The Sparse Representation Of Signal And Its Application

Sparse representation has drawn many researchers’attention in the field of signal and image processing. It represents a signal as a linear combination of small number of atoms in a redundant dictionary. Applications for sparse representation are many and include image denoising, image steganography, image super-resolution, image separation and feature extraction, and so on.Whether all of the applications related to sparse representation will be successfully implemented depends on the dictionary. It is necessary to design an efficient dictionary learning algorithm to construct a dictionary which better reflects the intrinsic characteristic of the signals and further improves the performance of signal processing.Noise may be produced in many cases like image acquisition, transmission and processing. How to remove it from images has become a key issue in many applications. Meanwhile, many scientists carry on deep research on steganography. It embeds the secret messages into some normal looking carriers in order to make them undetectable in the cases of storage or transmission.The contributions of this thesis are as follows.(1) Dictionary learning with weighted stochastic gradient descentWe construct a new cost function by introducing a weighting matrix and solve this problem by stochastic gradient descent. This novel algorithm is called dictionary learning with weighted stochastic gradient descent. And this method is extended to non-negative matrix factorization. It is demonstrated from synthetic experiments that our method and its non-negative variant have a good performance in signal representation capability and the ability to recover the original dictionary.(2) The algorithm for image denoising based on double dictionariesIn this thesis, an image classification method based on edge detection is proposed. We utilize this method to divide the image blocks into two classes, the smooth ones and the rough ones. Based on the two classes, two dictionaries are constructed, separately. Finally, the two classes of blocks are denoised based on their respective dictionaries. Seen from the experimental results, this method improves the performance of image denoising to some extent.(3) Research on channel selection method in steganography based on sparse representation To apply sparse representation into image steganography, first, we must decompose the image blocks to obtain the coefficient vectors, and then embed the secret messages into the non-zero coefficients. This thesis studies the channel selection problem, that is, which of the coefficients are chosen as carriers. We introduce two new factors, the complexity of the image blocks and the magnitude of the coefficients, and discuss how these factors influence the detectable distortion of the stego images. By combining them and another factor, the decomposition order of the coefficients, a novel channel selection approach is proposed. The steganalysis experiments show that this method can improve the security of steganography.