Generalized wavelet frames

Similar generalized frames

Generalized frames are an extension of frames in Hilbert  spaces and  Hilbert $C^*$-modules. In this paper, the concept ''Similar" for modular $g$-frames is introduced and all of operator duals (ordinary duals) of similar $g$-frames with respect to each other are characterized. Also, an operator dual of a given $g$-frame is studied where $g$-frame is constructed by a primary $g$-frame and an or...

Learning Steerable Wavelet Frames

We present a functional framework for the adaptive design of dictionaries where the invariance to translation, dilation, and rotation is built upfront into the primary representation space. Our key idea is to build an invariant signal representation prior to the learning stage. By doing so, we focus our effort on adapting the dictionary to the distinctive features of the signal, rather than to ...

Density of Wavelet Frames

Density conditions for wavelet systems with arbitrary sampling points to be frames are studied. We show that for a wavelet system generated by admissible functions and irregular affine lattices to be a frame, the sampling points must have a positive lower Beurling density. The same is true for wavelet systems with arbitrary sampling points and nice generating functions.

Generalized Frames in Hilbert Spaces

Wavelet-type frames and wavelet-type bases

The concepts of basis and frame are studied in the classical literature of functional analysis, Fourier analysis, and wavelet theory in a wide range. In this paper, we consider an operator-theoretic approach to discrete frame theory on a separable Hilbert space. For this purpose, we define a special type of frames and bases, called wavelet-type frames and wavelet-type bases, obtained by acting ...