Restoration methods for biomedical images in confocal microscopy

Abstract

This thesis introduces new solutions to the problem of image restoration in biomedical fields. The confocal microscope is a relatively new imaging technique that is emerging as a standard tool in biomedical studies. This technique is capable of collecting a series of 2D images of single sections inside a specimen to form a 3D image of the object. Moreover, the use of laser light increases the resolving capabilities of the microscope. Despite of its improved imaging properties, the observed images are blurred due to the finite size of the the point spread function and corrupted by Poisson noise due to the counting nature of image detection. Image restoration aims at reversing the degradation and recovering an estimate of the true image. This thesis starts with the description of the confocal microscope and the sources of degradation. Then, the existing image restoration methods are studied and compared. The work done in this thesis is divided into three parts: In the first part, a new constrained blind deconvolution method is introduced. In this method, re-parameterization is used to strictly enforce apriori knowledge. For the PSF, a parametric model based on a set of constrained basis functions is used. This re-parameterization ensures circular symmetry, and band-limitedness. For the image, quadratic re-parameterization ensures non-negativity. The deconvolution method is evaluated on both simulated and real confocal microscopy data sets. The comparison with a non-parameterized algorithm shows that the proposed method exhibits improved performance and faster convergence. In the second part, a new method to correct the effect of anisotropic, depthvariant blur is introduced. When objects of tubular-like structure, like neurons, are imaged, the acquired images are degraded and the extraction of accurate morphology of neurons is hampered due to these anisotropic deformations. A new method to estimate the PSF from the acquired image without any prior knowledge about the imaging system is proposed. This method which is based on the estimation of the original object and is suitable for cases in which, the object being imaged has a known geometry. Using the proposed deconvolution method, geometric distortions are eliminated and the restored images are more suitable for further analysis. In the third part, a new method for adaptive regularization is proposed. The proposed technique adapts its behavior depending on the local activities in the