This paper is a tutorial on Grobner bases and a survey on the applications of Grobner bases
in the broad field of signals and systems. A reasonably detailed review is given of several …

An intrinsic M-channel lifting factorization of perfect reconstruction filter banks (PRFBs) is
presented as an extension of Sweldens' conventional two-channel lifting scheme. Given a …

Symmetric extension is explored as a means for constructing nonexpansive reversible
integer-to-integer (ITI) wavelet transforms for finite-length signals. Two families of reversible …

The traditional image enhancement algorithms enhance noise signal in image while they
enhance image, which leads to the de-scent of information entropy. Designing image …

针对传统小波变换过程复杂的缺点和SPIHT 算法编码过程重复运算, 存储量大的问题,
提出了基于提升方案快速SPIHT 的压缩方法. 该方法采用提升方案弥补传统小波变换的不足 …

Group lifting structures are introduced to provide an algebraic framework for studying lifting
factorizations of two-channel perfect reconstruction finite-impulse-response (FIR) filter …

This paper deals with the problem of multispectral image compression. In particular, we
propose to substitute the built-in JPEG 2000 wavelet transform by an adequate …

The current widely used edge detection algorithm have Sobel, Roberts, Laplacian etc. The
core idea of these algorithms is that the edge points correspond to the local maximal points …

现有Lifting 分解(Lifting Factorization, LF) 算法不能在较短时间内求解出较长离散小波变换(
Discrete Wavelet Transform, DWT) 滤波器组的所有数值稳定LF, 更无法计算最优LF. 在LF …

This paper introduces some properties of symmetric Laurent polynomials, and then extends
Euclidean algorithm to symmetric Laurent polynomials. The new results are used to …