Compressed Sensing in microscopy with random projections in the Fourier domain

In this paper we propose a Compressed Sensing-based image acquisition and recovery method that combines Fourier magnitude measurements and Fourier phase estimation for sequential microscopy image acquisition. The main idea is to combine sequential Optical Fourier Transform (OTF) magnitude measurements with Fourier phase estimation from complete keyframes acquisition. For images with homogeneous objects and background, Compressed Sensing (CS) provides indeed an optimal reconstruction framework from a set of random projections in Fourier domain, while constraining bounded variations in the spatial domain. As in many others optical systems, in microscopy we can observe the magnitude of the Fourier coefficients. However, getting the phase of these coefficients can be an very expensive task. Initial experiments simulating the proposed microscopy image acquisition protocol confirm the feasibility of the CS computational framework to recover image sequences in microscopy with a very high frame rate while preserving high SNR levels.