Three dimensional (3D) fluorescence microscopy through optical sectioning is a powerful technique for visualizing biological specimens. The microscope objective is focused at different depths in order to image the biological sample that one wishes to study. Yet, the observation process is never perfect and there are always uncertainties in measurements occurring as blur, aberration and noise. Often, the 3D observed images are never an ideal representation of the true object, and restoration approaches assume that the underlying degradation process is known. However, in fluorescence microscopy, often the degradation varies with imaging conditions and is also sometimes specimen dependent. Blind restoration approaches, tackle this much more realistic but difficult situation of restoration from a single observation of the sample. As the degradation is characterized by the system's point-spread function (PSF), the focus of this thesis is on estimating it along with the fluorescence distribution of the specimen. These problems are ill-posed, under-determined, and so we treat restoration as a Bayesian inferencing problem.
In the first part, we recall briefly how the diffraction-limited nature of an optical microscope's objective, and the intrinsic noise can affect an observed image's resolution. We use statistical approaches for restoration as the physics underlying the production of the images could be considered statistical in nature. The state of the art algorithms related to this subject are reviewed and also the modeling of the imaging process with the optical system is examined. As the imaging involves a photon counting process, the model chosen for the observation is based on the theoretically correct Poisson distribution. An alternative minimization (AM) approach, in the Bayesian framework, restores the lost frequencies beyond the diffraction limit by using a regularization on the object and a constraint on the PSF. Furthermore, new methods are proposed to learn the free-parameters, like the regularization parameter, which conventionally is chosen manually. When imaging into deeper sections of the specimen, the approximation of an aberration-free imaging, as assumed previously, is not realistic anymore. This is because the refractive index mismatch between the specimen and the immersion medium of the objective lens becomes significant with depth under the cover slip. An additional difference in the path is introduced in the emerging wavefront of the light due to this difference in the index, and the phase aberrations of the wavefront becomes significant. The spherical aberrated (SA) PSF in this case becomes dependent on the axially varying depth.
In the second part, we show that an object's location and its original intensity distribution can be recovered by retrieving this phase from the observed intensities. However, due to the incoherent nature of the acquisition system, phase retrieval from the observed intensities will be possible only if the phase restoration is constrained. We use geometrical optics to model the refracted wavefront phase, and modify the AM algorithm to retrieve the PSF from some simulated images. Finally, we propose an extension of this method to restore specimens affected by SA. In this case, as the PSF is depth varying, the linear space invariant model is not suitable. The observation process is defined by a quasi-stationary model, and the PSF approximated so that, excluding the object, there is only one free parameter to be estimated.
Keywords: confocal laser scanning microscopy, point-spread function, blind deconvolution, spherical aberration, Bayes' theorem, maximum likelihood, expectation maximization, maximum a posteriori, alternate minimization.