| Image signal processing relies heavily on image data models. Obviously, imagesignal modeling makes signals within compact expression by forcing a dimensionalityreduction of some sort. Sparse representation model means that the signals can have asparse redundant representation on an over-complete dictionary learned from thesignals themselves. Compared to the traditional model, sparse model can fit better tothe signals and reduce the modeling error. So, sparse model has been focused on theresearch hotspots in the past decade.Actually, sparse representation model means the synthesis sparse model, whichrepresent the signal in the synthesis way. However, in recent two years the appearinganalysis sparse model enriched the sparse model and expanded the application regionof sparse representation model. Both the synthesis model and the analysis modelreshape the two dimensional (2D) image to the one dimensional (1D) vector, whichleads to the following problem: First, the2D spatial structure of the image are broken,so that the local correlations within images cannot be utilized. Second, in order to getmore reliable and robust estimation, a large number of training samples in thehigh-dimensional space is needed. So we proposed a novel2D synthesis sparse modeland a novel2D analysis sparse model, and proposed the corresponding sparse codingalgorithm and dictionary learning algorithm. The thesis includes the following threeparts:First, we proposed a novel2D synthesis sparse model. In the traditional sparsemodel, an image patch is always reshaped to a vector in the horizontal direction or thevertical direction. The vector can be linear combination of few atoms of the dictionary,every atom of which is a vector. The traditional1D model ignores2D structurefeatures and the diversity of the distribution on different dimensions, which imposethe restriction on the sparsity of the sparse model and the effect of sparsereconstruction. So, the proposed2D model means the image patch can be combinationof the element of the space spanned by the horizontal dictionary and the verticaldictionary, which can depict the distinct features to preserve the image structure,respectively. Then we proposed the corresponding sparse coding optimizationalgorithm and the dictionary learning algorithm. Finally, the effectiveness of ourproposed model as well as the dictionary learning algorithm is evaluated with imagedenoising. Experimental results demonstrate that our proposal can outperform thetraditional one in terms of the objective and subjective quality, and our proposal canreduce the memory usage of the dictionary and the computation complexity.Secondly, we propose a2D analysis sparse model. In the traditional analysissparse model, the two dimensional structure and the diversity of the distribution on different dimension are also ignored, which also restrict the sparsity of the model andthe efficiency of the sparse reconstruction. So, the proposed2D analysis sparse modelmeans that the two analysis dictionary, corresponding to the horizontal and verticalfeatures of the image patch, are presented to generate a sparse matrix instead of thesparse vector in the traditional1D analysis sparse model. We propose a cascadingdictionary learning algorithm, which learn the horizontal dictionary and the verticaldictionary in sequence. Then we propose a novel sparse coding optimizationalgorithm to reconstruct image. We give the experiments about the sparsity analysisand the image denoising to demonstrate the efficiency of the proposed model.Experimental results demonstrate our model can achieve some gain compared to thetraditional one. However, the cascading dictionary learning algorithm has somelimitation. The dictionary learning order has some impact on the learned dictionary,which cannot get a tradeoff to depict the distinct dimensional feature totally andcannot get better image denoising result.Thirdly, considering the existing problem in the cascading dictionary learningalgorithm, we found that the horizontal dictionary and the vertical dictionary areinteractive and should have the same position on the2D analysis sparse model. Sotaking the relevance of the vertical dictionary and the horizontal dictionary intoconsideration, we propose a coordinated dictionary learning algorithm to learndictionaries making the image patch more sparsity. With regard to the proposeddictionary learning algorithm and the sparse coding algorithm, we analyze thecompute complexity of the algorithm and the memory usage of the dictionary.Compared to the traditional1D analysis sparse model, our proposal can reduce thecomputation complexity and the memory usage. The effectiveness of our proposedmodel as well as the coordinated dictionary learning algorithm is evaluated withimage denoising. Experimental results demonstrate our proposal outperforms thetraditional one in terms of the objective and subjective quality. Compared to thecascading dictionary learning algorithm, the coordinated algorithm can reduce thetraining iteration number and the compute complexity, and the coordinated dictionarylearning can make sure the horizontal and vertical dictionary can better depict thedistinct feature of the image. |
