1、附录 B Wavelet transform in image processing in simulation and Application 1, task significance In the traditional analysis of signal in frequency domain, is completely unfolded, does not contain any time frequency information, which for some applications it is appropriate, because the frequency of th
2、e signal to its information is very important. But its discarded time information may be possible for some applications also is very important, so the analysis of the promotion, put forward a lot of time domain and frequency domain information signal analysis methods, such as short Fourier transform
3、, Gabor transform, time-frequency analysis, wavelet transform. Wavelet analysis overcomes the STFT in a single resolution on the defect, has the characteristics of multi-resolution analysis, which has been widely applied in image processing. The traditional signal theory, is built on the basis of th
4、e analysis of Fourier, Fourier transform is a kind of global change, it has some limitations. In practical application, the people start to Fourier transform are improved, thus resulting in wavelet analysis. Wavelet analysis is a new branch of mathematics, it is a universal function, Fourier analysi
5、s, harmonic analysis, numerical analysis of the most perfect crystalline； in the fields of application, especially in signal processing, image processing, speech processing and nonlinear science domain, it is considered to be the Fourier analysis after another effective when frequency analysis metho
6、d. Wavelet transform and Fourier transform, is a time and frequency domain of the local transform which can effectively extracted from the signal information, through dilation and shift operation function to function or signal multiscale analysis ( Multiscale Analysis ), to solve the Fourier transfo
7、rm can not solve many difficult problems Wavelet transform is a rapid development and more popular signal analysis method, the image processing is a very important application, including image compression, image denoising, image fusion, image decomposition, image enhancement. Wavelet analysis is the
8、 analysis method of thinking in the development and continuation. In addition to continuous wavelet, discrete wavelet transform ( CWT ) ( DWT ), and the wavelet packet ( Wavelet Packet ) and multidimensional wavelet Wavelet analysis in image processing applications are very important, including imag
9、e compression, image denoising, image fusion, image decomposition, image enhancement. Wavelet transform is a new transform analysis method, it has inherited and developed the STFT localization of thought, and also overcomes the window size does not vary with frequency and other shortcomings, to prov
10、ide a frequency changing with time frequency window, is a time-frequency signal analysis and processing the ideal tool. It is mainly characterized by transform can highlight some aspects of characteristics, therefore, the wavelet transform in many areas have been successfully applied, especially wav
11、elet transform discrete digital algorithm has been widely used in many of the problems of the transformation research. Since then, the wavelet transform is more and more the introduction of peoples attention, its application fields more and more widely. 2, problem overview ( a ) the application of w
12、avelet analysis and development The application of wavelet analysis and wavelet analysis theory to work closely together. Now, it has been in the information technology industry has made the achievement attract peoples attention. Electronic information technology is the six new and high technology a
13、n important field, which is an important aspect of image and signal processing. Nowadays, signal processing has become an important part of the work of contemporary science and technology, the purpose of signal processing is: accurate analysis, diagnosis, coding and quantization, fast transmission o
14、r storage, accurately reconstruct ( or return ). From a mathematical perspective, signal and image processing can be unified as a letter Course number processing ( image can be viewed as a two-dimensional signal ), the wavelet analysis of the many analysis for many applications, can be attributed to
15、 the signal processing problems. Now, for its properties with time stable signal ( stationary random process ), an ideal tool in processing is still a Fourier analysis. But in the practical application of the vast majority of signal is unstable ( non stationary random process ), and is especially su
16、itable for the unstable signal wavelet analysis tool is. In fact the wavelet analysis applied field is very extensive, it includes many disciplines: mathematics； signal analysis, image processing； quantum mechanics, theoretical physics； military electronic warfare and weapons computer intelligent； c
17、lassification and recognition； music and language artificial synthesis； medical imaging and diagnosis； seismic data processing； mechanical the fault diagnosis and so on； for example, in mathematics, it has been used in numerical analysis, structure, fast numerical method of curve and surface structu
18、re, solving differential equations, control theory. In signal analysis, noise filtering, compression, transmission and so on. In the image processing of the image compression, classification, identification and diagnosis, such as the decontamination. In medical imaging, the reduction of B ultrasound
19、, CT nuclear magnetic resonance imaging time, improve the resolution (1) application of wavelet analysis in signal and image compression wavelet analysis is an important application of the. It is characterized by high compression ratio, compression speed, the compressed signal can be maintained and
20、image feature invariant, and the transfer of anti interference. The compression method based on wavelet analysis, comparative success of wavelet packet best base method, wavelet texture model method, wavelet transform Zerotree compression, wavelet transform vector compression. (2) the wavelet in the
21、 signal analysis are widely used. It can be used for boundary processing and filtering, time-frequency analysis, signal-noise separation and extraction of weak signal, fractal index, signal recognition and diagnosis as well as the multi-scale edge detection. In conclusion, because wavelet has low entropy, multi-resolution, decorrelation, selected medium characteristics such as flexibility, the theory of wavelet in denoising fields by many scholars, and obtained good results. But how to take certain technology to eliminate image noise while preserving image detail is an important
