Wavelet transform through basic operations such as scaling and translation, Realize the multi-scale decomposition and reconstruction of the signal, Thus, to a great extent Fourier Many problems caused by transformation. Wavelet analysis and Fourier Transform compared to, Wavelet transform is a local transform in spatial domain and frequency domain, Therefore, information can be effectively extracted from the signal. Wavelet analysis is a difficult branch, Users use wavelet transform, Can achieve image compression, Decomposition and reconstruction of vibration signal, Therefore, it is widely used in practical engineering. This chapter will focus on the application of wavelet in image analysis. Image compression in image processing 、 classification 、 Identification and diagnosis, Remove noise, etc. Filtering in signal analysis 、 De noise 、 Compress 、 Deliver, etc.
Wavelet analysis is widely used in many fields, In Mathematics, It has been used in numerical analysis 、 Construct a fast numerical method 、 Curve and surface construction 、 Solving differential equations 、 Cybernetics, etc. 1974 year, French engineers J.Morlet Firstly, the concept of wavelet transform is proposed ,1986 Famous mathematician Y.Meyer Accidentally construct a real wavelet base, And with S.Mallat A multi-scale analysis method for constructing wavelet bases is established, Wavelet analysis began to flourish.