Parameter estimation approach to banding artifact reduction in balanced steady-state free precession.

PURPOSE: The balanced steady-state free precession (bSSFP) pulse sequence has shown to be of great interest due to its high signal-to-noise ratio efficiency. However, bSSFP images often suffer from banding artifacts due to off-resonance effects, which we aim to minimize in this article. METHODS: We present a general and fast two-step algorithm for 1) estimating the unknowns in the bSSFP signal model from multiple phase-cycled acquisitions, and 2) reconstructing band-free images. The first step, linearization for off-resonance estimation (LORE), solves the nonlinear problem approximately by a robust linear approach. The second step applies a Gauss-Newton algorithm, initialized by LORE, to minimize the nonlinear least squares criterion. We name the full algorithm LORE-GN. RESULTS: We derive the Cramér-Rao bound, a theoretical lower bound of the variance for any unbiased estimator, and show that LORE-GN is statistically efficient. Furthermore, we show that simultaneous estimation of T1 and T2 from phase-cycled bSSFP is difficult, since the Cramér-Rao bound is high at common signal-to-noise ratio. Using simulated, phantom, and in vivo data, we illustrate the band-reduction capabilities of LORE-GN compared to other techniques, such as sum-of-squares. CONCLUSION: Using LORE-GN we can successfully minimize banding artifacts in bSSFP.

A robust methodology for in vivo T1 mapping.

In this article, a robust methodology for in vivo T(1) mapping is presented. The approach combines a gold standard scanning procedure with a novel fitting procedure. Fitting complex data to a five-parameter model ensures accuracy and precision of the T(1) estimation. A reduced-dimension nonlinear least squares method is proposed. This method turns the complicated multi-parameter minimization into a straightforward one-dimensional search. As the range of possible T(1) values is known, a global grid search can be used, ensuring that a global optimal solution is found. When only magnitude data are available, the algorithm is adapted to concurrently restore polarity. The performance of the new algorithm is demonstrated in simulations and phantom experiments. The new algorithm is as accurate and precise as the conventionally used Levenberg-Marquardt algorithm but much faster. This gain in speed makes the use of the five-parameter model viable. In addition, the new algorithm does not require initialization of the search parameters. Finally, the methodology is applied in vivo to conventional brain imaging and to skin imaging. T(1) values are estimated for white matter and gray matter at 1.5 T and for dermis, hypodermis, and muscle at 1.5 T, 3 T, and 7 T.

Spectral estimation of irregularly sampled exponentially decaying signals with applications to RF spectroscopy.

The problem of estimating the spectral content of exponentially decaying signals from a set of irregularly sampled data is of considerable interest in several applications, for example in various forms of radio frequency spectroscopy. In this paper, we propose a new nonparametric iterative adaptive approach that provides a solution to this estimation problem. As opposed to commonly used methods in the field, the damping coefficient, or linewidth, is explicitly modeled, which allows for an improved estimation performance. Numerical examples using both simulated data and data from NQR experiments illustrate the benefits of the proposed estimator as compared to currently available nonparametric methods.