Frames in Hilbert bimodules are a special case of frames in Hilbert C*-modules. The paper considers A-frames and B-frames and their relationship in a Hilbert A-B-imprimitivity bimodule. Also, it is given that every frame in Hilbert spaces or Hilbert C*-modules is a semi-tight frame. A relation between A-frames and K(H_B)-frames is obtained in a Hilbert A-B-imprimitivity bimodule. Moreover, the ...

We present a design scheme to generate tight and semi-tight frames in the space of discrete-time periodic signals, which are originated from four-channel perfect reconstruction periodic filter banks. The filter banks are derived from interpolating and quasi-interpolating polynomial splines. Each filter bank comprises one linear phase low-pass filter (in most cases interpolating) and one high-pa...

In this paper, we introduce a unified theory of tight wavelet frames on non-flat domains in both continuum setting, i.e. on manifolds, and discrete setting, i.e. on graphs; discuss how fast tight wavelet frame transforms can be computed and how they can be effectively used to process graph data. We start from defining multiresolution analysis (MRA) generated by a single generator on manifolds, ...

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.

We present diverse families of tight and semi-tight frames in the space of discrete-time periodic signals, which are generated by threeand four-channel perfect reconstruction periodic filter banks. The filter banks are derived from the interpolating and quasi-interpolating polynomial and discrete splines. Each filter bank comprises one interpolating linear phase low-pass filter and one high-pas...

In This paper, we give a necessary condition for function in $L^2$ with its dual to generate a dual shearlet tight frame with respect to admissibility.

We present an efficient algorithm for image restoration from highly noised originals. The algorithm is based on diverse library of tight and semi-tight wavelet frames. Unlike majority of current denoising methods, which threshold the transform coefficients, our algorithm performs direct and inverse multiscale transforms using properly modified frame filters. No thresholding is applied. The proc...

algebraic frames are generalizations of fourier transforms on locally compact abelian groups in the sense that the family of vectors forming the frame are replaced by a family of unbounded linear functionals. the paper studies the indexing measure space of the algebraic frames; as the investigation narrows down to the class of lower semiframes, more relations are revealed between the discret...

in this paper, we characterize multiresolution analysis(mra) parseval frame multiwavelets in l^2(r^d) with matrix dilations of the form (d f )(x) = sqrt{2}f (ax), where a is an arbitrary expanding dtimes d matrix with integer coefficients, such that |deta| =2. we study a class of generalized low pass matrix filters that allow us to define (and construct) the subclass of mra tight frame multiwav...