The Natural Analysis Of Shearlets And Its Application

Fourier transform is a kind of basic transformation of harmonic analysis, it’s not only an effective mathematical tool, but also it has made a wide range of applications in the field of information, control, and the computer. This is mainly due to its intuitive and mathematical perfection and the validity of the calculation. Fourier transform of the signal through a standard can accurately obtain the function of the frequency components, it also can better deal with stable and unchanging signal. It is within the scope of integration within the timeline, which means a global characteristic of the signal. But if we need to analysis the signal of local characteristics, it is not suitable for use again. We can’t get the corresponding time-frequency localization information for unsteady signal, wavelet is introduced to solve the problem.The classical wavelet transform has widely applied in the real life, the field of application is becoming more and more extensive. It was used in computer, medicine, engineering, space technology and so on and it also got skilled development in terms of theory. With the deepening of the application, the faults of wavelet transform are gradually reflected, we cannot show the sparse representation very well for higher dimensional singularity point, and we also cannot describe its singular set of geometry characteristics. People have tried to use multi-scale geometric method to solve the problem. During this process, the second generation wavelet such as the ridge wave, Qu Bo, strip wave and contour wave has produced. But they often can only deal with one or several high-dimensional singular types, and they do not have multi-scale analysis of the classical wavelet and simple small mother wavelet function. The formation of shear wave compensate for the defects of the previous two wavelets, it also has good mathematical structures as well as good applied properties. In this paper, through theoretical proof and practical test, shear wave not only has the good theoretical value, but also has far-reaching applied value.We discuss from practice to theory and from theoiy to practice in this paper. On the one hand, the experiment of image shows the geometric characteristics of shearlets; on the other hand, we explore the nature of the shearlets and compare with classical wavelet’s properties. With the discussing of the properties about shearlets, We have the feasibility of using shearlets to deal with images and specific algorithms of image processing. Through the analogy experiment, we can understand the role of shearlets in dealing with images problems.