High-speed laser scanning microscopy frequently relies on resonant scanners due to their order of magnitude increase in imaging rate compared to conventional galvanometer scanners. However, the use of a nonlinear scan trajectory introduces distortion that must be corrected. This manuscript derives a new algorithm based on filtered Hermite polynomial interpolation that provides the optimal shot-noise-limited SNR for a fixed number of photons and provides higher spatial accuracy than previous methods. An open-source library is presented using the Intel advanced vector instruction set (AVX) to process up to 32 samples in parallel. Using this approach, I simultaneously demonstrate lower shot noise variance, moderately higher spatial accuracy and greater than 1 gigapixel per second interpolation rate on a desktop CPU.