Solving the boundary artifact for the enhanced deconvolution algorithm SUPPOSe applied to fluorescence microscopy

The SUPPOSe enhanced deconvolution algorithm relies in assuming that the image source can be described by an incoherent superposition of virtual point sources of equal intensity and finding the number and position of such virtual sources. In this work we describe the recent advances in the implementation of the method to gain resolution and remove artifacts due to the presence of fluorescent molecules close enough to the image frame boundary. The method was modified removing the invariant used before given by the product of the flux of the virtual sources times the number of virtual sources, and replacing it by a new invariant given by the total flux within the frame, thus allowing the location of virtual sources outside the frame but contributing to the signal inside the frame.