Image Sparse Representation And Its Application In Compressed Sensing Based On Learning Dictionaries

The overcomplete sparse representation is an effective pattern of image sparserepresentation, which encoding mechanism matches with neurophysiology theory of themammalian visual system. Overcomplete sparse representation of images includes twomodels: synthesis model and analysis model. The paper focuses on on the learning of thesynthesis dictionary and the analysis dictionary, the main work are as follows:Firstly, using the spherical K-means algorithm to learn dictionaries with the differentredundancies, and comparing them on the ability of sparse approximation and denoisingperformance. The experiments show that the performances of the sparse approximationand images denoising have been improved with the increasing redundancy.Secondly, aiming to the adaptive problem between image and dictionary, and anovel algorithm is proposed for learning an adaptive dictionary employing theincomplete information of the image blocks, which address the issue that how to learnadaptive dictionary using measurements in the CS system. In this algorithm, the initialdictionary can adaptively select from a large size global dictionary, and making full useof the global sparsity of the all patches when iterating between the adaptive dictionarylearning and restructuring the images. Experiments show that the proposed algorithm isfeasible, effective and robust.Finally, to address the problem that learning analysis dictionary based on theanalysis model, proposing a valid algorithm that Compressed Sensing Based on learningthe analysis dictionary and optimizing measurement matrix. In the algorithm, the entireimage space is divided into different subspaces based on the image semantic properties ofdirection, then learning analysis dictionary in different subspaces respectively, using theanalysis dictionary and the optimized measurement matrix in the CS that can effectivelyreconstruct images.