A recently designed hyperspectral imaging device enables multiplexed acquisition of an entire data volume in a single snapshot thanks to monolithically-integrated spectral filters. Such an agile imaging technique comes at the cost of a reduced spatia
l resolution and the need for a demosaicing procedure on its interleaved data. In this work, we address both issues and propose an approach inspired by recent developments in compressed sensing and analysis sparse models. We formulate our superresolution and demosaicing task as a 3-D generalized inpainting problem. Interestingly, the target spatial resolution can be adjusted for mitigating the compression level of our sensing. The reconstruction procedure uses a fast greedy method called Pseudo-inverse IHT. We also show on simulations that a random arrangement of the spectral filters on the sensor is preferable to regular mosaic layout as it improves the quality of the reconstruction. The efficiency of our technique is demonstrated through numerical experiments on both synthetic and real data as acquired by the snapshot imager.
The implicit objective of the biennial international - Traveling Workshop on Interactions between Sparse models and Technology (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific ora
l/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in The Arsenal building within walking distance of both hotels and town center. iTWIST14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the sparsity paradigm: Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? Whats next?; Sparse machine learning and inference.
This paper studies the effect of discretizing the parametrization of a dictionary used for Matching Pursuit decompositions of signals. Our approach relies on viewing the continuously parametrized dictionary as an embedded manifold in the signal space
on which the tools of differential (Riemannian) geometry can be applied. The main contribution of this paper is twofold. First, we prove that if a discrete dictionary reaches a minimal density criterion, then the corresponding discrete MP (dMP) is equivalent in terms of convergence to a weakened hypothetical continuous MP. Interestingly, the corresponding weakness factor depends on a density measure of the discrete dictionary. Second, we show that the insertion of a simple geometric gradient ascent optimization on the atom dMP selection maintains the previous comparison but with a weakness factor at least two times closer to unity than without optimization. Finally, we present numerical experiments confirming our theoretical predictions for decomposition of signals and images on regular discretizations of dictionary parametrizations.
