This article considers constrained l1 minimization methods for the recovery of high dimensional sparse signals in three settings: noiseless, bounded error and Gaussian noise. A unified and elementary treatment is given in these noise settings for two l1 minimization methods: the Dantzig selector and l1 minimization with an l2 constraint. The results of this paper improve the existing results in...

Sixty years ago, S. B. Myers and N. E. Steenrod (Ann. of Math. 40 (1939), 400-416) showed that the isometry group of a Riemannian manifold without boundary has a stru ture of Lie group. Re ently A. V. Bagaev and N. I. Zhukova (Siberian Math. J. 48 (2007), 579-592) proved the same result for a Riemannian orbifold. In this paper, we rstly show that the isometry group of a Riemannian manifold M wi...

In the theory of compressed sensing, restricted isometry analysis has become a standard tool for studying how efficiently a measurement matrix acquires information about sparse and compressible signals. Many recovery algorithms are known to succeed when the restricted isometry constants of the sampling matrix are small. Many potential applications of compressed sensing involve a data-acquisitio...

We show that every locally compact Polish group is isomorphic to the isometry group of a proper separable metric space. This answers a question of Gao and Kechris. We also analyze the natural action of the isometry group of a separable ultrametric space on the space. This leads us to a structure theorem representing an arbitrary separable ultrametric space as a bundle with an ultrametric base a...

We establish the restricted isometry property for finite dimensional Gabor systems, that is, for families of time–frequency shifts of a randomly chosen window function. We show that the s-th order restricted isometry constant of the associated n×n Gabor synthesis matrix is small provided s ≤ c n/ log n. This improves on previous estimates that exhibit quadratic scaling of n in s. Our proof deve...

The isometry group of a compact n-dimensional hyperbolic man-ifold is known to be finite. We show that for every n ≥ 2, every finite group is realized as the full isometry group of some compact hyperbolic n-manifold. The cases n = 2 and n = 3 have been proven by Greenberg [G] and Ko-jima [K], respectively. Our proof is non constructive: it uses counting results from subgroup growth theory to sh...

Let R be an associative ring with 1 and R the multiplicative group of invertible elements of R. In the paper, subgroups of R which may be regarded as analogues of the similitude group of a non-degenerate sesquilinear reflexive form and of the isometry group of such a form are defined in an abstract way. The main result states that a unipotent abstractly defined similitude must belong to the cor...

We study the large scale geometry of the upper triangular subgroup of PSL2(Z[ 1 n ]), which arises naturally in a geometric context. We prove a quasi-isometry classification theorem and show that these groups are quasi-isometrically rigid with infinite dimensional quasi-isometry group. We generalize our results to a larger class of groups which are metabelian and are higher dimensional analogue...

We consider sub-Riemannian spaces admitting an isometry group that is maximal in the sense any linear of horizontal tangent realized by a global isometry. will show these have canonical partial connection defined on their bundle. However, unlike Riemannian case, such are not uniquely determined curvature and metric cone. Furthermore, number invariants needed to determine model with same cone ge...

We consider the non-square matrix sensing problem, under restricted isometry property (RIP) assumptions. We focus on the non-convex formulation, where any rank-r matrix X ∈ R is represented as UV , where U ∈ R and V ∈ R. In this paper, we complement recent findings on the nonconvex geometry of the analogous PSD setting [5], and show that matrix factorization does not introduce any spurious loca...