The most effective superresolution methods proposed in the literature require precise knowledge of the so-called point spread function of the imager, while in practice its accurate estimation is nearly impossible. This paper presents a new superresolution method, whose main feature is its ability to account for the scant knowledge of the imager point spread function. This ability is based on representing this imprecise knowledge via a non-additive neighborhood function. The superresolution reconstruction algorithm transfers this imprecise knowledge to output by producing an imprecise (interval-valued) high-resolution image. We propose some experiments illustrating the robustness of the proposed method with respect to the imager point spread function. These experiments also highlight its high performance compared with very competitive earlier approaches. Finally, we show that the imprecision of the high-resolution interval-valued reconstructed image is a reconstruction error marker.