Compressive Sensing With Prior Information: Requirements and Probabilities of Reconstruction in ${\mbi \ell}_{\bf 1}$ -Minimization

作者: C. J. Miosso , R. von Borries , J. H. Pierluissi

DOI: 10.1109/TSP.2012.2231076

关键词:

摘要: In compressive sensing, prior information about the sparse representation's support reduces theoretical minimum number of measurements that allows perfect reconstruction. This lower bound corresponds to ideal reconstruction procedure based on ${\ell_0}$ -minimization, which is not practical for most real-life signals. this paper, we show type also improves probability from limited linear when using more ${\ell_1}$ -minimization procedure, same considered stochastic signal. order prove result, present necessary and sufficient conditions signal by information. We then attaining these increases with locations in set, obtain expression final under specific conditions. Our results are compared empirical probabilities obtained Monte Carlo simulations. Finally, numerical reconstructions without information, as well a simulation illustrate how can be used improve reconstruction, example, context dynamic magnetic resonance imaging.

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