Micrometer-sized lenses are known to be able to resolve objects beyond the diffraction limit. In this paper, using the matrix formalism in imaging, we discuss two possible models of this phenomenon. The first model considers the transformation of the source field keeping the real image unchanged. The second model is focused on finding the scattering matrix a particle that gives super resolution in virtual image. Both approaches demonstrate the required super resolution. Disadvantages of the proposed models and possible ways to solve them are discussed.