My PhD work deals with the application of Compressed Sensing (or CompressiveSampling, CS) in fluorescence microscopy as a powerful toolkit for fundamental biologicalresearch. The recent mathematical theory of CS has demonstrated that, for aparticular type of signal, called sparse, it is possible to reduce the sampling frequencyto rates well below that which the sampling theorem classically requires. Its centralresult states it is possible to losslessly reconstruct a signal from highly incompleteand/or inaccurate measurements if the original signal possesses a sparse representation.We developed a unique experimental approach of a CS implementation in fluorescencemicroscopy, where most signals are naturally sparse. Our CS microscopecombines dynamic structured wide-field illumination with fast and sensitive singlepointfluorescence detection. In this scheme, the compression is directly integratedin the measurement process. Additionally, we showed that introducing extra dimensions(2D+color) results in extreme redundancy that is fully exploited by CS to greatlyincrease compression ratios.The second purpose of this thesis is another appealing application of CS forsuper-resolution microscopy using single molecule localization techniques (e.g.PALM/STORM). This new powerful tool has allowed to break the diffraction barrierdown to nanometric resolutions. We explored the possibility of using CS to drasticallyreduce acquisition and processing times.
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