The proof of non-existence for co-affine frames is extended from the one-dimensional setting [GLWW] to the case of expansive dilation matrices in Rd. The problem of identifying subspaces on which co-affine systems may admit frame-type inequalities is then considered. In the context of multiresolution analysis it is shown that frame-type inequalities may hold on certain fundamental subspaces of ...

Fusion frames are collection of subspaces which provide a redundant representation of signal spaces. They generalize classical frames by replacing frame vectors with frame subspaces. This paper considers the sparse recovery of a signal from a fusion frame. We use a block sparsity model for fusion frames and then show that sparse signals under this model can be compressively sampled and reconstr...

Let {Wi}i∈I be a (redundant) sequence of subspaces each being endowed with a weight vi, and let H be the closed linear span of the Wi’s, a composite Hilbert space. Provided that {(Wi, vi)}i∈I satisfies a certain property which controls the weighted overlaps of the subspaces, it is called a fusion frame. These systems contain conventional frames as a special case, however they go far “beyond fra...

We present a theory of finite frames for subspaces of C N. The definition of a subspace frame is given and results analogous to those from frame theory for C N are proven.

We de ne and characterize a frame-like stable decomposition for subspaces of a general separable Hilbert space. We call it pseudoframes for subspaces (PFFS). Properties of PFFS are discussed. A necessary and su cient characterization of PFFSs is provided. Analytical formulae for the construction of PFFSs are derived. Examples and applications of PFFSs are discussed.

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 ...

This paper is an investigation of shift invariant subspaces of L2(G), where G is a locally compact abelian group, or in general a local field, with a compact open subgroup. In this paper we state necessary and sufficient conditions for shifts of an element of L2(G) to be an orthonormal system or a Parseval frame. Also we show that each shift invariant subspace of L2(G) is a direct sum of princi...