Construction Of Shearlet Of A Kind Of Trigonometric Function And Image Processing

We can’t obtain good results with classic wavelet in the treatment of high dimensional problems. So in recent years, nonclassical wavelet have been proposed to overcome the deficiency of classical wavelets. The shearlets which is discussed in this article belongs to the one kind of nonclassical wavelets. The shearlets has many advantages without orthogonality which classic wavelets have. In order to complete task of reconstruction with the function without orthogonal columns, frame theory is applied in shearlet theory comprehensively with replacing orthogonal columns with frame.The paper is structured as follows.1. A concrete shearlet frame function is put forward based on shearlet framework construction method and it is popularized with polynomial function and piecewise function.2. We use discrete images and discrete frame functions during image processing procedure. Discrete Fourier transform and fast Fourier transform are used to compute approximate reconstruction value of the images. 3. We obtain some conclusions after comparing effects of image processing. Firstly, it is more ideal to use auxiliary function. Secondly, it does’t matter that using different auxiliary functions for image processing. Thirdly, the experiment results show that if we expand the compactly support, reconstructed images are closer to the original images. Finally, there are more details and shadows in the reconstructed images, which is very important because it shows that shearlets can be used to analyze images in reflecting the defects and the dizzy light of the original images which naked eyes can’t identify. It is obvious that shearlets have better prospects of application than wavelets.Frame functions constructed in this paper only support square images, and there are some questions for rectangle images. Another question is that image processing in this paper are based on the binary images, but the effect for the non-binary images is not very ideal. It needs further research to improve.