We provide explicit constructions of particularly convenient dual pairs of Gabor frames. We prove that arbitrary polynomials restricted to sufficiently large intervals will generate Gabor frames, at least for small modulation parameters. Unfortunately, no similar function can generate a dual Gabor frame, but we prove that almost any such frame has a dual generated by a B-spline. Finally, for fr...

Weighted and controlled frames have been introduced recently to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper we develop systematically these notions, including their mutual relationship. We will show that controlled frames are equivalent to standard frames and so this concept gives a generalized way to check the frame condition, while ...

The performance of a balanced, nonseparable orthogonal multiwavelet for edge detection is analized. We present two alternative methods to meet this objective: in the first one the normed fine detail coefficients of the multiwavelet transform are thresholded, in the other, we adapt the modulus maxima algorithm to nonseparable multiwavelets. Results are highly satisfactory.

2 Multiwavelets In this paper the efficient implementation of discrete multiwavelet transforms is examined. These rransforms can be used for image coding. The presented architecture is based on lattice structures and computationally efficient CORDICbased p-rotations. An exemplary VLSI-implementation for a multiwavelet-based lapped orthogonal transform is presented.

We use several fundamental results which characterize frames for a Hilbert space to give natural generalizations of Hilbert space frames to general Banach spaces. However, we will see that all of these natural generalizations (as well as the currently used generalizations) are equivalent to properties already extensively developed in Banach space theory. We show that the dilation characterizati...