SENSE phase‐constrained magnitude reconstruction with iterative phase refinement

Abstract

Conventional sensitivity encoding (SENSE) reconstruction is based on equations in the complex domain. However, for many MRI applications only the magnitude is relevant. If there exists an estimate of the underlying phase information, a magnitudeonly phase-constrained reconstruction can help to improve the conditioning of the SENSE reconstruction problem. Consequently, this reduces g-factor-related noise enhancement. In previous attempts at phase-constrained SENSE reconstruction, image quality was hampered by strong aliasing artifacts resulting from inadequate phase estimates and high sensitivity to phase errors. If a full-resolution phase image is used, a significant reduction in aliasing errors and better noise properties compared to SENSE can be obtained. An iterative scheme that improves the phase estimate to better approximate the phase is presented. The mathematical framework of the new approach is provided together with comparisons of conventional SENSE, phase-constrained SENSE, and the new phase-refinement method. Both theory and experimental verification demonstrate significantly better noise performance at high reduction factors, i.e., close to the theoretical limit. For applications that need only magnitude data, an iterative phase-constrained SENSE reconstruction can provide substantial SNR improvement over SENSE reconstruction and less artifacts than phaseconstrained SENSE. Magn Reson Med 58:910 -921, 2007.

Recent advances in parallel imaging for MRI

“…Such phase discontinuities can occur near air-tissue boundaries, in fatty tissues, or around blood vessels. The phase constraints may be regularized to decrease artifacts at the expense of lower SNR [132], or high-resolution phase maps may be recovered iteratively and then used to reduce artifacts [133]. …”

Improved matrix inversion in image plane parallel MRI

“…Iterative methods also have great flexibility in incorporating linear and nonlinear constraints for conditioning the problem, such as been discussed in Ref. [32,34]. The newly emerged compressed sensing (CS) technique [36,37] further generalizes the concept of image support to various transform domains; it has the distinctive feature that explicit knowledge of the support region is not required and could rather be derived via an optimization process.…”

“…Thus, special periodic sampling patterns on Cartesian grids are employed to achieve computational efficiency at reconstruction. On the other hand, iterative approaches have been taken to tackle the problem [32][33][34][35][36][37]. Computationally cheap algorithms such as conjugate gradient and projections onto convex sets are used to iteratively restore the final image instead of a direct inversion; they thus allow arbitrary Cartesian and nonCartesian k-space sampling patterns to be used.…”

Separation of parallel encoded complex-valued slices (SPECS) from a single complex-valued aliased coil image

“…With a single channel quadrature coil, magnitude-only models for separating simultaneously encoded slices have been investigated, although these models are constrained to only separating two slices [14,18–21]. These magnitude-only SMS reconstruction techniques are conceptually similar to phase constrained in-plane acceleration methods [22–23], but it has been well documented that the judicious use of appropriately characterized magnetization phase can vastly improve the un-aliasing process in parallel imaging [22–24]. Additionally, a recent line of research has illustrated that utilizing images in a time series with both magnitude and phase offer improved fMRI activation statistics [25–28] over those achieved through the gold standard magnitude-only models.…”