Modified Block Uniform Resampling (BURS) Algorithm Using Truncted Singular Value Decomposition: Fast Accurate Gridding With Noise and Artifact Reduction

The Block Uniform Resampling (BURS) algorithm is a newly proposed regridding technique for non-uniformly sampled k-space MRI. Even though it is a relatively computationally intensive algorithm since it uses singular value decomposition (SVD), it's procedure is simple because it requires neither a pre- nor post-compensation step. Furthermore, the reconstructed image is generally of high quality since it provides accurate gridded values when the local k-space data SNR is high. However, the BURS algorithm is sensitive to noise. Specifically, inaccurate interpolated data values are often generated in the BURS algorithm if the original k-space data are corrupted by noise, which is virtually guaranteed to occur to some extent in MRI. As a result, the reconstructed image quality is degraded despite excellent performance under ideal conditions. In this article, a method is presented that avoids inaccurate interpolated k-space data values from noisy sampled data with the BURS algorithm. The newly proposed technique simply truncates a series of singular values after the SVD is performed. This reduces the computational demand when compared with the BURS algorithm, avoids amplification of noise resulting from small singular values, and leads to image SNR improvements over the original BURS algorithm.

Water phantom and knee images from FLASH and radial MP-SSFP sequences. The MP-SSFP sequence produces the "marker-only" images necessary for accurate marker localization.