Abstract
Recently in the study of three-dimensional structure of a living cell, confocal laser scanning microscope (CLSM) has developed to become an excellent technique to the research of biological specimens. CLSM can acquire images with higher resolution and better contrast. It generates clearer images at various depths by blocking out-of-focus light through a spatial pinhole. With the obtained multiple focal plane images, biologists are able to reconstruct the three dimensional volume of the specimen. However, there are still several limitations on the performance of CLSM. The aliasing effect caused by point spread function (PSF) along the optical axis is much worse than that along the lateral axis. This disadvantage may restrain the spatial reliability of the reconstructed three dimensional volume data of the specimen. Therefore, recovering images from such aliasing effect has become an important goal. We propose a 3-D deconvolution method based on total variation regularizer and a parametric theoretical PSF model to reconstruct the corrupted 3-D image volume. In this algorithm, we first determine a theoretical PSF model that can best estimate the system optical properties of CLSM. Then by minimizing an objective function regularized by total variation regularizer, this process could be taken as an inverse procedure of PSF. The reason to use total variation regularizer rather than other regularizer is that it preserves important features while recovering the image. Since total variation deconvolution is non-linear and non-differentiable, it is very expensive in computation to minimize the objective function. Therefore, the concept of half-quadratic function is applied to split variables, so as to accelerate the computation.