-squares image reconstruction leads to contrast improvement and increased signal-to-noise ratio compared with image reconstruction based on regridding. As an appendix, an analytical calculation of the raw data corresponding to the well-known Shepp and Logan software head phantom is presented. © 2000 IEEE.
CITATION STYLE
Walle, R. V. D., Barrett, H. H., Cornelis, J., Altbach, M. I., Desplanques, B., Gmitro, A. F., & Lemahieu, I. (2000). Reconstruction of MR images from data acquired on a general nonregular grid by pseudoinverse calculation. IEEE Transactions on Medical Imaging, 19(12), 1160–1167. https://doi.org/10.1109/42.897806
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