Aiming at the noises and artifacts were introduced to Synthetic Aperture Radar (SAR) image in the process of imaging and transmission, which cause many problems such as reduction of definition and lack of details, an SAR image enhancement method based on the combination of Non-Subsampled Shearlet Transform (NSST) and fuzzy contrast was proposed. Firstly, the original image was decomposed into a low-frequency component and several high-frequency components by NSST. Then, the low-frequency component was linearly stretched to improve the overall contrast, and the threshold method was adopted for high-frequency components to remove noise. And then the reconstruction image was obtained by applying the inverse NSST to the processed low-frequency and high-frequency components. Finally, fuzzy contrast method was used to improve detail information and layering of reconstruction image and obtain the final image. The experimental results on 40 images show that, compared with Histogram Equalization (HE), Multi-Scale Retinex (MSR) enhancement algorithm, Remote sensing image enhancement algorithm based on shearlet transform and multi-scale Retinex, and medical image enhancement method based on improved Gamma correction in Shearlet domain, the Peak Signal-to-Noise Ratio (PSNR) of this proposed method promotes at least 22.9%, and the Root Mean Square Error (RMSE) optimizes at least 36.2%. And finally this proposed method can obviously improve image definition and obtains clearer texture information.

Since the efficiency of rule mining and validity of recommendation are not high in personalized friends recommendation based on association rules, an improved association rule algorithm based on bitmap and hashing, namely BHA, was proposed. The mining time of frequent 2-itemsets was decreased by introducing hashing technique in this algorithm, and the irrelevant candidates were compressed to decrease the traversal of data by using bitmap and relevant properties. In addition, on the basis of BHA, a friend recommendation algorithm named STA was proposed based on similarity and trust. The problem of no displayed trust relationship in microblog was resolved effectively through trust defined by similarity of out-degree and in-degree; meanwhile, the defect of the similarity recommendation without considering users' hierarchy distance was remedied. Experiments were conducted on the user data of Sina microblog. In the comparison experiment of digging efficiency, the average minging time of BHA was only 47% of the modified AprioriTid; in the comparison experiment of availability in friend recommendation with SNFRBOAR (Social Network Friends Recommendation algorithm Based On Association Rules), the precision and recall of BHA were increased by 15.2% and 9.8% respectively. The theoretical analysis and simulation results show that STA can effectively decrease average time of mining rules, and improve the validity of friend recommendation.

Aiming at the problem of low contrast, lack of the details and weakness of edge gradient retention in remote sensing images, a new remote sensing image enhancement method based on the combination of Non-Subsampled Shearlet Transform (NSST) and guided filtering was proposed. Firstly, the input image was decomposed into a low-frequency component and several high-frequency components by NSST. Then a linear stretch was adopted for the low-frequency component to improve the overall contrast of the image, and the adaptive threshold method was used to restrain the noise in the high-frequency components. After denoising, the high-frequency components were enhanced by guided filtering to improve the detail information and edge-gradient retention ability. Finally, the final enhanced image was reconstructed by applying the inverse NSST to the processed low-frequency and high-frequency components. Experimental results show that, compared with the Histogram Equalization (HE), image enhancement based on contourlet transform and fuzzy theory, remote sensing image enhancement based on nonsubsampled contourlet transform and unsharp masking as well as remote sensing image enhancement based on non-subsampled shearlet transform and parameterized logarithmic image processing, the proposed method can effectively increase the information entropy, the Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index Measurement (SSIM), which can obviously improve the visual effect of the image and make the texture of the image more clear.

Aiming at the problem that the traditional wavelet transform, curverlet transform and contourlet transform are unable to provide the optimal sparse representation of image and can not obtain the better enhancement effect, an image enhancement algorithm based on Shearlet transform was proposed. The image was decomposed into low frequency components and high frequency components by Shearlet transform. Firstly, Multi-Scale Retinex (MSR) was used to enhance the low frequency components of Shearlet decomposition to remove the effect of illumination on image; secondly, the threshold denoising was used to suppress noise at high frequency coefficients of each scale. Finally, the fuzzy contrast enhancement method was used to the reconstruction image to improve the overall contrast of image. The experimental results show that proposed algorithm can significantly improve the image visual effect, and it has more image texture details and anti-noise capabilities. The image definition, the entropy and the Peak Signal-to-Noise Ratio (PSNR) are improved to a certain extent compared with the Histogram Equalization (HE), MSR and Fuzzy contrast enhancement in Non-Subsampled Contourlet Domain (NSCT_fuzzy) algorithms. The operation time reduces to about one half of MSR and one tenth of NSCT_fuzzy.