| Fourier transform and Wavelet transform are important tools for signal processing. Fourier transform can convert the signal from the spatial-domain to the frequency-domain, and wavelet transform can not only analyze in the frequency-domain but retain time information in the spatial-domain. The good result can be achieved in the one-dimensional signal processing by Wavelet transform, but in the two-dimensional signal processing like digital image processing, it cannot perform its excellent properties.Therefore, Multiscale Geometric Analysis appeared. MGA achieves good results in two-dimensional or higher dimensional signal processing, it not only inherits the advantages of Wavelet but also solves the Wavelet directional limited shortcomings. Through a variety of multi-scale geometric analysis tool for development, the latest tool is Shearlet transform. Shearlet transform can effectively approximate the image,but also has “sparse” nature, and its simple mathematical structure makes it become a hot area of MGA.This paper depth studies the continuous Shearlet transform, discrete Shearlet transform frame property of Shearlet and realize Cone-Adapted Shearlet transform. This method is a non-subsample arithmetic base on Fourier transform, by constructing window function to filter original image in order to achieve multi-scale, multi-directional decomposition purpose.On the basis of Cone-Adapted Shearlet Transform, this paper presents a scanned document image skew estimation and correction algorithm. Main components of Chinese Characters with horizontal,vertical trend, in which horizontal trend is more obvious, utilizing the directional and localized property, to detect the angle of inclination of complex document image, then tilt correction.Shearlet transform can be better used for image denoising because of its multi-scales and multi-directional property. This paper presents an image denoising method based on the threshold by Shearlet transform, and achieved good results. |
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