A new compressed sensing model based on median filter with application to reconstruct brain mr images

The technology of reconstructing an unknown signal from a very few sample data by the L1 minimization method is called compressed sensing technology. This technique has been successfully applied to reduce the long MR images scan duration by recovering underling images from partial k-space data and receiving a faithful MR image. However, these low sampling strategy models violate the Shannon sampling theorem, resulting in a number of artifacts in the reconstructed MR images. The authors of this paper find that applying a median filtering to every iteration result of the reconstruction process can alleviate those artifacts. Therefore, a new compressed sensing model with median filtering is established for reconstructing MR images in this paper. In order to speed up the convergence speed of the algorithm, the authors use the split Bregman method to minimize the proposed new model. Finally, the authors use several human brain MR images and a synthetic MR image to verify the validity of the proposed model and also present comparison results with other models to demonstrate the superiority of the proposed model.