What Is Wavelet Compression?

The term wavelet, as its name implies, is a small wave. The so-called "small" means that it is attenuating; and the term "wave" refers to its volatility, which is a form of oscillation with positive and negative amplitude. Compared with the Fourier transform, the wavelet transform is a localized analysis of time (space) frequency. It gradually refines the signal (function) by multi-scale through the scaling and translation operation, and finally achieves time subdivision at high frequencies and frequency subdivision at low frequencies. It can automatically adapt to the requirements of time-frequency signal analysis, so that it can focus on any details of the signal, solve the difficult problem of Fourier transform, and become a major breakthrough in scientific method since Fourier transform. Some people call the wavelet transform a "math microscope".

The wavelet function is derived from multi-resolution analysis. The basic idea is to represent the expanding function f (t) as a series of successive approximation expressions, each of which is a smoothed form of f (t) motion, and they correspond to different of

The application of wavelet analysis is closely combined with the theoretical research of wavelet analysis. It has made remarkable achievements in the field of science and technology information industry.

Wavelet analysis is a rapidly developing new field in applied mathematics and engineering. After nearly 30 years of exploration and research, an important formal system of mathematics has been established and the theoretical foundation is more solid. Compared with Fourier transform,

In fact, wavelet analysis has a wide range of applications, including: many disciplines in the field of mathematics; signal analysis,

The application prospects of wavelet analysis are as follows: ^[2]

1. The sudden points of transient signals or images often contain important fault information, such as mechanical faults, power system faults, EEG, abnormalities in ECG, location and shape of underground targets, etc., all correspond to test signals. Break point. Although these problems occur in different backgrounds, they can all be attributed to the problem of how to extract the position of the mutation point in the signal and determine its singularity (or smoothness). For images, sharply changing points usually correspond to the edge parts representing the image structure, that is, the main part of the image information. After mastering it, the basic characteristics of the image are also mastered. Therefore, the application of wavelet analysis in fault detection and multi-scale edge feature extraction of signals has a broad application prospect.

2. The combination of neural network and wavelet analysis. The combination of fractal geometry and wavelet analysis is one of the hot topics in the world. Based on the neural network intelligent processing technology, the study of the combination of fuzzy computing, evolutionary computing and neural networks, it is difficult to achieve a breakthrough without the embeddedness of wavelet theory. The research of non-linear science is calling for wavelet analysis. Perhaps non-linear wavelet analysis is an ideal tool for solving non-linear scientific problems.

3. Wavelet analysis is used to compress data or images. At present, most of them are researched on still images. For a long time, network-oriented moving image compression has mainly used discrete cosine transform (DCT) plus motion compensation (MC) as the coding technology. However, this method has two main problems: block effect and mosquito noise. Multi-scale analysis using wavelet analysis can not only overcome the above problems, but also first obtain the outline of the image on the coarse scale, and then decide whether to transmit a fine image to improve the transmission speed of the image. Therefore, researching a parallel algorithm for wavelet analysis of low-rate image compression for the network has high explorability and novelty, and also has high application value and wide application prospects.

4. The two-dimensional and high-dimensional wavelet bases currently used are mainly separable. The structure, properties, and application research of inseparable two-dimensional and high-dimensional wavelet bases are relatively complicated in theory. Perhaps the research of vector wavelet and high-dimensional wavelet can open up a new world for the application of wavelet analysis.