Performance limits of covariance-driven super resolution imaging

This paper studies the role of correlation in the problem of super-resolution fluorescence microscopy for cellular and molecular imaging. Inspired by our prior work on nested arrays, it is shown that if the sources are statistically uncorrelated, a novel sum co-array structure emerges for the widely used Gaussian point spread function. Combining this sum co-array with our previously proposed spatial smoothing based two dimensional MUSIC algorithm, it is possible to localize more sources than sensors. The proposed framework overcomes limitation of conventional correlation-based super resolution techniques such as SOFI. Moreover, unlike recent algorithms like SPARCOM that restrict the emitters to lie on a known high-resolution grid, our algorithm considers the original off-grid super-resolution model where the target resolution is not restricted by the size of the grid.