A Nullspace Based L1 Minimizing Kalman Filter Approach to Sparse CS Reconstruction

Konferenz: EUSAR 2016 - 11th European Conference on Synthetic Aperture Radar
06.06.2016 - 09.06.2016 in Hamburg, Germany

Tagungsband: EUSAR 2016

Seiten: 5Sprache: EnglischTyp: PDF

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Loffeld, Otmar; Seel, Alexander; Heredia Conde, Miguel (Center for Sensorsystems, University of Siegen, Germany)
Wang, Ling (Key Lab. of Radar Imaging and Microwave Photonics, Nanjing University of Aeronautics and Astronautics, China)

This paper describes a recursive L1-minimizing approach to CS reconstruction by Kalman filtering. We consider the L1-norm as an explicit constraint, formulated as a nonlinear observation of the state to be estimated. Interpreting a sparse vector to be estimated as a state which is observed from erroneous (undersampled) measurements we can address time- and space-variant sparsity, any kind of a priori information and also easily address nonstationary error influences in the measurements available. Inherently in our approach we move slightly away from the classical RIP-based approaches to a more intuitive understanding of the structure of the nullspace which is implicitly related to the well understood engineering concepts of deterministic and stochastic observability in estimation theory