Quantitative susceptibility mapping (QSM) is a novel MRI method for quantifying tissue magnetic property. In the brain, it reflects the molecular composition and microstructure of the local tissue. However, susceptibility maps reconstructed from single-orientation data still suffer from streaking artifacts which obscure structural details and small lesions. We propose and have developed a general method for estimating streaking artifacts and subtracting them from susceptibility maps. Specifically, this method uses a sparse linear equation and least-squares (LSQR)-algorithm-based method to derive an initial estimation of magnetic susceptibility, a fast quantitative susceptibility mapping method to estimate the susceptibility boundaries, and an iterative approach to estimate the susceptibility artifact fromill-conditioned k-space regions only. With a fixed set of parameters for the initial susceptibility estimation and subsequent streaking artifact estimation and removal, the method provides an unbiased estimate of tissue susceptibility with negligible streaking artifacts, as compared to multi-orientation QSM reconstruction. This method allows for improved delineation of white matter lesions in patients with multiple sclerosis and small structures of the human brain with excellent anatomical details. The proposed methodology can be extended to other existing QSM algorithms. (C) 2014 Published by Elsevier Inc.