Abstract In this paper, a class of deterministic sensing matrices are constructed by selecting rows from Fourier matrices. These matrices have better performance in sparse recovery than random partial Fourier matrices. The coherence and restricted isometry property of these matrices are given to evaluate their capacity as compressive sensing matrices. In general, compressed sensing requires ran...

We consider a distributed compressed sensing scenario where multiple sensors observe correlated sparse signals and the sensors are connected through a network. The signal correlation is realized by a partial common support-set. For such a system, the main objective of this paper is to develop a greedy pursuit algorithm. To fulfill the objective, we develop distributed parallel pursuit algorithm...

We study the recovery conditions of weighted mixed l2/lp (0 < p ≤ 1) minimization for block sparse signal reconstruction from compressed measurements when partial block support information is available. We show that the block p-restricted isometry property (RIP) can ensure the robust recovery. Moreover, we present the sufficient and necessary condition for the recovery by using weighted block p...

We present, for the isospectral family of oscillator Hamiltonians, a systematic procedure for constructing raising and lowering operators satisfying any prescribed 'distorted' Heisenberg algebra (including the q-generalization). This is done by means of an operator transformation implemented by a shift operator. The latter is obtained by solving an appropriate partial isometry condition in the ...

We shall begin by recalling some material from quadrics1.pdf, which gave the classification of hyperquadrics in R and C up to affine equivalence: CONGRUENCE OR ISOMETRY CLASSIFICATION PROBLEM. Given two affine hyperquadrics Σ1 and Σ2 in R , is there a congruence or isometry T from R to itself mapping Σ1 onto Σ2? There are two possible versions of the question. An arbitrary isometry T from R to ...

We propose a novel local isometry based dimensionality reduction method from the perspective of vector fields, which is called parallel vector field embedding (PFE). We first give a discussion on local isometry and global isometry to show the intrinsic connection between parallel vector fields and isometry. The problem of finding an isometry turns out to be equivalent to finding orthonormal par...

A classification is given for regular positions D ⊕ D ⊆ D of Jones index 4 where D = alg lim −→ M n k (C) is an even matroid algebra and where the individual sum-mands have index 2. A similar classification is obtained for positions of direct sums of 2-symmetric algebras and, in the odd case, for the positions of sums of 2-symmetric C*-algebras in matroid C*-algebras. The approach relies on an ...

A set of points W in Euclidean space is said to realize the finite group G if the isometry group of W is isomorphic to G. We show that every finite group G can be realized by a finite subset of some R n, with n < |G|. The minimum dimension of a Euclidean space in which G can be realized is called its isometry dimension. We discuss the isometry dimension of small groups and offer a number of ope...

We prove that PSL2(Z[ 1 p ]) gives the first example of groups which are not quasi-isometric to each other but have the same quasi-isometry group. Namely, PSL2(Z[ 1 p ]) and PSL2(Z[ 1 q ]) are not quasi-isometric unless p = q, and, independent of p, the quasi-isometry group of PSL2(Z[ 1 p ]) is PSL2(Q). In addition, we characterize PSL2(Z[ 1 p ]) uniquely among all finitely generated groups by ...

We study sparse recovery with structured random measurement matrices having independent, identically distributed, and uniformly bounded rows a nontrivial covariance structure. This class of arises from sampling Riesz systems generalizes partial Fourier matrices. Our main result improves the currently available results for null space restricted isometry properties such The novelty our analysis i...