In It's stunning and quite amazingly rich and no ... it's not your father's signal processing, we highlighted how the reconstruction of images could take full advantages of advanced Matrix Factorization. Then it was about TILT, Cable and I have since played with the low rank solvers to provide some entertaining (and more serious) examples, but TILT is back again in the spotlight. This time it is used on top of different regularization in order to enable superresolution. The idea being that as Moore's law continues, our TV screens are getting bigger, with higher resolution and we want to either have better cameras or enlarge/digitally upsample the current set of movies in the Hollywood studios databanks. I still wonder how a TILT implementation could be applied random imagers. Without further due, here is the paper and attendant implementation.
Super-resolution via transform-invariant group-sparse regularization by Carlos Fernandez-Granda and Emmanuel Candès.
We present a framework to super-resolve planar regions found in urban scenes and other man-made environments by taking into account their 3D geometry. Such regions have highly structured straight edges, but this prior is challenging to exploit due to deformations induced by the projection onto the imaging plane. Our method factors out such deformations by using recently developed tools based on convex optimization to learn a transform that maps the image to a domain where its gradient has a simple group-sparse structure. This allows to obtain a novel convex regularizer that enforces global consistency constraints between the edges of the image. Computational experiments with real images show that this data-driven approach to the design of regularizers promoting transform-invariant group sparsity is very effective at high super-resolution factors. We view our approach as complementary to most recent superresolution methods, which tend to focus on hallucinating high-frequency textures.
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