Blind Deconvolution in 3d Biological Microscopy

Confocal microscopy o ers several advantages over conventional optical microscopy with its small depth-ofeld, its reduction of out-of-focus blur, and its full three-dimensional (3D) image scanning ability. For biomedical applications, it can also acquire images of living cells, usually labeled with one or more uorescent probes. The confocal laser scanning microscope (CLSM) is an optical uorescence microscope associated to a laser that scans the specimen in 3D and uses a pinhole to reject most out-of-focus light. The ability of CLSM to image optical sections of thick specimens explains its rapidly increasing use in biological research [15]. Despite the advantages of the CLSM, the quality of confocal microscopy images su ers from two basic physical limitations. First, out-of-focus blur due to the di raction-limited nature of optical microscopy remains substantial, even though it is reduced compared to wide eld microscopy. Second, the confocal pinhole drastically reduces the amount of light detected by the photomultiplier, leading to Poisson noise [15]. The images produced by CLSM can therefore bene t from postprocessing by reconstruction methods designed to reduce blur and/or noise. The aim of this proposal is two folds : First, we want to propose methods for image deconvolution, assuming we know the point spread function (PSF), which models the degradation of the optical acquisition system. We also assume the noise is known (Poisson noise or approximated Gaussian noise with known standard deviation). Second, we want to propose solutions for the real case, when the degradation is not exactly known. So we have to estimate both the degradation and the restored image from the observations only.