Sparse Geometric Super-Resolution

What is the maximum signal resolution that can be recovered from partial noisy or degraded data ? This inverse problem is a central issue, from medical to satellite imaging, from geophysical seismic to HDTV visualization of Internet videos. Increasing an image resolution is possible by taking advantage of "geometric regularities", whatever it means. Super-resolution can indeed be achieved for signals having a sparse representation which is "incoherent" relatively to the measurement system. For images and videos, it requires to construct sparse representations in redundant dictionaries of waveforms, which are adapted to geometric image structures. Signal recovery in redundant dictionaries is discussed, and applications are shown in dictionaries of bandlets for image super-resolution.