Orthogonal matching pursuit (OMP) is a canonical greedy algorithm for sparse signal reconstruction. When the signal of interest is block sparse, i.e., it has nonzero coefficients occurring in clusters, the block version of OMP algorithm (i.e., Block OMP) outperforms the conventional OMP. In this paper, we demonstrate that a new notion of block restricted isometry property (Block RIP), which is ...

It is consistent with the axioms of set theory that for every metric space X which is isometric to some separable Banach space or to Urysohn’s universal separable metric space U the following holds: (?)X There exists a nowhere meager subspace of X of cardinality א1 and any two nowhere meager subsets of X of cardinality א1 are almost isometric to each other. As a corollary, it is consistent that...

In compressed sensing, it is often desirable to consider signals possessing additional structure beyond sparsity. One such structured signal model – which forms the focus of this paper – is the local sparsity in levels class. This class has recently found applications in problems such as compressive imaging, multi-sensor acquisition systems and sparse regularization in inverse problems. In this...

The near-horizon geometries of the extremal Kerr black hole and certain generalizations thereof are considered. Their isometry groups are all given by SL(2,R) × U(1). The usual boundary conditions of the Kerr/CFT correspondence enhance the U(1) isometry to a Virasoro algebra. Various alternatives to these boundary conditions are discussed. Partial classifications are provided of the boundary co...

The heat kernel measure μt is constructed on GL(H), the group of invertible operators on a complex Hilbert space H. This measure is determined by an infinite dimensional Lie algebra g and a Hermitian inner product on it. The Cameron-Martin subgroup GCM is defined and its properties are discussed. In particular, there is an isometry from the Lμt -closure of holomorphic polynomials into a space H...

The smallest known three-dimensional closed orientable hyperbolic manifoldM 1 , which volume is equal to 0:94 : : :, was obtained independently by A. Fomenko and S. Matveev and by J. Weeks. It is known, that the isometry group of the manifold M 1 is isomorphic to the dihedral group ID 6 of order 12. We study the lattice of the action of the isometry group on the manifoldM 1 and obtain all orbif...

We study groups acting by length-preserving transformations on spaces equipped with asymmetric, partially-defined distance functions. We introduce a natural notion of quasi-isometry for such spaces and exhibit an extension of the Švarc-Milnor Lemma to this setting. Among the most natural examples of these spaces are finitely generated monoids and semigroups and their Cayley and Schützenberger g...