We have developed a new L1-norm based generalized minimum norm estimate (GMNE) and have fully characterized the concept of sparseness regularization inherited in the proposed algorithm, which is termed as sparse source imaging (SSI). The new SSI algorithm corrects inaccurate source field modeling in previously reported L1-norm GMNEs and proposes that sparseness a priori should only be applied to the regularization term, not to the data term in the formulation of the regularized inverse problem. A new solver to the newly developed SSI has been adopted and known as the second-order cone programming. The new SSI is assessed by a series of simulations and then evaluated using somatosensory evoked potential (SEP) data with both scalp and subdural recordings in a human subject. The performance of SSI is compared with other L1-norm GMNEs and L2-norm GMNEs using three evaluation metrics, i.e., localization error, orientation error, and strength percentage. The present simulation results indicate that the new SSI has significantly improved performance in all evaluation metrics, especially in the metric of orientation error. L2-norm GMNEs show large orientation errors because of the smooth regularization. The previously reported L1-norm GMNEs show large orientation errors due to the inaccurate source field modeling. The SEP source imaging results indicate that SSI has the best accuracy in the prediction of subdural potential field as validated by direct subdural recordings. The new SSI algorithm is also applicable to MEG source imaging. Hum Brain Mapp 2008. © 2007 Wiley-Liss, Inc.