Analysis_GAMM_2013.pdf

Recent Results on the Co-Sparse Analysis Model Michael Elad The Computer Science Department The Technion – Israel Institute of technology Haifa 32000, Israel * *Joint work with Ron Rubinstein Tomer Peleg Remi Gribonval, Sangnam Nam, Mark Plumbley, Mike Davies, Raja Giryes, Boaz Ophir, Nancy Bertin The research leading to these results has received funding from: The European Council under the European unions Seventh Framework Programme (FP/2007-2013) ERC grant Agreement ERC-SPARSE- 320649 Google Faculty Research Award Contributed Session: Mathematical Signal and Image Processing The Co-Sparse Analysis Model: Recent Results By: Michael Elad 2 Voice Signal Radar Imaging Still Image Stock Market Heart Signal ? It does not matter what is the data you are working on – if it carries information, it must have an inner structure. ? This structure = rules the data complies with. ? Signal/image processing relies on exploiting these “rules” by adopting models. ? A model = mathematical construction describing the properties of the signal. ? In the past decade, sparsity-based models has been drawing major attention. Informative Data ? Inner Structure CT MRI Traffic info The Co-Sparse Analysis Model: Recent Results By: Michael Elad 3 Sparsity-Based Models Synthesis Analysis Sparsity and Redundancy can be Practiced in (at least) two different ways Well … now we know better !! The two are VERY DIFFERENT The attention to sparsity-based models has been given mostly to the synthesis option, leaving the analysis almost untouched. For a long-while these two options were confused, even considered to be (near)- equivalent. The co-sparse analysis model is a very appealing alternative to the