This research thesis addresses the problems of microscopic pathology analysis. It presents a general framework for computer-aided diagnostics. The aim of the framework is unification and improvement of the pathological examination routine. The framework combines telepathology with computer-aided diagnostics algorithms. The framework targets image acquisition and interpretation stages. The image acquisition subsystem solves problems related to microscopical slide digitization such as biomedical image registration, data representation, and processing. The interpretation subsystem uses a support vector machine classifier together with a feature selection for computer-aided diagnostics. The histopathological and cytopathological systems for computer-aided diagnostics are implemented using the presented framework. In microscopy, regions of interest are considerably smaller than the whole slide area. Various microscopy related medical applications, such as telepathology and computer aided diagnosis, are liable to benefit greatly from automatic determination of field of view coordinates. In this thesis we present a method for image-based positioning on a microscope slide. The method is based on localization of a microscopic query image using a previously acquired slide map. It uses geometric hashing, a highly efficient technique of object recognition. The algorithm exhibits high tolerance to possible variations of microscopic field of view due to slide rotations and illumination changes. Problems of computer-aided diagnostics systems based on analysis of color or gray-scale images are addressed. The first problem is large color variance of the same dyes attached to the same specimen types. The second problem concerns the physical overlapping of different kinds of objects resulting in color mixtures. The algorithm for automated decomposition of microscopic hyperspectral biological images is proposed. The decomposed compounds are described by their spectral characteristics and optical density. The multiplicative physical model of image formation in transmission light microscopy is presented, a reduction of a hyperspectral image decomposition problem to a Blind Source Separation (BSS) problem is justified, and a method for hyperspectral restoration of separated compounds is provided. The obtained results may be used for improving automatic microscope hardware calibration and computer-aided diagnostics. The method for decomposition of hyperspectral images is extended to a case of  multichannel noisy signals separation. The cases when the source signals have a sparse representation in some dictionary are considered. The dependency of decomposition coefficients is modeled by the joint sparsity prior. The joint sparsity prior is explored in the context of BSS problem and denoising problem, where the mixing matrix and the sources are unknown.