Comparison of fast discrete wavelet transform algorithms

1 Introduction 1 With the development of the application of wavelet transform (WT), the speed of wavelet transform as a hot issue has been put forward. Fast algorithms of wavelet transform have been studied by many scholars. The Mallat pyramid algorithm put forward by Mallat, as the earliest one in this category, greatly reduces the arithmetic complexity of WT, and plays an important role in the theoretical research of the theory of wavelets. Since its coming into being, various fast algori…

Comparison of fast discrete wavelet transform algorithms

This paper presents an analysis on and experimental comparison of several typical fast algorithms for discrete wavelet transform (DWT) and their implementation in image compression, particularly the Mallat algorithm, FFT-based algorithm, Short-length based algorithm and Lifting algorithm. The principles, structures and computational complexity of these algorithms are explored in details respectively. The results of the experiments for comparison are consistent to those simulated by MATLAB. It is found that there are limitations in the implementation of DWT. Some algorithms are workable only for special wavelet transform, lacking in generality. Above all, the speed of wavelet transform, as the governing element to the speed of image processing, is in fact the retarding factor for real-time image processing.