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We report some recent algorithmic refinements and the resulting simulated and real image reconstructions of fluorescence micrographs by using a blind-deconvolution algorithm based on maximum likelihood estimation. Blind-deconvolution methods encompass those that do not require either calibrated or theoretical predetermination of the point-spread function (PSF). Instead, a blind deconvolution reconstructs the PSF concurrently with deblurring of the image data. Two-dimensional computer simulations give some definitive evidence of the integrity of the reconstructions of both the fluorescence concentration and the PSF. A reconstructed image and a reconstructed PSF from a two-dimensional fluorescent data set show that the blind version of the algorithm produces images that are comparable with those previously produced by a precursory nonblind version of the algorithm. They furthermore show a remarkable similarity, albeit not perfectly identical, with a PSF measurement taken for the same data set, provided by Agard and colleagues. A reconstructed image of a three-dimensional confocal data set shows a substantial axial smear removal. There is currently an existing trade-off in using the blind deconvolution in that it converges at a slightly slower rate than the nonblind approach. Future research, of course, will address this present limitation.

We have been developing algorithms for 3D image reconstruction of biological specimens with absorbing stains. This is important because there are many absorbing stains which are widely used in conjunction with transmitted light brightfield (TLB) microscopy, yet most of the 3D microscopic imaging research has been directed toward fluorescence microscopy. For instance, horseradish peroxidase (HRP) is used widely in the neurosciences for its many advantages as a tracer and intracellular marker. It is readily injected into individual neurons, transported long distances, and fills both the dendritic and axonal fields, while it may double as an electron microscopy stain for correlative analysis. With such advantages, it is clear that absorbing stains will continue to be widely used. Their utility will furthermore broaden with 3D visualization and quantitation.The main principles behind our methodology are the following. Standard optical serial sectioning data collection is used. The iterative, constrained image reconstruction algorithm is designed to reconstruct the 3D optical density distribution .

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The Maximum Likelihood based blind deconvolution (ML-blind) algorithm is used to deblur three dimensional microscope images. This approach was first introduced to the microscope community by us circa 1992. The basic advantage of a blind algorithm is that it simplifies the user interface protocols and reconstructs both the object and the Point Spread Function. In this paper we will discuss the recent improvements to the algorithm that robustize the performance and accelerate the speed of convergence. For instance, powerful and physically justified constraints are enforced on the reconstructed PSF at every iteration for robustization. A line search technique is added to the object reconstruction to accelerate the convergence of the object estimate. A simple modification to the algorithm enables adaptation for the transmitted light brightfield modality. Finally, we incorporate montaging in order to process large data fields. Introduction and SignificanceMicroscope images are collected using the optical sectioning method [fl. A two dimensional (2D) data set is collected by focusing the objective lens of the microscope onto a plane of interest and capturing the image using a cooled Charged Coupled Device (CCD) camera [2]. The position of the focal plane is stepwise incremented from the bottom to the top of the sample and, each time, a 2D image frame is collected. These 2D frames are stacked one after the other to form a three dimensional (3D) data set.A 2D optical section contains both sharp features from the in-focus plane and blurred out-of-focus features from adjacent planes. Therefore, a collected 3D image displays considerable haze and blur along both the axial and lateral directions. The main purpose of a deblurring algorithm is to remove random noise and out-of-focus haze, and to restore the sharp in-focus features.The Maximum Likelthood (ML) based blind deconvolution (ML-blind) [3-6] method is a model-based deblurring approach that utilizes the iterative Estimation-Maximization (EM) technique and removes blurry out-of-focus features from a 3D microscope image. This method does not require prior knowledge of the Point Spread Function (PSF) of the system. Instead, it reconstructs the PSF and the image data simultaneously.The advantage of using the ML-blind method over other non-blind (requires a PSF) algorithms is that it simplifies the user interface protocols. To obtain an input PSF for non-blind algorithm one may measure [7]aPSF or calculate it from theoretical formulations [8], [9]. The disadvantage of measuring a microscope PSF [7] is that the details of the PSF measuring techniques are not esoteric. The disadvantages of using a theoretically calculated PSF are: 1) It contains simplified mathematical assumptions about the optics [8].2) The PSF calculation requires careful calibration of physical parameters [9] (such as depth of the sample from the cover-glass, and refractive index accuracy of the embedding medium to within three decimal places) which are tedious, and difficult to obtain for routine ...