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We address the problem of super-resolution-obtaining high-resolution images and videos from multiple low-resolution inputs. The increased resolution can be in spatial or temporal dimensions, or even in both. We present a unified framework which uses a generative model of the imaging process and can address spatial super-resolution, space-time super-resolution, image deconvolution, single-image expansion, removal of noise, and image restoration. We model a high-resolution image or video as a Markov random field and use maximum a posteriori estimate as the final solution using graph-cut optimization technique. We derive insights into what super-resolution magnification factors are possible and the conditions necessary for super-resolution. We demonstrate spatial super-resolution reconstruction results with magnifications higher than predicted limits of magnification. We also formulate a scheme for selective super-resolution reconstruction of videos to obtain simultaneous increase of resolutions in both spatial and temporal directions. We show that it is possible to achieve space-time magnification factors beyond what has been suggested in the literature by selectively applying super-resolution constraints. We present results on both synthetic and real input sequences.