The application of the wavelet transform in image processing is most frequently based on a separable transform. Lines and columns in an image are treated independently and the basis functions are simply products of corresponding onedimensional functions. Such a method keeps simplicity in design and computation. In this paper, a new two-dimensional approach is proposed, which retains the simplic...

the article introduces cyclic dilation groups and finite affine groups for prime integers, and  as an application of this theory it presents a unified group theoretical approach for the  cyclic wavelet transform (cwt) of prime dimensional periodic signals.

Abstract— In this paper we propose an effective, robust and imperceptible video watermarking algorithm by applying DWT (Discrete Wavelet transform) on video frames. The video frames will be first decomposed using DWT and the binary watermark will be embedded in the wavelet coefficients. The experimental results demonstrate that the propose algorithm can produce watermarked contents in good visu...

The construction of wavelet bases and frames on the Vilenkin group Gp is studied. Wavelet systems consisting functions that are compactly supported band-limited at same time our interest. A complete description all refinable providing such given.

Here we present a method of constructing steerable wavelet frames in L2(R) that generalizes and unifies previous approaches, including Simoncelli’s pyramid and Riesz wavelets. The motivation for steerable wavelets is the need to more accurately account for the orientation of data. Such wavelets can be constructed by decomposing an isotropic mother wavelet into a finite collection of oriented mo...

Finite normalized tight frames are interesting because they provide decompositions in applications and some physical interpretations. In this article, we give a recursive method for constructing them.

A wavelet-based spatially scalable video coding scheme with in-band prediction is investigated. The wavelet decomposition of the video frames is followed by the computation of a blockwise motion compensated prediction for the individual subbands. The shift-invariant overcomplete wavelet transform is exploited to obtain half-pixel motion vector accuracy without the need of interpolation. JPEG 20...

This paper surveys the progress made on pairwise orthogonal wavelet frames and comments on the construction methods. There are a few known constructions based on the unitary extension principle, a paraunitary matrix and a given modulation matrix. A polyphase matrix based construction method has been presented which satisfies the condition of unitary extension principle yielding pairwise orthogo...

An important tool for the construction of tight wavelet frames on local fields of positive characteristic with the help of unitary extension principles was presented by Shah and Debnath [Tight wavelet frames on local fields, Analysis, 33 (2013), 293–307]. In this paper, we continue the study based on the extension principles and give an explicit construction of a class of tight framelet packets...