In recent years, several pioneering works were dedicated to imaging systems based on simple diffractive structures like Fresnel lenses or phase zone plates. Such systems are much lighter and cheaper than classical refractive optical systems. However, the quality of images obtained by diffractive optics suffers from stronger distortions of various types. In this paper, we show that a combination of the high- precision lens design with post-capture computational reconstruction allows one to attain a much higher image quality. The proposed reconstruction procedure uses a sequence of color correction, deconvolution, and a feedforward deep learning neural network. An improvement both in lens manufacturing and in image processing may contribute to the emergence of ultra-lightweight imaging systems varying from cameras for nano- and picosatellites to surveillance systems.