It has been demonstrated that the combination of state-of-the-art hybrid pixel semiconductor detectors with newly micro- and nano-focus x-ray sources opens wholly new possibilities in radiation imaging. Semiconductor single particle counting pixel detectors (Medipix2, Timepix) offer many advantages for x-ray imaging: high detection efficiency, energy discrimination, noiseless digital integration (counting), high frame rate and virtually unlimited dynamic range. All these properties allow achieving high quality micro radiographs including very low contrast and low absorption objects. It has been also developed a set of techniques for data processing and image correction (flat field correction, beam hardening correction) to eliminate residual drawbacks of pixel detectors and of the usage of polychromatic x-ray sources. The spatial resolution of x-ray micro radiography (alike any other imaging method) is the crucial parameter and its improvement still remains an experimental and data processing challenge. From theoretical principles it is clear, that the lower limit of the spatial resolution of a radiographic method is given by the spot size of the imaging x-ray source (e.g., pinhole collimated x-ray radiation, micro- or nanofocus roentgen tube radiation, divergence of the synchrotron source beam, x-ray laser). The main aim of this work is the development of a method based on the precise measurement of the x-ray spot size and the implementation of deconvolution, which should lead to improvement of the spatial resolution under the theoretical limitation given by the finite source size.