Computational imaging is undergoing a revolution. This is the discipline of making images using computational techniques rather than optical ones. Its best known breakthrough is the ability to record high resolution images and movies using a single pixel.
As an alternative to conventional multi-pixel cameras, single-pixel cameras enable images to be recorded using a single detector that measures the correlations between the scene and a set of patterns. However, to fully sample a scene in this way requires at least the same number of correlation measurements as there are pixels in the reconstructed image. Therefore single-pixel imaging systems typically exhibit low frame-rates. To mitigate this, a range of compressive sensing techniques have been developed which rely on a priori knowledge of the scene to reconstruct images from an under-sampled set of measurements. In this work we take a different approach and adopt a strategy inspired by the foveated vision systems found in the animal kingdom - a framework that exploits the spatio-temporal redundancy present in many dynamic scenes. In our single-pixel imaging system a high-resolution foveal region follows motion within the scene, but unlike a simple zoom, every frame delivers new spatial information from across the entire field-of-view. Using this approach we demonstrate a four-fold reduction in the time taken to record the detail of rapidly evolving features, whilst simultaneously accumulating detail of more slowly evolving regions over several consecutive frames. This tiered super-sampling technique enables the reconstruction of video streams in which both the resolution and the effective exposure-time spatially vary and adapt dynamically in response to the evolution of the scene. The methods described here can complement existing compressive sensing approaches and may be applied to enhance a variety of computational imagers that rely on sequential correlation measurements.