Modern fluorescent microscopy imaging is still limited by the optical aberrations and the photon budget available in the specimen. A direct consequence is the necessity to develop flexible and “off-road” algorithms in order to recover structural details and improve spatial resolution, which is critical when restraining the illumination to low levels in order to limit photo-damages. Here, we report SPITFIR(e) a flexible method designed to accurately and quickly restore 2D–3D fluorescence microscopy images and videos (4D images). We designed a generic sparse-promoting regularizer to subtract undesirable out-of-focus background and we developed a primal-dual algorithm for fast optimization. SPITFIR(e) is a ”swiss-knife” method for practitioners as it adapts to any microscopy techniques, to various sources of signal degradation (noise, blur), to variable image contents, as well as to low signal-to-noise ratios. Our method outperforms existing state-of-the-art algorithms, and is more flexible than supervised deep-learning methods requiring ground truth datasets. The performance, the flexibility, and the ability to push the spatiotemporal resolution limit of sub-diffracted fluorescence microscopy techniques are demonstrated on experimental datasets acquired with various microscopy techniques from 3D spinning-disk confocal up to lattice light sheet microscopy.
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