Construction, Extension Of Complex Contourlet And Its Application To Image Processing

In the image Multiscale Gometric Analysis, contourlet transform is the representational one that has good characteristics of multi-resolution, localization, directionality and anisotropy. Compared with wavelet transform, it is a real sparse represenation for two-dimensional images. Since contourlet transform is capable of representing the images with the least coefficients along the image edges, it can describe the image in a better performance of the edge and texture information. However, the original contourlet transform has a certain redundancy and lacks translation invariance, it tends to have its limitation in the applications such as image processing. To overcome these shortcomings, a Nonsubsampled Complex Contourlet Transform was constructed in this paper. In addition, the concept of complex contourlet transform was expanded and we firstly proposed Complex Contourlet Packet Transform. These new transforms inherit the good characteristics of contourlet transform, and have their own property. As a result, they can represent the images more efficiently in image processing.The main contributions of this thesis are as follows:(1) Studied the basic theory of contourlet transform and its corresponding properties. Because ordinary contourlet transform has a certain redundancy and lacks translation invariance, we improved it to construct a Nonsubsampled Complex Contourlet Transform by using dual-tree complex wavelet transform and nonsubsampled directional filter banks. The new transform overcomes the shortcomings of contourlet transform and includes more direction components, so it achieves a better details representation in the course of image processing.(2) Proposed the image denoising algorithm based on the Nonsubsampled Complex Contourlet Transform We applied the Nonsubsampled Complex Contourlet Transform into image denoising and induced three main image denoising method. These methods include:algorithm based on thresholding function, algorithm based on neighbouring information and algorithm based on coefficients distribution model. Among them, algorithm based on thresholding function is simple but effective, while algorithm based on neighbouring information considers relativities between the coefficients of the same scale and the same sub-band to eliminate the noise more efficiently. Since the algorithm based on coefficients distribution model can establish accurate mathematical model, it shows better performance in image denoising than the first two methods.(3) Proposed an image enhancing algorithm based on the Nonsubsampled Complex Contourlet Transform. In order to enhance the blurry edges and preserve the clear edges, we corrected the coefficients of the Nonsubsampled Complex Contourlet Transform by using a self-adaptive enhancing operator, and applied different strategy to the different image region. The experiment result demonstrates that the image enhancing algorithm based on the Nonsubsampled Complex Contourlet Transform has greater improved enhancing effect and details representation.(4) According to the concept of complex wavelet packet, we put forward and constructed the Complex Contourlet Packet Transform by using analytic dual-tree complex wavelet packet and nonsubsampled directional filter banks. The transform has the advantages of complex contourlet transform and decomposes the high frequency part except the low frequency part, so it can preserve abundant detail information.(5) Proposed an image denoising algorithm based on the Complex Contourlet Packet Transform. Using the relativities of coefficients between different scale and different sub-band, we classified the adjacent coefficients and estimateed the bigger by the Mean Square Error method to perform image denoising efficiently. Because the Complex Contourlet Packet Transform takes the high frequency information of images into account, it can achieve very good performance of noise restraint.(6) Analyzed the speckle noise of SAR image and proposed a SAR image Despeckling algorithm based on the Complex Contourlet Packet Transform. In the paper, we adopted an optimal threshold training method to find the appropriate threshold and realized SAR image Despeckling. The experiment result shows that its equivalent number of looks ENL and edge saving index ESI excel ordinary methods. At the same time, the image details are more legible, and the vision quality is better.The theoretical research results mentioned above have already been published on the magazine of "Journal of Optoelectronics.Laser", "Acta Photonica Sinica", "Journal of Harbin Engineering" and "Journal of Dalian Maritime University" (No.200736). Some related applications have been applied in the project of "National Laboratory Fund of Underwater Intelligent Robot Technology". All the studies provide beneficial reference for the application of complex contourlet transform, and lay the positive foundations of theory and application research for the further work on Multiscale Gometric Analysis.