In order to more effectively combine the detail information of high resolution PANchromatic (PAN) image and the spectral information of low resolution MultiSpectral (MS) image, an improved panchromatic sharpening algorithm based on sparse representation was proposed. Firstly, the intensity channel of an MS image was down-sampled and then up-sampled to get its low-frequency components. Secondly, the MS image intensity channel minus low-frequency components to obtain its high-frequency components. Random sampling was performed in the acquired high and low frequency components to construct a dictionary. Thirdly, the PAN image was decomposed to get the high-frequency components by using the constructed overcomplete dictionary. Finally, the high-frequency components of the PAN image were injected into the MS image to obtain the desired high-resolution MS image. After a number of experiments, it was found that the proposed algorithm subjectively retains the spectral information and injects a large amount of spatial details. Compared with component substitution method, multiresolution analysis method and sparse representation method, the reconstructed high resolution MS image by the proposed algorithm is more clear, and the correlation coefficient and other objective evaluation indicators of the proposed algorithm are also better.

In order to solve the problem that classifiers do not make full use of the differences between different types of face samples in face recognition, an effective method for face recognition was proposed, namely Complement Null-Space (CNS) algorithm; and further more, another method which combined CNS and nearest space Distance (CNSD) was proposed. Firstly, subspaces and complement null-spaces of all types of training images were constructed. Secondly, the distances between the test image and all types of subspaces as well as the distances between the test image and all types of complement null-spaces were calculated. Finally, the test image was classified into the type which has the minimum subspace distance and the maximum complement null-space distance. On ORL and AR face databases, the recognition rates of CNS and CNSD are much higher than those of Nearest Neighbor (NN), Nearest Space (NS) method and Nearest-Farthest Subspace (NFS) method when the number of training samples is small; and it is a little higher than that of NN, NS and NFS when dealing with large samples. Simulation results show that the proposed algorithm can make full use of the differences between different types of images and has good recognition ability.