Evolving generation and fast algorithms of slantlet transform and slantlet-Walsh transform

Xiuqiao Xiang and Baochang Shi

Applied Mathematics and Computation, 2015, vol. 269, issue C, 731-743

Abstract: The recently developed slantlet transform (SLT for short) is a wavelet with two zero moments, which can achieve a better balance between the time domain localization and smoothness. Due to its excellent characteristics, SLT is expected to be widely used in the information science fields such as compression and denoising of various signals. However, SLT without the in-place algorithm is not suitable for the parallel implementation, and the matrix formation and algorithm design of SLT lack universality, either. To address these issues, we present a new method for generating SLT recursively from the perspective of matrix rather than wavelet, by utilizing the basic techniques of bisection evolution, including so called Haar copy, Walsh mutation, slant mutation and slantlet mutation techniques. Meanwhile, we obtain a new orthogonal transform named as the slantlet-Walsh (SLW for short) transform, design the in-place fast algorithms of SLT and SLW transforms with the symmetry structure, which are very suitable for the parallel computing. In addition, the proposed scheme is clear and easy to be extended, we may take other copy means or select other mutation parameter value to generate new orthogonal matrices with required properties that may have special application value in some fields. As validated in our experiment, the proposed SLT is well-suited to deal with piecewise linear signal in comparison with transforms such as Haar, Walsh, Slant, Slant Haar, SLW transforms and DCT.

Keywords: Slantlet transform; Slantlet-Walsh transform; Mutation; Fast algorithm; Signal processing (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300315010164
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:269:y:2015:i:c:p:731-743

DOI: 10.1016/j.amc.2015.07.094

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().