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1On the Effective Measure of Dimension in the Analysis Cosparse Model
"... Abstract—Many applications have benefited remarkably from lowdimensional models in the recent decade. The fact that many signals, though high dimensional, are intrinsically low dimensional has given the possibility to recover them stably from a relatively small number of their measurements. For exa ..."
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Abstract—Many applications have benefited remarkably from lowdimensional models in the recent decade. The fact that many signals, though high dimensional, are intrinsically low dimensional has given the possibility to recover them stably from a relatively small number of their measurements. For example, in compressed sensing with the standard (synthesis) sparsity prior and in matrix completion, the number of measurements needed is proportional (up to a logarithmic factor) to the signal’s manifold dimension. Recently, a new natural lowdimensional signal model has been proposed: the cosparse analysis prior. In the noiseless case, it is possible to recover signals from this model, using a combinatorial search, from a number of measurements proportional to the signal’s manifold