A system for reconstructing a space-time volume from a coded image, comprising: an image sensor (316, 416) that outputs the coded image; and at least one processor that: causes a projection of the space-time volume to be captured by the image sensor (316, 416) in a single image in accordance with a coded shutter function, the coded shutter function defining how pixels of the image sensor are exposed during the sensor integration time to capture the single image, thereby generating the coded image; receives the coded image; and performs a reconstruction process on the coded image to reconstruct the full space-time volume being captured in the single image, wherein the reconstruction process includes, for each spatial location in the coded image, performing the reconstruction process on a patch of pixels forming a neighbourhood around the spatial location to produce a set of spatially overlapping space-time volume patches, wherein the reconstruction process is based on the equation I=SDα being in matrix form, wherein I represents the patch of pixels of the coded image, S represents the coded shutter function, D is an over-complete dictionary representing a basis in which the space-time volume patch is sparse, and α is a sparse representation of the space-time volume patch, and wherein the reconstruction process further includes averaging the spatially overlapping space-time volume patches to obtain the full space-time volume. an image sensor (316, 416) that outputs the coded image; and at least one processor that: causes a projection of the space-time volume to be captured by the image sensor (316, 416) in a single image in accordance with a coded shutter function, the coded shutter function defining how pixels of the image sensor are exposed during the sensor integration time to capture the single image, thereby generating the coded image; receives the coded image; and performs a reconstruction process on the coded image to reconstruct the full space-time volume being captured in the single image, causes a projection of the space-time volume to be captured by the image sensor (316, 416) in a single image in accordance with a coded shutter function, the coded shutter function defining how pixels of the image sensor are exposed during the sensor integration time to capture the single image, thereby generating the coded image; receives the coded image; and performs a reconstruction process on the coded image to reconstruct the full space-time volume being captured in the single image, wherein the reconstruction process includes, for each spatial location in the coded image, performing the reconstruction process on a patch of pixels forming a neighbourhood around the spatial location to produce a set of spatially overlapping space-time volume patches, wherein the reconstruction process is based on the equation I=SDα being in matrix form, wherein I represents the patch of pixels of the coded image, S represents the coded shutter function, D is an over-complete dictionary representing a basis in which the space-time volume patch is sparse, and α is a sparse representation of the space-time volume patch, and wherein the reconstruction process further includes averaging the spatially overlapping space-time volume patches to obtain the full space-time volume.