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 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.