Combination of state-of-the-art hybrid pixel semiconductor detectors (Medipix2, Timepix) with new micro- and nano-focus X-ray sources opens many new possibilities in radiation imaging. The spatial resolution of X-ray micro radiography is the crucial parameter determining the possible application. From theoretical principles it is clear, that the lower limit of the spatial resolution of a radiographic method is given by the size of the so-called Point Spread Function (PSF) of imaging system. We demonstrate two methods based on the precise measurement of the PSF and the implementation of deconvolution. In the case of high geometrical magnification the X-ray spot size becomes the most important factor for PSF determination. We have developed methods for the precise 1-D and 2-D measurement of X-ray spot size. We present also the results of simulations, which show the ability and limitations of the Wiener deconvolution, regularized deconvolution, blind deconvolution, and Lucy-Richardson algorithm as a way to deblurring images in the X-ray radiography. The methods have been successfully demonstrated on the real radiograph images. The spatial resolution has been thus improved up to three-fold. The effect of geometrical magnification is commonly employed in the spatial resolution enhancement using divergent X-ray source beams. However, due to the limited detector size, the dimension of the observed area decreases with increasing geometrical magnification. Another possibility for resolution enhancement is subpixel micro-shifting of the X-ray detector used. Although this approach is quite common for optical imaging, it has not been investigated for X-ray imaging. The successful demonstration of X-ray radiograph spatial resolution enhancement based on the 1-D micro-shifting of Medipix2 detector and measurement of its PSF is presented as well.