Sparse CS reconstruction by nullspace based l1 minimizing Kalman filtering
Otmar Loffeld, Alexander Seel, Miguel Heredia Conde, Ling Wang · 2016
This paper describes a recursive ℓ1-minimizing approach to CS reconstruction by Kalman filtering. Unlike other approaches using sparsity enforcing a priory density distributions, we consider the ℓ1-norm as an explicit constraint, formulated as a nonlinear observation of some state to be estimated, which we can additionally (re-)weight, either according to confidence levels or with respect to reweighted ℓ1-minimization. Inherently in our approach we move slightly away from one of 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.