Research On Image/Video Super-Resolution Reconstruction Methods Based On The Continued Fractions Interpolation Kernel In Sparse Representation

Super-resolution reconstruction is an important topic studied in digital image processing and plays a crucial role in many practical applications such as image processing software, medical diagnosis, high-definition television, and so on. Currently, many researchers have presented plenty of algorithms for different applications which achieved some success. However, various problems and challenges still exist, especially in edges and texture regions of images which cannot be well processed by some existing algorithms. And it is surely the important goal of reconstruction to maintain abundant texture details and clear edges, so super-resolution reconstruction is still challenging. Starting with the theory of the continued fractions, this dissertation conducts an in-depth study and discussion on super-resolution reconstruction. The main contents are summarized as follows:1) A super-resolution reconstruction algorithm is presented by combining sparse principal component analysis (SPCA) and Newton-Thiele rational interpolation, which is based on the image’s degradation model. The key idea in our method is to firstly denoise the input image by using the SPCA, and then magnify the de-noised image by the continued fractions rational interpolation. SPCA can more sparsely extract the principal component of signal, so the SPCA is comined with the linear minimum mean square-error estimation method to remove the noise in the input image. In consideration of the fact that continued fractions, as specific nonlinear functions, have advantages in dealing with the texture details of image, the Newton-Thiele’s rational interpolation is used to up-sampling, and finally the super-resolution reconstructed image can be obtained.2) A super-resolution reconstruction method is presented based on polar Newton-Thiele’s rational kernel in sparse representation, which provides a new approach of the continued fractions rational interpolation in image processing. The key idea of the method is to construct a reconstruction framework based on the polar Newton-Thiele rational kernel in sparse representation, where the input image is magnified by means of Newton-Thiele rational interpolation in the polar coordinates without considering the noise, and then the magnified image is refined by combining the centralized sparse representation method. This algorithm adopts a suitable interpolation window in the polar coordinates other than the traditional rectangular window in the process of up-sampling. A video representation method based on the continued fractions in the polar coordinates is presented, which is combined with the reconstruction framework to get video super-resolution reconstruction results.3) A super-resolution reconstruction method based on the bivariate continued fractions interpolation in the polar coordinates is presented. The idea of this algorithm is to magnify the input image by using the Newton-Thiele’s rational interpolation, which is able to maintain the rich texture details of an image, and the Thiele-Newton’s rational interpolation both in the polar coordinates, and then segment the two magnified images to patches and judge if they are texture patches or flat patches, and an optimized image patch can be got after these patches are endowed to different balance factors and consequently a super-resolution result is obtained. After comparing the interpolation window in the Cartesian coordinates and that in the polar coordinates, a suitable interpolation window is adopted to magnify images. Compared with some other exising methods, the presented reconstruction algorithm is more simple, more effective and more robust.