Compressed-Sensing MRI Based on Adaptive Tight Frame in Gradient Domain

Abstract

Compressed-sensing magnetic resonance imaging (CSMRI) aims to reconstruct the magnetic resonance (MR) image from highly undersampled K-space data. In order to improve the reconstruction quality of the MR image, this paper proposes a new gradient-based tight frame (TFG) learning algorithm (TFG-MRI) for CSMRI. TFG-MRI effectively integrates the tight frame learning technique and total variation into the same framework. In TFG-MRI, the inherent gradient sparsity of the MR image in gradient domain is utilized to represent the sparse prior knowledge, and the sparse priors in the horizontal and vertical gradient directions are exploited to learn adaptive tight frames for reconstructing the desired images. Particularly, we employ the l₀-norm to promote the sparsity of the gradient image. The sparse representations of TFG are adapted for the horizontal and vertical gradient information of MR images. TFG-MRI can effectively help to capture edge contour structures in the gradient images, and to preserve more detail information of MR images. The experimental results demonstrate that the proposed TFG-MRI can reconstruct MR images more clearly in various sampling schemes. Compared with the existing MR image reconstruction algorithms, TFG-MRI can achieve higher accurate image reconstruction quality and better robustness to noises.