Study On Convolutional Sparse Coding Algorithm And Its Applications

Sparse representation is closely related to further image processing such asdenoising, compressing, scene classification and pattern recognition. The existed theoryof sparse representation can only deal with small-sized images, due to modeling based onone dimensional signal or image patch. However, image is a kind of high dimensionaldata with complex structures, and its inherent statistical characteristics are correspondingto information processing mechanism in human visual perception and neuron receptivefield properties. According to this, this paper performs the research on convolutionalsparse coding and its applications in view of convolutional networks model whichsimulates visual neural system’s structures. This paper proceeds as follows:Firstly, a denoising algorithm based on convolutional sparse coding is proposed toovercome the shortcomings of existed denoising methods using sparse representationwhich often can not deal with large scale images. Using convolutional networks forlearning dictionaries, image denoising is performed to control the residual energy inglobal sparse approximation with convolutional matching pursuit. Because of thedrawbacks of denoising method using convolutional sparse representation, we proposeusing threshold and feature response numbers to constrain the algorithm. The experimentresults show that the proposed algorithm could efficiently avoid noise in a certain extent.Secondly, because traditional overcomplete dictionaries have single features and lowredundancy, we study on two methods for learning translation invariant dictionaries. Thesimilar constraint is used during learning convolutional dictionaries to perform suchdictionaries with many features. Then, we use convolutional coding theory for learningtranslational invariant dictionaries based on image patches to reduce complexity. Theexperiment results show the algorithm validity.Finally, we propose an algorithm based on convolutional matching pursuit andorthogonal matching pursuit for sparse representation to overcome the shortcomings ofconvolutional sparse coding which can not represent the complex detail features. Usingadvantages of dictionaries based on K-SVD and convolution, the combined dictionaries based on nature images’global contour and local detail features can sparsely representimages. The experiment results show that, in comparison with overcomplete dictionariesbased on K-SVD and convolutional dictionary, the combined dictionary has sparserimage representation.