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This paper describes some new results on recursive l_1-minimizing by Kalmanfiltering. We consider the l_1-norm as an explicit constraint, formulated as anonlinear observation of the state to be estimated. Interpretiing a sparsevector 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 errorinfluences in the measurements available. Inherently in our approach we moveslightly away from the classical RIP-based approaches to a more intuitiveunderstanding of the structure of the nullspace which is implicitly related tothe well understood engineering concepts of deterministic and stochasticobservability in estimation theory

Some New Results on l1-Minimizing Nullspace Kalman Filtering for Remote Sensing Applications