Blind Deconvolution and 3d Psf Modeling in Biological Microscopy

Multidimensional microscopy is an essential tool for research and industry in the areas of cellular biology and molecular medicine, cell-based drug discovery and cellular therapies. Modern microscopic methodologies have brought the possibility to follow live cells in action, responding to various perturbations. These capabilities include not only detailed dynamic information about cell morphology, but highly sensitive spatio-temporal data about the behavior of specific proteins in cells. Experimental systems are being developed to model mechanisms in healthy and sick cell lines, and probe the various components mediating these mechanisms, thus resolving the molecular networks underlying complex cellular processes. While microscopy has been vastly employed in the analysis of abundant proteins, the detection of rare ones is facing difficulties. One of the most limiting factor is the fact that the full resolution of the microscope cannot be realized for three-dimensional thick samples. The reason is that imaging without aberrations (in practice, with aberrations smaller then the diffraction-limit resolution) can only be achieved under well defined conditions. For biological microscopy these are set for samples just under a cover-slide of well defined thickness. As soon as the focus of the objective is moved into the sample depth, the resolution of the optical system degrades. There are several ways to correct these depth aberrations: the most flexible method is to use objectives with correction collar. However, this imposes severe limitations on the speed of three-dimensional image acquisition. It is the purpose of this project to develop computational alternative methods that will be compatible with modern three-dimensional microscope imaging procedures. Three-dimensional image deconvolution is a post-acquisition method that uses the known properties of the microscope optics to reconstruct better images. Deconvolution has been used for over two decades with great success for a wide range of applications in astronomy and in microscopy. Many deconvolution methods have already been proposed for 3D microscopy, such as Agard and Sedat [1, 3], Tikhonov-Miller inverse filter [26], Carrington [24] and Richardson-Lucy (RL) algorithms [18, 22]. The latter has been used extensively in astrophysical or microscopic imaging [26], and is of particular interest for confocal microscopy because it is adapted to Poisson noise. An important drawback of RL deconvolution, however, is that it amplifies noise after a few iterations. This sensitivity to noise can be avoided with the help of regularization constraints, leading to much improved results. Conchello et al. [6] and van Kempen et al. [24, 25] have presented a RL algorithm using energy-based regularization applied to biological images. Conchello’s regularization term introduces oscillations enhanced with the number of RL iterations in homogeneous areas. Tikhonov-Miller based term, on the contrary, regularizes too much, resulting in smoothed edges. The previous work of the team financed first by ARC Demitri funded by INRIA from 2002 to 2004 and then by the P2R program for the period 2005-2006 has resulted in a deconvolution method based on the Richarson-Lucy algorithm regularized by the Total Variation [9, 10] in order to reduce the influence of noise on the performances of the RL method used alone and provides smoothing in homogeneous areas while preserving edges. A second class of restoration methods contains multiresolution models. In particular, wavelet denoising offers an alternative method of regularization for deconvolution. Boutet de Monvel et al. [8] propose a denoising method for confocal image stacks, using Daubechies’ wavelets for each