The vision system of arthropods such as insects and crustaceans is based on the compound-eye architecture, consisting of a dense array of individual imaging elements (ommatidia) pointing along different directions. This arrangement is particularly attractive for imaging applications requiring extreme size miniaturization, wide-angle fields of view, and high sensitivity to motion. However, the implementation of cameras directly mimicking the eyes of common arthropods is complicated by their curved geometry. Here, we describe a lensless planar architecture, where each pixel of a standard image-sensor array is coated with an ensemble of metallic plasmonic nanostructures that only transmits light incident along a small geometrically-tunable distribution of angles. A set of near-infrared devices providing directional photodetection peaked at different angles is designed, fabricated, and tested. Computational imaging techniques are then employed to demonstrate the ability of these devices to reconstruct high-quality images of relatively complex objects.