Study On Some Key Problems Of Non-Aliasing Contourlet Transform For High-Resolution Images Processing

High-resolution and high-clarity are not only the aim of effective observation of detail structure for imaging system, but also the development trends of modern imaging system. However, as the modern imaging system is affected by many factors, the image quality goes down during the process of image acquisition, for instance, image noise, image blur and low contrast appeare and could cause some details of high-resolution image to be lost. The dissertation relies on the project supported in part by National Natural Science Foundation, Army-Engineering projects and some related research projects, trying to find a transform method to effectively describe detail information of image edge and texture, namely, Non-Aliasing Contourlet Transform. Therefore, we develop research on some key problems of Non-Aliasing Contourlet Transform for high-resolution images processing in order to show the potential application prospect of Non-Aliasing Contourlet Transform in the high resolution image processing of modern imaging system. This dissertation mainly discusses:(1)Lead the way in developing the research on frequency aliasing of Contourlet TransformFrom the aspects of image singularity and approximation of function, the dissertation discusses the limitations the wavelet has when it analyzes 2D image, and reveals the sparse expression of high-dimension singularity is the fundamental reason why multi-scale geometric analysis is better than wavelet. As one of the multi-scale geometric analysis, Contourlet Transform is full of application potentials in the field of image process due to its good capability of capturing direction and low redundancy. Nevertheless, frequency aliasing would stop it going further. For this reason, base on 2-D multi-rate system, we elaborate the constitutive principle and realization approach of the two basic modules in Contourlet transform, those are Directional Filter Banks(DFB) and Laplacian Pyramidal Transform(LP transform), and then analyze frequency aliasing in the decomposition of DFB and LP to make sure that the frequency aliasing of Contourlet transform is caused by the reason that the two lowpass filters of LP transform don't satisfy with Nyquist-Shannon sampling theorem, and it leads to frequency crosstalk among different subbands as well, in addition, it could weaken the frequency localization of Contourlet transform. In terms of this, the paper presents a scheme to restrain aliasing. The scheme requires us to define a filter in the frequency domain directly, what's more, the Nyquist-Shannon sampling theorem must be satisfied strictly, normally speaking, it takes use of dual-iterative structure to realize a new multi-scale decomposition instead of LP decomposition, then combines with DFB to realize multi-scale and multi-directional decomposition of image. The preliminary experiment result indicates that this scheme is superior to Contourlet transform in the respects of nonlinear approximation and the regularity and localization of basis function. It is fairly effective to improve the frequency aliasing of Contourlet transform.(2)Research on the construction of Non-Aliasing Contourlet TransformWe present a new Non-Aliasing Contourlet Transform, namely NACT, based on the scheme mentioned above, to avoid the frequency aliasing of Contourlet Transform and the extraordinary disparity in the spatial domain dimensions of fan filter banks. NACT consists of non-aliasing pyramidal filter banks (NPFB) and DFB. NPFB decomposes image into an approximation subband and several detail subbands with different resolutions; whilst DFB decomposes the detail subbands into directional subbands. In the dissertation, we firstly represent the definition and specific parameter setting of NPFB in the frequency domain. Secondly, we apply Bernstein polynomial to design mapping function, and expanded McClelland transform to map 1-D 9/7 bi-orthogonal filter banks into fan filter banks, which indeed makes the dimension ratio of spatial domain better. Not only has the basis function of NACT a variety of characteristics such as multi-resolution, multi-direction, localization to meet demands of anisotropy scale relations, but also are their regularity and localization better that those of Contourlet Transform in the spatial domain. Notwithstanding, the average redundancy of NACT is a little bit higher than Contourlet Transform, the former restrains the frequency aliasing of Contourlet transform much more remarkably. That is why it has better direction selectivity. Results from the experiments of nonlinear approximation and noise reduction show that NACT has a significant improvement both visually and in terms of PSNR, compared with Contourlet transform.(3)Research on statistical distribution model of NACT coefficientsStudy the coefficients statistical model for marginal distribution and joint distribution of NACT transform. The paper analyzes the statistical dependency and non-independency of NACT coefficient qualitatively and quantitatively, and on the basis of the comparison of Laplace distribution, Generalized Gaussian distribution and BKF distribution describing NACT coefficient, takes use of Pearlsonχ2 hypothesis test to verify that the NACT coefficient marginal distribution obeys Generalized Gaussian distribution. For joint distribution, we put forward Generalized Bivariate model for joint distribution of coefficients, it paves the way for NACT filter based on statistical model.(4)Research on the method of Noise reduction for high-altitude photo and contrast enhancement for retinal blood vessel image based on NACTOn the close analysis of the main noise origin and noise type of high-altitude photo, focused on their abundant texture detail information, we present a noise reduction algorithm with hybrid NACT coefficients model. The procedure of algorithm makes use of the interscale correlation differences between signal and noise in NACT domain to classify NACT coefficient into two categories: important and non-important, by means of SSNF algorithm. We model the two kinds of coefficient by different distribution models, according to the differences between their statistical properties, and denoise image under the framework of Bayes probability. Both the denoising results of standard test images and actual high-altitude photo show this algorithm holds texture and detail of image effectively, and cracks down on"scratch"in reconstructed image greatly, in addition, it has much higher computational efficiency and meets the need of noise reduction in high-altitude photo.There are some problems in the retinal blood vessel images, such as low contrast, low clarity for minute vessel, we propose a contrast enhancement algorithm to enhance minute vessel and avoid noise amplification based on the excellent capability of edge representation of NACT transform. The algorithm selects distinct enhancement functions to weaken or enhance NACT coefficientss in terms of the different distribution characteristics of noise and vessel in NACT domain. In order to make the enhancement effect of minute vessel more remarkable we should enhance the weak edge (minute vessel) while weakening the strong edge. The experimental results show that this algorithm takes on pleasant contrast enhancement to retinal blood vessel image, and the enhanced image has the homogeneous gray distribution of background without obvious noise amplification.The theoretical research results mentioned above have already been published on the journal of"Pattern Recognition Letters","OptoElectronics Letters","Computer Simulation"and"Opto-Electornics Engineering". Some related applications have been applied in the project of"high-resolution science grade CCD digital imaging system for photography and measurement". All the studies lay the positive foundations of theory and application research for the further work on Non-Aliasing Contourlet Transform in modern imaging system.