Sensitivity encoding reconstruction with nonlocal total variation regularization

In sensitivity encoding reconstruction, the issue of ill conditioning becomes serious and thus the signal-to-noise ratio becomes poor when a large acceleration factor is employed. Total variation (TV) regularization has been used to address this issue and shown to better preserve sharp edges than Tikhonov regularization but may cause blocky effect. In this article, we study nonlocal TV regularization for noise suppression in sensitivity encoding reconstruction. The nonlocal TV regularization method extends the conventional TV norm to a nonlocal version by introducing a weighted nonlocal gradient function calculated from the weighted difference between the target pixel and its generalized neighbors, where the weights incorporate the prior information of the image structure. The method not only inherits the edge-preserving advantage of TV regularization but also overcomes the blocky effect. The experimental results from in vivo data show that nonlocal TV regularization is superior to the existing competing methods in preserving fine details and reducing noise and artifacts. Magn Reson Med, 2011.