Vector optimization for gridding kernels: a Pareto-based framework for NUFFT accuracy control

Gridding algorithms are essential for applying the Fast Fourier Transform (FFT) to nonuniformly sampled data, as commonly encountered in MRI and CT imaging. These algorithms interpolate irregular samples onto a uniform grid before FFT computation, and their accuracy depends critically on the choice of the gridding kernel. This work introduces a new optimization framework based on vector optimization, where kernel optimality is defined through Pareto efficiency of the error shape operator Λ, a mapping that quantifies how interpolation errors vary across frequencies. Using scalarization techniques, we design kernels that approximate user-defined target error shapes, enabling customized accuracy in regions of interest. Numerical experiments show significant improvements over classical kernels such as prolate spheroidal wave functions and state-of-the-art NUFFT implementations, paving the way for adaptive and application-specific gridding strategies.