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 regridding technique for nonuniformly‐sampled k‐space MRI. Even though it is a relatively computationally intensive algorithm, since it uses singular value decomposition (SVD), its procedure is simple because it requires neither a pre‐ nor a postcompensation 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 which 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. Magn Reson Med 46:1189–1201, 2001. © 2001 Wiley‐Liss, Inc.