Image restoration applied to x-ray microscopy: application to images with low signal-to-noise ratio

X-ray microscopy makes it possible to obtain images at a higher spatial resolution (about 20 nm) as compared to optical microscopy. Moreover, x-ray microscopy permits direct acquisition from the specimen in 2D or 3D mode, without any preparation step (staining, fixation, ...), which is not possible in electron microscopy. Here we present deblurring methods to restore images after the acquisition process. An additive Poisson noise is generated by the use of x rays and also contributes to image degradation. Our purpose is to analyze such noise and to restore images. Due to the optical properties of the Fresnel zone plate, we presently associate it to an optical circular lens as is done for the optical microscope. Here we use the Richardson Lucy algorithm to deconvolute. A first step is to observe results of restoration obtained on an image grating (a star pattern) with inner zones of dimensions near the resolution. The next step involves the suppression of noise effects arising from the deconvolution process. The characteristics of the noise after deconvolution are evaluated by Fourier analysis. These effects are eliminated by a filtering process in the Fourier spectrum. This filtering is applied on images with different signal to noise ratio (obtained after different time exposures), in order to compare results obtained on noisy images with long time exposure images.