1. A system, comprising: one or more processors; and a memory coupled to the one or more processors and storing program instructions executable by the one or more processors to implement: accessing data representing an input image to be upsampled; for each of a plurality of potential upsampling solutions: evaluating the potential upsampling solution with respect to an objective function, wherein the objective function is dependent on a sparse derivative prior in which sparse derivative prior probabilities for one or more second derivatives of the potential upsampling solution are multiplied by sparse derivative prior probabilities for one or more first derivatives of the potential upsampling solution; identifying one of the plurality of potential upsampling solutions as an acceptable solution, dependent on said evaluating; storing the identified solution as a higher-resolution version of the input image.