Modified block uniform resampling (BURS) algorithm using truncated singular value decomposition: Fast accurate gridding with noise and artifact reduction

The block uniform resampling (BURS) algorithm is a newly proposed regriddin g technique for nonuniformly-sampled k-space MRI. Even though it is a relat ively computationally intensive algorithm, since it uses singular value dec omposition (SVD), its procedure is simple because it requires neither a pre nor a postcompensation step. Furthermore, the reconstructed image is genera lly of high quality since it provides accurate gridded values when the loca l k-space data SNR is high. However, the BURS algorithm is sensitive to noi se. Specifically, inaccurate interpolated data values are often generated i n the BURS algorithm if the original k-space data are corrupted by noise, w hich is virtually guaranteed to occur to some extent in MRI. As a result, t he reconstructed image quality is degraded despite excellent performance un der ideal conditions. In this article, a method is presented which avoids i naccurate 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. (C) 2001 Wiley-Liss, Inc.