Fluctuation-based deconvolution in fluorescence microscopy using plug-and-play denoisers
This work addresses the challenge of studying sub-diffraction-limit entities in living samples for microscopy researchers, but it is incremental as it builds on existing plug-and-play and deconvolution techniques.
The paper tackled the problem of reconstructing super-resolved images in fluorescence microscopy, particularly for filament structures, by using a plug-and-play denoising approach with a pre-trained network and second-order statistics, achieving high peak signal-to-noise ratio (PSNR) values in evaluations on simulated and real images.
The spatial resolution of images of living samples obtained by fluorescence microscopes is physically limited due to the diffraction of visible light, which makes the study of entities of size less than the diffraction barrier (around 200 nm in the x-y plane) very challenging. To overcome this limitation, several deconvolution and super-resolution techniques have been proposed. Within the framework of inverse problems, modern approaches in fluorescence microscopy reconstruct a super-resolved image from a temporal stack of frames by carefully designing suitable hand-crafted sparsity-promoting regularisers. Numerically, such approaches are solved by proximal gradient-based iterative schemes. Aiming at obtaining a reconstruction more adapted to sample geometries (e.g. thin filaments), we adopt a plug-and-play denoising approach with convergence guarantees and replace the proximity operator associated with the explicit image regulariser with an image denoiser (i.e. a pre-trained network) which, upon appropriate training, mimics the action of an implicit prior. To account for the independence of the fluctuations between molecules, the model relies on second-order statistics. The denoiser is then trained on covariance images coming from data representing sequences of fluctuating fluorescent molecules with filament structure. The method is evaluated on both simulated and real fluorescence microscopy images, showing its ability to correctly reconstruct filament structures with high values of peak signal-to-noise ratio (PSNR).