Super-Resolution with Structured Motion

We consider the limits of super-resolution using imaging constraints. Due to various theoretical and practical limitations, reconstruction-based methods have been largely restricted to small increases in resolution. In addition, motion-blur is usually seen as a nuisance that impedes super-resolution. We show that by using high-precision motion information, sparse image priors, and convex optimization, it is possible to increase resolution by large factors. A key operation in super-resolution is deconvolution with a box. In general, convolution with a box is not invertible. However, we obtain perfect reconstructions of sparse signals using convex optimization. We also show that motion blur can be helpful for super-resolution. We demonstrate that using pseudo-random motion it is possible to reconstruct a high-resolution target using a single low-resolution image. We present numerical experiments with simulated data and results with real data captured by a camera mounted on a computer-controlled stage.