Аннотация:A set of LiFePO4 samples has been studied by small-angle X-ray scattering (SAXS). Using the technique of artificial neural networks, the shape of SAXS curves has been reconstructed taking into account the hardware function. Estimates of homogeneitiessizes and shapes in the studied LiFePO4 samples have been obtained. Keywords: Small-angle X-ray scattering, artificial neural network, lithium-ion rechargeable batteries, incorrect tasks regularization.