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... opposed to signal reconstruction under the erasures discussed in [11, 34, 36]. If there are positive weights {ωj}nj=1 such that {(Vj , ωj)}nj=1 forms a tight p-fusion frame as recently introduced in =-=[5]-=-, then we are able to reconstruct the erased p norms at least up to permutation. We can then reconstruct ±x from the entire set of n magnitude subspace components. In other words, we found conditions ...

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...ithout loss of generality, let us suppose that the first p norms were erased. If there are positive weights {ωj} n j=1 such that {(Vj,ωj)} n j=1 forms a tight p-fusion frame as recently introduced in =-=[5]-=-, then we are able to reconstruct the erased norms {‖PVj(x)‖} p j=1 at least up to permutations. Here, we need to verify that a certain system of algebraic equations has only finitely many solutions. ...

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...e that enable beneficial signal decomposition and synthesis. For fusion frames on Rd, whose elements have the same rank, the relations to Grassmannian designs and cubatures were fully investigated in =-=[6]-=-. While the elements of a fusion frame on Rd are not necessarily required to lie in one single Grassmannian, cubatures and designs have not yet been considered in unions of Grassmannians. The present ...

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... a set of positive semi-definite (PSD) operators. In [17], collections of orthogonal projectors were considered under the name fusion frames, and the concept of tight p-fusion frames was developed in =-=[3]-=-. In the present paper, we address the following points: (1) We first introduce the Paulsen problem in the context of generalized frames. Given a generalized frame {Tj}nj=1 whose elements have unit Hi...

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... norm ‖T ‖HS of T is induced by ‖T ‖2HS := 〈T, T 〉. We obtain lower estimates on (4) by generalizing the simplex bound as derived in [2] for orthogonal projections of equal rank and later extended in =-=[1]-=- to orthogonal projections of mixed ranks: Proposition 4.1. If {Ti}mi=1 is a collection of self-adjoint, positive semi-definite operators on Hn scaled such that ∑m i=1 trace(Ti) = n, then (5) max i6=j...

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...(v, v) = M∑ k=1 (v, vk) 2, ∀ v ∈ V. Tight frames are connected to a wide variety of problems in pure and applied mathematics and they have been studied intensively in recent years (see, for examples, =-=[1, 2, 3, 4, 9]-=- and references therein). We construct tight frames with the Hahn and Krawtchouk polynomials of several variables, and use them to construct several families of tight frames for the Euclidean spaces t...

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...v, v) = M∑ (v, vk) 2 , ∀ v ∈ V. k=1 Tight frames are connected to a wide variety of problems in pure and applied mathematics and they have been studied intensively in recent years (see, for examples, =-=[1, 2, 3, 4, 9]-=- and references therein). We construct tight frames with the Hahn and Krawtchouk polynomials of several variables, and use them to construct several families of tight frames for the Euclidean spaces t...