Investigations of the effects of random sampling schemes on the stability of generalized sampling

Generalized sampling is a mathematical technique for obtaining approximations of signals with respect to different representations in a numerically stable manner. This can for example be relevant in processing MRI images, where hardware often enforces initial frequency measurements, but where a wavelet basis may be better suited for representing the image. Recently the theory of generalized sampling was extended to work with arbitrary patterns in R ^d. In this article we investigate how the choice of the probability distribution generating random sampling schemes in R ² affects the numerical stability of generalized sampling.