‎we present an application of the dual gabor frames to image‎ ‎processing‎. ‎our algorithm is based on finding some dual gabor‎ ‎frame generators which reconstructs accurately the elements of the‎ ‎underlying hilbert space‎. ‎the advantages of these duals‎ ‎constructed by a polynomial of gabor frame generators are compared‎ ‎with their canonical dual‎.

In this paper, we introduce frames generated by double sequences (d-frame) in Hilbert spaces and describe some of their properties. Furthermore, discuss frame operators, alternate dual stability for d-frames.

in this paper, g-dual function-valued frames in l2(0;1) are in-troduced. we can achieve more reconstruction formulas to ob-tain signals in l2(0;1) by applying g-dual function-valued framesin l2(0;1).

We show that there exists a frame wavelet ψ with fast decay in the time domain and compact support in the frequency domain generating a wavelet system whose canonical dual frame cannot be generated by an arbitrary number of generators. On the other hand, there exists infinitely many alternate duals of ψ generated by a single function. Our argument closes a gap in the original proof of this fact...

A dimension invariance property of finite frames of translates and Gabor frames is discussed. Under appropriate support conditions among the frame and dual frame generating functions, we show that a pair of dual frames evaluated in a given space remains a valid dual set if they are naturally embedded in the underlying space of almost arbitrarily enlarged dimension. Consequently, the evaluation ...

Hilbert frames theory have been extended to frames in Hilbert $C^*$-modules. The paper introduces equivalent $*$-frames and presents ordinary duals of a constructed $*$-frame by an adjointable and invertible operator. Also, some necessary and sufficient conditions are studied such that $*$-frames and ordinary duals or operator duals of another $*$-frames are equivalent under these conditions. W...

in this paper we introduce and study besselian $g$-frames. we show that the kernel of associated synthesis operator for a besselian $g$-frame is finite dimensional. we also introduce $alpha$-dual of a $g$-frame and we get some results when we use the hilbert-schmidt norm for the members of a $g$-frame in a finite dimensional hilbert space.

‎We present an application of the dual Gabor frames to image‎ ‎processing‎. ‎Our algorithm is based on finding some dual Gabor‎ ‎frame generators which reconstructs accurately the elements of the‎ ‎underlying Hilbert space‎. ‎The advantages of these duals‎ ‎constructed by a polynomial of Gabor frame generators are compared‎ ‎with their canonical dual‎.

in this paper, we give a necessary condition for function in l^2with its dual to generate a dual shearlet tight frame with respect to admissibility.

Fusion frames, and, more generally, operator-valued frame sequences are generalizations of classical frames, which are today a standard notion when redundant, yet stable sequences are required. However, the question of stability of duals with respect to perturbations has not been satisfactorily answered. In this paper, we quantitatively measure this stability by considering the associated devia...