The Research Of Image Processing Based On Shearlet Theory

Wavelet analysis is an effective tool for time-frequency analysis. It appears to solve the Fourier transform in signal analysis which can not get a better deal with the limitations of non-stationary signals. Wavelet analysis has been widely used in the field of signal processing and communications technology.Classic wavelet transform used more and more deeper in real life and field of application are increasingly being used, such as in the field of data compression, image processing, it has a successful application. It has also been a rapid development in theory. With the application of in-depth, the shortcomings of wavelet transform gradually exposed. For the singular points in high dimensional space, the sparse representation can not be good in wavelet transform. To overcome the lack of classic wavelet analysis, the researchers inspired by the non-classical methods, trying to find a variant of classic wavelet. In the nearly 10 years of time, they put forward many non-classical wavelet method, wherein the multi-scale geometric analysis MGA(Multiscale Geometric Analysis) is a kind of new high-dimensional a new high-dimensional sparse signal representation tool, which includes Ridgelet transformation, contourlet transform, curvelet transformation. Compared to the transform from the classical wavelet transform, although they can better solve the high dimensional data sparse representation problem, they can only processing one or several high dimensional singularity types, and they are barrier breakdowns in frequency space, thereby to some extent affected the sparse representation of high-dimensional data. Subsequently, the Shearlet produced to overcome the shortcomings of the previous several transformations, it has a better, simpler mathematical structure, it also has a more excellent properties in the application.Firstly it lists the basic theory of Shearlet transform, which shows that the Shearlet transform has a good theoretical significance, then proposed the improved adaptive median filtering image denoising algorithm based on Shearlet,the edge detection algorithm based on shearlet and Image fusion algorithm based on shearlet Finally, the experimental results of algorithm analysis to verify the validity of the algorithm.