Sparse CS Reconstruction by Nullspace Based L1 Minimizing Kalman Filtering

This paper describes a recursive l(1)-minimizing approach to CS reconstruction by Kalman filtering. Unlike other approaches using sparsity enforcing a priory density distributions, we consider the l(1)-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 l(1)-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.