Research On Dual-tree Complex Wavelet For Image Denoising And Edge Detection

In the age of digital information,digital image has been widely applied in many fields of our life.As a key technology of the age of digital information,digital image processing technology plays a significant role in human life.Among the digital image processing technology,image denoising technology and edge detection technology are important research subjects.During the procedure of image acquisition and transmission,the image is always disturbed due to the noise,which is caused by the external environment factor and the digital image equipments own factor.Image quality will be decreased.The edge of image is one of the important features of image.It reflects the shape and structure of subjects in the image and provides the research foundation for the subsequent image analysis and image understanding.During the edge detection processing,since the existence of noise,the detected edge image will be affected.The edge of image will be disconnected and unclear,and there also exists pseudo edge in the edge image.Therefore,retaining the edge information of image simultaneously during the noise removal and detecting clear,accurate edge are the objectives of image denoising and edge detection,which have important theoretical significance and practical application value.Multi-scale transform possesses excellent time-frequency characteristic and it can achieve the sparse representation of signal.It has received widespread attention.In the fields of image denoising and edge detection,multi-scale transform also achieved good research performance.The wavelet transform is a typical example for the multi-scale transform.The wavelet transform is widely applied in the fields of image denoising,image segmentation,image coding.etc.However,there still exists some limitation.Since there exists down-sampling during the processing,the wavelet transform doesn't possess the property of shift-invariance.Furthermore,the directional selectivity of wavelet transform is poor.It can only provide the detail information of horizontal,vertical and diagonal orientation,which is to the disadvantage of capturing the directional information of image.The dual-tree complex wavelet transform is proposed which solves the above problems effectively.The dual-tree complex wavelet transform inherits the excellent characteristic of wavelet transform,and it also possesses the property of shift-invariance and good directional selectivity.The dual-tree complex wavelet transform can achieve the sparse representation better.In this paper,the dual-tree complex wavelet transform is the main research content and the application of dual-tree complex wavelet transform in the fields of image denoising and edge detection is researched.The main research content is arranged as follows;The basic theories of image denoising are introduced in this paper,and then we do research and analysis on the conventional image denoising methods and the threshold methods based on wavelet transform.Since the wavelet transform doesn't possess the property of shift-invariance and its directional selectivity is poor,the dual-tree complex wavelet transform which can solve these problems of wavelet transform is researched in this paper.Aiming at the problem of that the edge information of image cannot be well retained simultaneously during the noise removal,the non-local means algorithm of dual-tree complex wavelet transform for image denosing is proposed which takes the advantage of the excellent characteristic of dual-tree complex wavelet transform.The experimental results and evaluation index verify the validity of the proposed method.Then,the correlation model of wavelet coefficients is researched.Considering the inter-scale correlation of wavelet coefficients,the bivariate model which describes the inter-scale correlation of wavelet coefficients is studied.An image denoising method based on dual-tree complex wavelet transform and bivariate model is proposed.The proposed method makes full use of the difference of inter-scale correlation between the wavelet coefficients and noise coefficients.The original coefficients are estimated through the maximum a posteriori estimation theory according to the priori knowledge of wavelet coefficients.The proposed method can achieve the suppression of noise effectively.Finally,the basic theories of image edge detection are researched.Aiming at the problem of that the edge cannot be detected effectively under the noise interference,an image edge detection method based on dual-tree complex wavelet transform is put forward.The proposed method can detect clear and integral edge and suppress the noise simultaneously.