Research On Enhancement And Interpolation Algorithms In Medical Image Processing

As an interdisciplinary field with practical value and wide application prospect, medical images processing has attracted various specialized staff in electronics, mathematics and physics to participate in its research. Medical images are characterized by large information amount, fuzziness and processing complexity. Though, owing to the fast development and application of computer graphics and image processing, the imaging quality and displaying method have been greatly improved along with the accuracy and correctness of clinical diagnosis, which not only brings the effectiveness and potential of medical imaging equipment into full play, but also improves the diagnostic and therapeutic level as well as people's health. Hence, it's of great realistic and theoretical significance to research on medical images processing.Aiming at the practical requirement in medical images processing, the dissertation focuses more on the study of algorithms. By such mathematical tools as multiscale geometric analysis and structure tensor, research is done on mammographic image enhancement, diffusion tensor image interpolation and image filtering, proper mathematical models are built based on the characteristics of the images acquired by the medical equipment, corresponding algorithm and fast implementation are presented to improve image quality, thus offering scientific references for effective diagnosis and a good foundation for further study. The main work and contributions of the dissertation are outlined as follows:1. Introduces the basic theory of multiscale geometric analysis, analyses the advantages and disadvantages of several typical transforms, such as bandelet, curvelet etc. On this basis, studies particularly contourlet transform and its features, proves that the family of contourlet basis functions in contourlet decomposition generated by biorthogonal filter bank makes a Riesz basis of L2 (R2), which further improves contourlet transform theory.2. Puts forward a mammographic enhancement algorithm based on contourlet transform. Firstly by contourlet decomposition on mammographs with utilizing multiresolution and multidirection of contourlet transform, modifies the contourlet coefficient correspondingly; then by selecting proper threshold function and non-linear gain function, fulfils image denoising and enhancement, and displays explicitly the areas of interest such as microcalcification characterizing early breast cancer. Finally, utilizes evaluation indexes based on standard deviation to compare various enhancement algorithms in processing. Simulation shows that this enhancement algorithm has an apparent effect on mammographs, which not only offers convincing help and reference for diagnosis, but also lays a good foundation for other applications such as subsequent image segmentation and feature extraction.3. Studies interpolation to diffusion tensor images. By analyzing the structural features of tensor images, presents two interpolation methods based on local gradient and linear structure tensor respectively with their fast implementation, where the former has a faster speed while the latter has a higher precision. Last, it is pointed out that image interpolation based on structure tensor is a generalized framework that contains an interpolation algorithm based on partial differential equation. Simulation shows that more precise results can be obtained by using these two interpolation algorithms compared with the traditional linear ones. Besides, structural features such as the raw signal edge can be reserved effectively, hence facilitating further research such as neural fasciculus tracing.4. Studies effective image denoising algorithms. Further discusses nonlinear structure tensor based on linear structure tensor, presents a new image denoising algorithm by combing Wiener filtering, and its fast implementation by using AOC scheme, and simulations show thatbetter denoising effect is obtained by using the method.Finally, sums up the work and research results, brings forward future research considerations and objects.