Fractional Wavelet Transform Using an Unbalanced Lifting Structure
نویسندگان
چکیده
In this article, we introduce the concept of fractional wavelet transform. Using a two-channel unbalanced lifting structure it is possible to decompose a given discrete-time signal x[n] sampled with period T into two sub-signals x1[n] and x2[n] whose average sampling periods are pT and qT , respectively. Fractions p and q are rational numbers satisfying the condition: 1/p+ 1/q = 1. The low-band sub-signal x1[n] comes from [0, π/p] band and the high-band wavelet signal x2[n] comes from (π/p, π] band of the original signal x[n]. Filters used in the lifting structure are designed using the Lagrange interpolation formula. It is straightforward to extend the proposed fractional wavelet transform to two or higher dimensions in a separable or non separable manner.
منابع مشابه
Directionally Selective Fractional Wavelet Transform Using a 2-D Non-separable Unbalanced Lifting Structure
In this paper, we extend the recently introduced concept of fractional wavelet transform to obtain directional subbands of an image. Fractional wavelet decomposition is based on two-channel unbalanced lifting structures whereby it is possible to decompose a given discretetime signal x[n] sampled with period T into two sub-signals x1[n] and x2[n] whose average sampling periods are pT and qT , re...
متن کاملLifting-based Wavelet Transform with Directionally Spatial Prediction
This paper incorporates the directionally spatial prediction (DSP) into the conventional lifting-based wavelet transforms and proposes a novel, efficient and flexible lifting structure (referred as DSP-lifting hereafter). Each lifting stage can be performed at the direction, where pixels have a strong correlation, rather than always at the horizontal or vertical direction. The proposed DSP enab...
متن کاملBarbell Lifting Wavelet Transform for Highly Scalable Video Coding
This paper proposes a generic lifting technology (Barbell Lifting), where each predicting or updating signal is generated with a Barbell function instead of always a sample from single direction or bi-direction, to incorporate various motion alignment methods into temporal wavelet transform. The proposed lifting technology embraces fractional pixel motion alignment, variable block size motion a...
متن کاملFast Algorithm for Binary Field Wavelet Transform for Image Processing
Lifting scheme for the real field wavelet transform has provided a new insight into its practical implementation. This paper shows that a similar scheme can be developed for the binary field wavelet transform. In particular, by using the Euclidean algorithm, the binary filters can be decomposed into a finite sequence of simple lifting steps over the binary field. This provides an alternative me...
متن کاملShift Invariant Biorthogonal Discrete Wavelet Transform for EEG Signal Analysis
Since the discovery of the compactly supported conjugate quadrature filter (CQF) based discrete wavelet transform (DWT) (Smith & Barnwell, 1986; Daubechies, 1988), a variety of data and image processing tools have been developed. It is well known that real-valued CQFs have nonlinear phase, which may cause image blurring or spatial dislocations in multi-resolution analysis. In many applications ...
متن کامل