How to sufficiently exploit the self-similarity of natural images for image restoration has attracted extensive interest in the field of image processing in recent years.In fact,the self-similarity implies two-directi...How to sufficiently exploit the self-similarity of natural images for image restoration has attracted extensive interest in the field of image processing in recent years.In fact,the self-similarity implies two-direction similarity structures inherent in images,when a group of similar patches are rearranged to form a matrix,there exists similarity between both columns and rows of this matrix.In this paper,we propose a two-direction nonlocal model (TDNL) to symmetrically exploit the two-direction similarity structures in images,the model directly takes the similar patches as local adaptive dictionary to represent each patch in the image and constrain the representation coefficients by Tikhonov regularization.TDNL can achieve the best results so far and obtain significant gains over the existing methods,in terms of both peak signal to noise ratio (PSNR) measure and the visual quality when it is applied to the problem of image interpolation.展开更多
A new type of homoclinic arid heteroclinic solutions, i.e. homoclinic and heteroclinic breather solutions, for Zakharov system are obtained using extended homoclinic test and two-soliton methods, respectively. Moreove...A new type of homoclinic arid heteroclinic solutions, i.e. homoclinic and heteroclinic breather solutions, for Zakharov system are obtained using extended homoclinic test and two-soliton methods, respectively. Moreover, the homoclinic and heteroclinic structure with local oscillation and mechanicaL feature different from homoclinic and heterocliunic solutions are investigated. Result shows complexity of dynamics for complex nonlineaR evolution system. Moreover, the similarities and differences between homoclinic （heteroclinic） breather and homoclinic （heteroclinic） tube are exhibited. These results show that the diversity of the structures of homoclinic and heteroclinic solutions.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 61001156,61105011,11101292,60872138 and61271294)the Natural Science Foundation of Ningxia University(Grant No. ZR1206)
文摘How to sufficiently exploit the self-similarity of natural images for image restoration has attracted extensive interest in the field of image processing in recent years.In fact,the self-similarity implies two-direction similarity structures inherent in images,when a group of similar patches are rearranged to form a matrix,there exists similarity between both columns and rows of this matrix.In this paper,we propose a two-direction nonlocal model (TDNL) to symmetrically exploit the two-direction similarity structures in images,the model directly takes the similar patches as local adaptive dictionary to represent each patch in the image and constrain the representation coefficients by Tikhonov regularization.TDNL can achieve the best results so far and obtain significant gains over the existing methods,in terms of both peak signal to noise ratio (PSNR) measure and the visual quality when it is applied to the problem of image interpolation.
基金Supported by the Natural Science Foundation of China under Grant No.11061028
文摘A new type of homoclinic arid heteroclinic solutions, i.e. homoclinic and heteroclinic breather solutions, for Zakharov system are obtained using extended homoclinic test and two-soliton methods, respectively. Moreover, the homoclinic and heteroclinic structure with local oscillation and mechanicaL feature different from homoclinic and heterocliunic solutions are investigated. Result shows complexity of dynamics for complex nonlineaR evolution system. Moreover, the similarities and differences between homoclinic （heteroclinic） breather and homoclinic （heteroclinic） tube are exhibited. These results show that the diversity of the structures of homoclinic and heteroclinic solutions.
