A two-level Bregmanized method with graph regularized sparse coding （TBGSC） is presented for image interpolation. The outer-level Bregman iterative procedure enforces the observation data constraints, while the inne...A two-level Bregmanized method with graph regularized sparse coding （TBGSC） is presented for image interpolation. The outer-level Bregman iterative procedure enforces the observation data constraints, while the inner-level Bregmanized method devotes to dictionary updating and sparse represention of small overlapping image patches. The introduced constraint of graph regularized sparse coding can capture local image features effectively, and consequently enables accurate reconstruction from highly undersampled partial data. Furthermore, modified sparse coding and simple dictionary updating applied in the inner minimization make the proposed algorithm converge within a relatively small number of iterations. Experimental results demonstrate that the proposed algorithm can effectively reconstruct images and it outperforms the current state-of-the-art approaches in terms of visual comparisons and quantitative measures.展开更多
The approximate expressions of the travelling wave solutions for a class of nonlinear disturbed long-wave system are constructed using the generalized variational iteration method.
Face recognition has been widely used and developed rapidly in recent years.The methods based on sparse representation have made great breakthroughs,and collaborative representation-based classification(CRC)is the typ...Face recognition has been widely used and developed rapidly in recent years.The methods based on sparse representation have made great breakthroughs,and collaborative representation-based classification(CRC)is the typical representative.However,CRC cannot distinguish similar samples well,leading to a wrong classification easily.As an improved method based on CRC,the two-phase test sample sparse representation(TPTSSR)removes the samples that make little contribution to the representation of the testing sample.Nevertheless,only one removal is not sufficient,since some useless samples may still be retained,along with some useful samples maybe being removed randomly.In this work,a novel classifier,called discriminative sparse parameter(DSP)classifier with iterative removal,is proposed for face recognition.The proposed DSP classifier utilizes sparse parameter to measure the representation ability of training samples straight-forward.Moreover,to avoid some useful samples being removed randomly with only one removal,DSP classifier removes most uncorrelated samples gradually with iterations.Extensive experiments on different typical poses,expressions and noisy face datasets are conducted to assess the performance of the proposed DSP classifier.The experimental results demonstrate that DSP classifier achieves a better recognition rate than the well-known SRC,CRC,RRC,RCR,SRMVS,RFSR and TPTSSR classifiers for face recognition in various situations.展开更多
It is proved that each su?ciently large integer N ≡ 5 (mod24) can be written as N = p21+p22+p23+p24+p25 with |pj? N/5| ≤ U = N 12? 135+ε, where pj are primes. This result, which is obtained by an iterative method a...It is proved that each su?ciently large integer N ≡ 5 (mod24) can be written as N = p21+p22+p23+p24+p25 with |pj? N/5| ≤ U = N 12? 135+ε, where pj are primes. This result, which is obtained by an iterative method and a hybrid estimate for Dirichlet polynomial, improves the previous results in this direction.展开更多
基金The National Natural Science Foundation of China (No.61362001,61102043,61262084,20132BAB211030,20122BAB211015)the Basic Research Program of Shenzhen(No.JC201104220219A)
文摘A two-level Bregmanized method with graph regularized sparse coding （TBGSC） is presented for image interpolation. The outer-level Bregman iterative procedure enforces the observation data constraints, while the inner-level Bregmanized method devotes to dictionary updating and sparse represention of small overlapping image patches. The introduced constraint of graph regularized sparse coding can capture local image features effectively, and consequently enables accurate reconstruction from highly undersampled partial data. Furthermore, modified sparse coding and simple dictionary updating applied in the inner minimization make the proposed algorithm converge within a relatively small number of iterations. Experimental results demonstrate that the proposed algorithm can effectively reconstruct images and it outperforms the current state-of-the-art approaches in terms of visual comparisons and quantitative measures.
基金＊Supported by the National Natural Science Foundation of China under Grant No. 40876010, the Main Direction Program of the Knowledge Innovation Project of Chinese Academy of Sciences under Grant No. KZCX2-YW-Q03-08, the R ＆： D Special Fund for Public Welfare Industry （Meteorology） under Grant No. GYHY200806010, the LASG State Key Laboratory Special Fund and the Foundation of E-Institutes of Shanghai Municipal Education Commission （E03004）
文摘The approximate expressions of the travelling wave solutions for a class of nonlinear disturbed long-wave system are constructed using the generalized variational iteration method.
基金Project(2019JJ40047)supported by the Hunan Provincial Natural Science Foundation of ChinaProject(kq2014057)supported by the Changsha Municipal Natural Science Foundation,China。
文摘Face recognition has been widely used and developed rapidly in recent years.The methods based on sparse representation have made great breakthroughs,and collaborative representation-based classification(CRC)is the typical representative.However,CRC cannot distinguish similar samples well,leading to a wrong classification easily.As an improved method based on CRC,the two-phase test sample sparse representation(TPTSSR)removes the samples that make little contribution to the representation of the testing sample.Nevertheless,only one removal is not sufficient,since some useless samples may still be retained,along with some useful samples maybe being removed randomly.In this work,a novel classifier,called discriminative sparse parameter(DSP)classifier with iterative removal,is proposed for face recognition.The proposed DSP classifier utilizes sparse parameter to measure the representation ability of training samples straight-forward.Moreover,to avoid some useful samples being removed randomly with only one removal,DSP classifier removes most uncorrelated samples gradually with iterations.Extensive experiments on different typical poses,expressions and noisy face datasets are conducted to assess the performance of the proposed DSP classifier.The experimental results demonstrate that DSP classifier achieves a better recognition rate than the well-known SRC,CRC,RRC,RCR,SRMVS,RFSR and TPTSSR classifiers for face recognition in various situations.
文摘It is proved that each su?ciently large integer N ≡ 5 (mod24) can be written as N = p21+p22+p23+p24+p25 with |pj? N/5| ≤ U = N 12? 135+ε, where pj are primes. This result, which is obtained by an iterative method and a hybrid estimate for Dirichlet polynomial, improves the previous results in this direction.
