Separable Dictionary Optimization And Its Applications To Image Processing

The sparse representation can efficiently extract the most intrinsic structures of a signal.It has been widely used in the signal processing fields,including signal compression,feature extraction,de-noising,super-resolution reconstruction and so on.The compressive sensing theory(abbreviated as CS),which has been paid the utmost attentions of scholars from abroad and at home in recent years,is just based on sparse representation.CS theory fucher reveals that sparse representation is of great scientific value and has broad application prospects.However,there are still some problems to be solved in sparse representation theory.Taking 2D image as an example,it is needed to be converted into vectors in existing sparse representation algorithms.However,this kind of operator not only breaks the potential correlations and local structural information in images,but also is restricted due to the complexity of computation in the dictionary optimization and sparse coding procedure.Therefore,we focus on the sparse representation theory,and extend the traditional vector based sparse representation model to the processing of 2-dimentional or higher dimenstional signals(images,video signals,etc).Some sparse decomposition algorithms for the image signals via separable dictionary were proposed in this dissertation,and applied to image de-noising,restoration and image super-resolution reconstruction.The main contributions of this dissertation are as follows:(1)Two separable dictionaries optimization algorithms based on manifold theory were proposed.First of all,we analysed the mathematical relationships between sparse representation based on matrix and the traditional sparse representation theory.Then,two improved separable dictionaries optimization algorithms based on manifold theory were proposed in view of the shortages of the existing separable dictionaries optimization algorithms.Considering the differences of sparse coefficient matriices and dictionaries,we divided the dictionary optimization process into two phases:2D sparse coding and dictionary update.The experimental results showed that these algorithms effectively improved the convergence of the objective function in dictionary optimization process,and preserved the details of the images in de-noising and facial images restoration process.(2)A multi-separation dictionaries optimization algorithm was proposed.In this section,we firstly analyzed luminance and texture features of the training samples.Then,the training samples were classified,and the underdetermined separable dictionaries were optimized for each class.Because separable dictionaries for each cluster represent the special type of signals,the number of columns in these dictionaries is less than the number of rows.The experimental results showed that the dictionaries based on classified sample can not only improve the visual results of the images in de-noising and restoration process,and also have obvious superiority in the reconstruction speed.(3)Image super-resolution algorithms based on sepearble dictionaries were proposed.There are two advantges of separable dictioanries:the separable dictionaries can capture the intrinsic structure of image signals in different directions,and have remarkable advantage in speed.After the optimization of the low resolution separable dictionaries,we used the Lagrange duality problems to optimize the high resolution separable dictionaries.The experimental results showed that these image super-resolution algorithms can reconstruct the details of images compared with other alogrithms,and also accelerate the speed in the process of the image super-resolution reconstruction.