In this paper, we mainly discuss the nonuniform average sampling and reconstruction in multiply generated shift-invariant subspaces \[ V_{p,q}(\Phi_r) = \bigg\{ \sum_{k_{1} \in \mathbf{Z}} \sum_{k_{2} \mathbf{Z}^{d}} c^T(k_{1},k_{2}) \Phi_r(\,\cdot-k_{1},\,\cdot-k_{2}): (c(k_{1},k_{2}))_{(k_{1},k_{2}) \mathbf{Z} \times \big( \ell^{p,q}(\mathbf{Z} \mathbf{Z}^d) \big)^r \bigg\} \] of mixed Lebesg...

We consider a generator F 1⁄4 ðf1; y ;fNÞ for either a multi-frame or a super-frame generated under the action of a projective unitary representation for a discrete countable group. Examples of such frames include Gabor multi-frames, Gabor super-frames and frames for shift-invariant subspaces. We show that there exists a unique normalized tight multi-frame (resp. super-frame) generator C 1⁄4 ðc...

The problem of reconstructing a function from the magnitudes its frame coefficients has recently been shown to be never uniformly stable in infinite-dimensional spaces [5]. This result also holds for frames that are possibly continuous [2]. On other hand, is always finite-dimensional settings. A prominent example such phase retrieval recovery signal modulus Gabor transform. In this paper, we st...

In the more general framework ' shift invariant subspace", the paper obtains a different estimate of sampling in function subspace to our former work, by using the Frame Theory. The derived formula is easy to be calculated, and the estimate is relaxed in some shift invariant subspaces.

We analyze the structure of co-invariant subspaces for representations of the Cuntz algebras ON for N = 2, 3, . . . , N < ∞, with special attention to the representations which are associated to orthonormal and tight-frame wavelets in L (R) corresponding to scale number N .

We consider the problem of recovering fusion frame sparse signals from incomplete measurements. These signals are composed of a small number of nonzero blocks taken from a family of subspaces. First, we show that, by using a-priori knowledge of a coherence parameter associated with the angles between the subspaces, one can uniformly recover fusion frame sparse signals with a significantly reduc...

A SIC consists of N equiangular unit vectors in an N dimensional Hilbert space. The frame potential is a function of N unit vectors. It has a unique global minimum if the vectors form a SIC, and this property has been made use of in numerical searches for SICs. When the vectors form an orbit of the Heisenberg group the frame potential becomes a function of a single fiducial vector. We analytica...

Recent work on the automatic generation of frame axioms from action specifications that have complete fluent change specifications is extended to extract action invariants. An action invariant expresses a property that is preserved by all actions of that class. The extraction is achieved by combining automatically generated frame axioms and the original action axioms relativised to those states...

A notion of pseudoframes for subspaces (PFFS) is defined and characterized in a separable Hilbert space H. PFFS functions in a manner of a frame for a subspace X in H. Yet none of the pair of sequences {xn} and {x∗ n} is necessarily contained in X . This gives rise to attractive properties that center around the flexibility. A necessary and sufficient characterization of PFFSs is provided. Anal...

Finite tight frames for polynomial subspaces are constructed using monic Hahn polynomials and Krawtchouk polynomials of several variables. Based on these polynomial frames, two methods for constructing tight frames for the Euclidean spaces are designed. With r(d, n) := ( n+d−1 n ) , the first method generates, for each m ≥ n, two families of tight frames in R with r(d + 1,m) elements. The secon...