FIGURE S1. Balanced SSFP data employed for Simulation 2. T₁, T₂, and flip angle varied through T₂ and multifactorial b parameter for TR = 4.2 ms, with θ off-resonance variation overlaid. (A) ∆θ = 0°, (B) 90°, (C) 180°, and (D) 270° phase-cycled magnitude images with added bivariate Gaussian noise. Corresponding solutions from these phase cycles are the: (E) Center-of-Mass, the noiseless gold standard for the (I) Complex Sum of the (A–D) data, and (F) Cross-point M, the noiseless gold standard for the (G) Geometric Solution and the (H) Linearized Geometric Solution of the (A–D) data.

FIGURE S2. (A) Arduino circuit with automated controls, stepper motor, and linear actuator to oscillate syringe injection and introduce variable-speed water flow through tubes around a phantom. (B) Phantom consists of flexible tubing wound around a bottle of water.

FIGURE S3. Four balanced SSFP phase cycles ∆θ = 0°, 90°, 180°, and 270° are acquired of a water phantom with encircling tubes of water without flow (shown in Figure 6), and with 40 mL/60 s (0.7 mL/s), 40 mL/40 s (1 mL/s, also shown in Figure 6), and 40 mL/20 s (2 mL/s) tube flow during 1/4 phase cycles and 4/4 phase cycles. Reconstructions of phase-cycled data are computed for each of the flow scenarios, with the complex sum (CS) shown in 1(A)–6(A), and the linearized geometric solution (LGS) shown in 1(B)–6(B). Image differences for all flow scenarios – no-flow images are shown for the CS (1C–6C) and LGS (1D–6D), where static regions were masked to allow computation of flow error images alone. The error energy (EE) is computed, normalized, and listed for each scenario. EE values are plotted vs. flow velocity in Figure 6.