Using the notions of frame transform and of square integrable projective representation of a locally compact group G, we introduce a class of isometries (tight frame transforms) from the space of Hilbert-Schmidt operators in the carrier Hilbert space of the representation into the space of square integrable functions on the direct product group G × G. These transforms have remarkable properties...

In compressed sensing (CS) [1–3], we wish to sense a signal f ∈ RC by taking its product with a matrix Φ ∈ RN×C to obtain a measurement vector y ∈ R . We refer to the rows of Φ as the projection vectors, as measurements y correspond to projections, or inner products, of the signal f onto the rows of the matrix Φ. When N C, this acquisition scheme effectively compresses the signal f . Since in t...

This paper introduces and formalizes a frame of reference for projective relations in 3D space that can be used to model human visual perception. While in 2D space visibility information can be derived from the concept of collinearity (thus, as ternary relations), in 3D space it can be derived from coplanarity, which calls for quaternary relations. Yet, we can retain ternary relations by anchor...

In this paper we introduce the notion of J-fusion frame for a Krein space K. We prove some basic results regarding J-fusion frame. We also approximate J-fusion frame bounds of a J-fusion frame by the upper and lower bounds of the synthesis operator. Finally we provide a necessary and sufficient condition under which the image of J-fusion frame under a bounded invertible linear map is also a J-f...

The high performance, low cost, and flexibility of commodity hardware systems make them appealing for network processing applications. However, the standard software architecture of such systems imposes significant limitations. At high rates (e.g., Gigabit Ethernet) and small frame sizes (64 byte) each frame must be processed in less than 672 ns. System calls, synchronization, and memory latenc...

In a previous companion paper (Part I: A Plastic Hinge Approach), adaptive elasto-plastic analysis of space frames was discussed in the context of a plastic hinge approach. The present paper extends the concept of automatic mesh refinement to deal with accurate elasto-plastic large displacement analysis accounting for the spread of yield within structural members. This is achieved through the u...

Let {φk}1 be a frame for Hilbert space H. The purpose of this paper is to present an approximation formula of any f ∈ H by a linear combination of finitely many frame elements in the frame {φk}1 and show that the obtained approximation error depends on the bounds of frame and the convergence rate of frame coefficients of f as well as the relation among frame elements.

LetM be an n-dimensional Riemannian manifold. ThenM is a differentiable manifold with a smoothly varying inner product 〈, 〉x on each tangent space TxM . An orthonormal frame at the point x ∈ M is an orthonormal basis {e1, . . . , en} of the tangent space TxM . The set of orthonormal frames at each point is isomorphic to the Lie group O(n), and the set of orthonormal frames on M forms a principa...