A Space-variant 3D Deconvolution Method For Fluorescence Microscopy Image Deblurring

Deconvolution is a powerful technique for fluorescence microscopy image restoration and reconstruction.It is capable to process not only the wide field microscopy image but also the laser scanning confocal microscopy and light sheet fluorescence microscopy(LSFM)image.Conventional deconvolution methods consider the optical imaging system space-invariant,resulting remarkable errors to the restoration results.The point spread functions(PSF)in those methods(either theoretical or experimental)is also space invariant.In this study,we developed a method to more precisely estimate space-variant point-spread function(PSF)from sparse measurements by considering the formation of shift variation.To generate more precise space-variant PSFs for an actual optical system,we measured several responds of the micro-fluosphere(100nm in diameter)at different depths and locations.A similarity transformation(STM)based numerical model we proposed for PSF estimation,was then used to interpolate those PSF measurements.In this way,we are able to reconstruct PSF at any specific depth and location.In developing robust space-variant deconvolution algorithm for fluorescence image restoration,we adopted several space-variant restoration methods have been proposed in recent,which regards the imaging formation as a Poisson process.The algorithm of space-variant deconvolution we proposed reduces the blur via maximizing the log-likelihood function.To avoid noise amplification in such algorithm,a regularization term related to prior knowledge should be taken in consideration.Therefore,we introduced a total variant regularization term to the space-variant deconvolution framework,which smooths homogeneous areas and preserves object edges simultaneously.Combining the regularized maximum likelihood algorithm along with the experimental space-variant PSFs,we propose an alternating optimization scheme,without knowing the relative depth of the specimen to cover slip.Moreover,we optimized the calculation of the three-dimensional(3D)space-variant convolution and proposed a STM based 3D restoration method for releasing the computation cost.We then compared our proposed space-variant PSF model with different models on synthetic and real image data.Validation with both simulation and real data showed that our PSF model is more accurate than the piecewise-invariant model and the blending model.Comparing with the orthogonal basis decomposition based PSF model,our proposed model also performed with a considerable improvement.We also evaluated the proposed deblurring algorithm.Results showed significant improvement on signal-to-noise ratio and image quality,comparing with conventional space-invariant algorithm.Our method should be highly useful for image restoration and 3D reconstruction of Wide field,LSCM and LSFM.