Discrete SUPPOSe: A new, faster and accurate superresolution method for applications to fluorescence microscopy images

In this article we define Discrete SUPPOSe, a new and faster version of the single shot super resolution SUPPOSe (Superposition of virtual point sources) method. The SUPPOSe method for super-resolution of fluorescent microscope images relies in assuming that the sample source distribution can be modeled as a superposition of virtual point sources of equal intensities distributed in a continuous space, converting the ill posed deconvolution problem into a well posed one. In this work we present a faster new method that consists on discretizing the continuum problem, using a normalized covariance instead of a ${\chi }^2$ for the fitting function and hence transforming the convolution (the main computational time) into a multiplication, and modifying the mutation step of the genetic algorithm. We compare precision, accuracy, resolution and computation time. It is also shown that despite the spatial discretization in Discrete SUPPOSe similar figures for precision, accuracy and resolution are obtained. The algorithm was implemented in Matlab running on a CPU obtaining with a speed improvement factor of more than 15 for one image of 48 × 48 pixels. Processing images in parallel in a 16 cores CPU a 1Mpixel image is computed 240 times faster than the standard SUPPOSe in a 2600 core GPU. Experimental images were used to validate the method.