Laurent Duval just sent me the following:
Hi IgorFrom Québec City, a paper that caught my attention, a nice mix between CS and compression:Colas Schretter, David Blinder, Tim Bruylants, Peter Schelkens and Adrian Munteanu, Efficient scalable compression of sparsely sampled images, IEEE International Conference on Image Processing 2015, Quebec City, Canada, September 27-30 2015.
Thanks Laurent for the heads-up. Something is at play here but I am not sure what it is. In a way, if the CDF dictionary is complete, the initial dirac-like subsampling mask of the image requires it to be incoherent with that CDF dictionary. The L_1 recovery of these coefficients then makes sense in that framework (modulo the recent work in infinite compressive sensing) but I wonder what the EBCOT nonlinear coding does to the resulting picture.Advanced sparse sampling acquisition systems capture only scattered information from the continuous image domain. Unfortunately, conventional image encoders are not yet able to properly compress arbitrarily subsampled image data. This work introduces a system leveraging the JPEG 2000 image compression framework by enabling scalable compression of the selected image samples. Using a complete dictionary of CDF 9/7 wavelets, a minimum l1-norm compressed sensing solution is recovered which can be fed directly into the encoder, producing a bitstream that can be decoded with existing JPEG 2000-compliant implementations. Experiments on standard images with quasi-random subsampling demonstrate that the proposed system outperforms regular JPEG 2000 compression of stacked sample images and quad-tree based compression for point-clouds. We also demonstrate the robustness of the technique for images that infringe the sparsity prior of compressed sensing.
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