Regularized sensitivity encoding (SENSE) reconstruction using bregman iterations

Abstract

In parallel imaging, the signal-to-noise ratio (SNR) of sensitivity encoding (SENSE) reconstruction is usually degraded by the ill-conditioning problem, which becomes especially serious at large acceleration factors. Existing regularization methods have been shown to alleviate the problem. However, they usually suffer from image artifacts at high acceleration factors due to the large data inconsistency resulting from heavy regularization. In this paper, we propose Bregman iteration for SENSE regularization. Unlike the existing regularization methods where the regularization function is fixed, the method adaptively updates the regularization function using the Bregman distance at different iterations, such that the iteration gradually removes the aliasing artifacts and recovers fine structures before the noise finally comes back. With a discrepancy principle as the stopping criterion, our results demonstrate that the reconstructed image using Bregman iteration preserves both sharp edges lost in Tikhonov regularization and fines structures missed in total variation (TV) regularization, while reducing more noise and aliasing artifacts. Magn Reson Med 61: 145-152, 2009.

Calibration-Less Multi-coil MR image reconstruction

“…The CS-based techniques exploit the sparsity in some transform domains (e.g., finite difference [15], wavelet [15,16]) of the MR images, when reconstructing them from their partially sampled K-space data. The same CS formulation has been extended into the SENSE framework in [11,[17][18][19][20][21].…”

Regularization in parallel MR image reconstruction

“…There can be three possible solutions to avoid the effects of ill-conditioning of encoding matrix: 1) by optimizing the coil geometry (15), 2) by optimizing sampling trajectory, 3) by introducing regularization (2). Regularization is the only method that does not require any hardware modifications in the MRI system or changes in the data acquisition methods.…”

A hybrid total-variation minimization approach to compressed sensing

“…In MRI, the measurement is made in k-space or the spatial frequency domain. In CS reconstruction, total variation (TV) or 1  -norm of the image gradient is usually used in the constrained minimization [9,10]. The TV of an image is defined as…”