Superresolution method for a single wide-field image deconvolution by superposition of point sources

In this work, we present a new algorithm for wide-field fluorescent micrsocopy deconvolution from a single acquisition without a sparsity prior, which allows the retrieval of the target function with superresolution, with a simple approach that the measured data are fit by the convolution of a superposition of virtual point sources (SUPPOSe) of equal intensity with the point spread function. The cloud of virtual point sources approximates the actual distribution of sources that can be discrete or continuous. In this manner, only the positions of the sources need to be determined. An upper bound for the uncertainty in the position of the sources was derived, which provides a criteria to distinguish real facts from eventual artefacts and distortions. Two very different experimental situations were used for the test (an artificially synthesized image and fluorescent microscopy images), showing excellent reconstructions and agreement with the predicted uncertainties, achieving up to a fivefold improvement in the resolution for the microscope. The method also provides the optimum number of sources to be used for the fit. LAY DESCRIPTION: A new method is presented that allows the reconstruction of an image with superresolution from a single frame taken with a standard fluorescent microscope. An improvement in the resolution of a factor between 3 and 5 is achieved depending on the noise of the measurement and how precisely the instrument response function (point spread function) is measured. The complete mathematical description is presented showing how to estimate the quality of the reconstruction. The method is based in the approximation of the actual intensity distribution of the object being measured by a superposition of point sources of equal intensity. The problem is converted from determining the intensity of each point to determining the position of the virtual sources. The best fit is found using a genetic algorithm. To validate the method several results of different nature are presented including an artificially generated image, fluorescent beads and labelled mitochondria. The artificial image provides a prior knowledge of the actual system for comparison and validation. The beads were imaged with our highest numerical aperture objective to show method capabilities and also acquired with a low numerical aperture objective to compare the reconstructed image with that acquired with a high numerical aperture objective. This same strategy was followed with the biological sample to show the method working in real practical situations.