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 paper. 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 (CRB), 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 CRB is high at common SNR. 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.

The Exponential Analysis via System Identification using Steiglitz-McBride algorithm provides an efficient and user-parameter-free alternative to non-negative least squares for estimating the parameters of multiple relaxation components and gives a new way of estimating the spatial variations of myelin in the brain.

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