Quantum fluctuations in Compressed Sensing

Abstract

Compressed Sensing (CS) is a new method of signal and image processing which allows for exact recovery of an image from a number of samples much smaller than that required by the Nyquist/Shannon theorem. Compressed Sensing uses a priori information about the object called “sparsity”, which means that only a small number of image samples are nonzero. We have analyzed the superresolution behavior of CS taking into account the quantum fluctuations in the image. Our analysis allows to characterize the ultimate capabilities of CS imposed by the quantum nature of the light.