We study the relationship between operators, orthonormal basis of subspaces and frames of subspaces (also called fusion frames) for a separable Hilbert space H. We get sufficient conditions on an orthonormal basis of subspaces E = {Ei}i∈I of a Hilbert space K and a surjective T ∈ L(K,H) in order that {T (Ei)}i∈I is a frame of subspaces with respect to a computable sequence of weights. We also o...

In this paper we give a combinatorial characterization of tight fusion frame (TFF) sequences using Littlewood-Richardson skew tableaux. The equal rank case has been solved recently by Casazza et al. [8]. Our characterization does not have this limitation. We also develop some methods for generating TFF sequences. The basic technique is a majorization principle for TFF sequences combined with sp...

We show that RIP frames, tight frames satisfying the restricted isometry property, give rise to nearly tight fusion frames which are nearly orthogonal and hence are nearly equi-isoclinic. We also show how to replace parts of the RIP frame with orthonormal sets while maintaining the restricted isometry property.

Fusion frame theory is an emerging mathematical theory that provides a natural framework for performing hierarchical data processing. A fusion frame can be regarded as a frame-like collection of subspaces in a Hilbert Communicated by Qiyu Sun. P.G.C. and A.H. were supported by NSF DMS 0704216. G.K. would like to thank the Department of Statistics at Stanford University and the Mathematics Depar...

For any fixed fusion frame, its optimal dual fusion frames for reconstruction is studied in case of erasures of subspaces. It is considered that a probability distribution of erasure of subspaces is given and that a blind reconstruction procedure is used, where the erased data are set to zero. It is proved that there are always optimal duals. Sufficient conditions for the canonical dual fusion ...

in this paper we introduce continuous $g$-bessel multipliers in hilbert spaces and investigate some of their properties. we provide some conditions under which a continuous $g$-bessel multiplier is a compact operator. also, we show the continuous dependency of continuous $g$-bessel multipliers on their parameters.

For a fusion Banach frame ({Gn, vn}, S) for a Banach space E, if ({v∗ n(E), v∗ n}, T ) is a fusion Banach frame for E∗, then ({Gn, vn}, S; {v∗ n(E), v∗ n}, T ) is called a fusion bi-Banach frame for E. It is proved that if E has an atomic decomposition, then E also has a fusion bi-Banach frame. Also, a sufficient condition for the existence of a fusion bi-Banach frame is given. Finally, a chara...

In this paper, we present a method for generating high dynamic range (HDR) video through fusion of exposure-controlled frames in a stationary video camera system. Frames captured by commercial video cameras have a limit dynamic range, even if we use auto-exposure control (AEC), and these frames often show saturation areas which may degrade the image quality. To overcome these, in the video sequ...