New iterative gridding algorithm using conjugate gradient method

Xuguang Jiang; Daniel Thedens

doi:10.1117/12.535685

12 May 2004 New iterative gridding algorithm using conjugate gradient method

Xuguang Jiang, Daniel Thedens

Proceedings Volume 5370, Medical Imaging 2004: Image Processing; (2004) https://doi.org/10.1117/12.535685
Event: Medical Imaging 2004, 2004, San Diego, California, United States

Abstract

Non-uniformly sampled data in MRI applications must be interpolated onto a regular Cartesian grid to perform fast image reconstruction using FFT. The conventional method for this is gridding, which requires a density compensation function (DCF). The calculation of DCF may be time-consuming, ambiguously defined, and may not be always reusable due to changes in k-space trajectories. A recently proposed reconstruction method that eliminates the requirement of DCF is block uniform resampling (BURS) which uses singular value decomposition (SVD). However, the SVD is still computationally intensive. In this work, we present a modified BURS algorithm using conjugate gradient method (CGM) in place of direct SVD calculation. Calculation of a block of grid point values in each iteration further reduces the computational load. The new method reduces the calculation complexity while maintaining a high-quality reconstruction result. For an n-by-n matrix, the time complexity per iteration is reduced from O(n*n*n) in SVD to O(n*n) in CGM. The time can be further reduced when we stop the iteration in CGM earlier according to the norm of the residual vector. Using this method, the quality of the reconstructed image improves compared to regularized BURS. The reduced time complexity and improved reconstruction result make the new algorithm promising in dealing with large-sized images and 3D images.

Citation Download Citation

Xuguang Jiang and Daniel Thedens "New iterative gridding algorithm using conjugate gradient method", Proc. SPIE 5370, Medical Imaging 2004: Image Processing, (12 May 2004); https://doi.org/10.1117/12.535685

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