Multiscale coherence regularization reconstruction using a nonlocal operator for fast variable-density spiral imaging

Purpose: Nonlinear reconstruction can suppress pseudo-incoherent aliasing artifacts from variable-density spiral (VDS) trajectories when interleaves are undersampled for acquisition acceleration during MR imaging. However, large-scale aliasing artifact suppression often conflicts with fine-scale structure preservation and may cause deterioration of image quality in the reconstructed images. To address this issue, a sequential, multiscale coherence regularization algorithm using a nonlocal operator (mCORNOL) is proposed. Methods: mCORNOL is formed by exploiting the scale-control capacity of nonlocal operators in image structure measurement. By changing the scale of the structure measurement, the smoothing constraint scales can be adjusted. Starting with a large value, mCORNOL gradually reduces the smoothing constraint scale until it reaches the same level as the noise. Therefore, the large-scale smoothing constraint dominates the first few iterations of the reconstruction and removes aliasing artifacts as well as fine structures. In the following iterations, the smoothing constraint is restricted to a smaller and smaller scale, so the fidelity term progressively dominates and restores lost structures. Thus, aliasing artifact removal and structure preservation can be decoupled and achieved sequentially, which alleviates the conflicts between them. Results: Numerical simulation and in vivo experiment results demonstrate the superiority of mCORNOL for aliasing artifact suppression and image structure preservation at high reduction factors, compared to SENSE, Total Variation and the original CORNOL reconstruction. Conclusions: mCORNOL reconstruction provides an effective way to improve image quality for undersampled VDS acquisitions.