A piecewise-polynomial basis for generalized diffusion encoding gradient waveforms

Diffusion-encoding gradient waveforms are a key parameter of experimental design in diffusion magnetic resonance imaging. Their optimization is important for e.g. maximizing the efficiency in B-tensor encoding, or improving the sensitivity and specificity to microstructure parameters of biophysical models. The main challenge in optimizing gradient waveforms and trajectories is the large dimension of the search space and the constraints associated with physical and physiological limitations. Here we propose an original piecewise polynomial representation, which natively enforces the linear constraints that arise from refocusing and regularity. We illustrate the basis on B-tensor encoding and Monte-Carlo simulation of the diffusion signal.