Powered by differentiable imaging, Uncertainty - Aware Fourier Ptychography (UA - FP) revolutionizes computational imaging.

Human hearing beats sound’s uncertainty limit, makes MP3s sound worse Not Heisenberg's, Fourier's. Knowing how it's beaten may help us encode music.

We give a real-variable proof of the Hardy uncertainty principle. The method is based on energy estimates for evolutions with positive viscosity, convexity properties of free waves with Gaussian decay ...