Compressive sensing MRI with laplacian sparsifying transform

Compressive sensing (CS) is an emerging technique to speed up the data acquisition in MRI. CS relies on the sparsity constraint of the underlying image. Currently total variation (TV) is being used ubiquitously in CS-MRI as a sparsity measurement. TV is based on the first-order difference, which works well for piece-wise constant images. In this paper, a sparsifying transform based on the second-order difference (SD), i.e., Laplacian (LP) filters, is introduced as an alternative to the first-order difference. The new transform compresses MR image signals better than in the conventional TV framework. Therefore it is expected to enable improved CS reconstruction, particularly for images that are not piece-wise constant such as those acquired with nonuniform B₁ sensitivities. Both simulated and experimental images are applied to the TV minimization and the proposed method. The result shows that the proposed method has potentials to improve the CS reconstruction. However, Laplacian appears to be more sensitive to noise than TV.