Aiming at the problems of high complexity and long reconstruction time of Generalized Orthogonal Matching Pursuit(GOMP)algorithm,a Stochastic support selection based GOMP(StoGOMP)algorithm was proposed. Firstly,the strategy of stochastic support selection was introduced,and a probability value was randomly generated in each iteration. Then the generated probability value was compared to the preset probability value to determine the selection method of candidate support set. If this probability value was less than the preset probability value,the matching calculation method was adopted,otherwise,the random selection method was adopted. Finally,the residual was updated according to the obtained candidate supports. In this way,the balance between the complexity of the single iteration and the number of iterations of the algorithm was fully considered,and the computational cost of the algorithm was reduced. The experiment of one-dimensional random signal reconstruction shows that the number of samples required for StoGOMP algorithm to achieve 100% reconstruction success rate is reduced by 9. 5% compared with that for GOMP algorithm when the preset probability is 0. 5 and the sparsity is 20. The actual image reconstruction experiment shows that the proposed algorithm has the same reconstruction accuracy as GOMP algorithm,and the reconstruction time of the proposed algorithm is reduced by more than 27% compared to that of the original algorithm when the sampling rate is 0. 5,which indicates that StoGOMP algorithm can effectively reduce the signal reconstruction time.

Aiming at the problem of large number of iterations and long reconstruction time of iterative hard thresholding algorithms in Compressed Sensing (CS), a Hybrid Gradient based Hard Thresholding Pursuit (HGHTP) algorithm was proposed. Firstly, the gradient and conjugate gradient at the current iteration node were calculated in each iteration, and the support sets in the gradient domain and conjugate gradient domain were mixed and the union of these two was taken as the candidate support set for the next iteration, so that the useful information of the conjugate gradient was fully utilized in the support set selection strategy, and the support set selection strategy was optimized. Secondly, the least square method was used to perform secondary screening on the candidate support sets to quickly and accurately locate the correct support and update the sparse coefficients. The experimental results of one-dimensional random signal reconstruction show that HGHTP algorithm needs fewer iterations than the similar iterative hard thresholding algorithms on the premise of guaranteeing the success rate of reconstruction. The two-dimensional image reconstruction experimental results show that the reconstruction accuracy and anti-noise performance of HGHTP algorithm are better than those of similar iterative thresholding algorithms, and under the condition of ensuring reconstruction accuracy, HGHTP algorithm has the reconstruction time reduced by more than 32% compared with similar algorithms.

For the Backtracking-based Iterative Hard Thresholding algorithm (BIHT) has the problems of large number of iterations and too long reconstruction time, a Backtracking-based Conjugate Gradient Iterative Hard Thresholding algorithm (BCGIHT) was proposed. Firstly, the idea of backtracking was adopted in each iteration, and the support set of the previous iteration was combined with the current support set to form a candidate set. Then, a new support set was selected in the space spanned by the matrix columns corresponding to the candidate set, so as to reduce times that the support set was selected repeatedly and ensure that the correct support set was found quickly. Finally, according to the criteria of whether or not the support set of the last iteration was equal to the support set of the next iteration, gradient descent method or conjugate gradient method was used to be the optimization method, so as to accelerate the convergence of algorithm. The reconstruction experimental results of one-dimensional random Gaussian signals show that, the reconstruction success rate of BCGIHT is higher than that of BIHT and similar algorithms, and its reconstruction time is less than that of BIHT by at least 25%. The reconstruction experiment results of Pepper image show that, the reconstruction accuracy and the anti-noise performance of the proposed BCGIHT algorithm is comparable with BIHT and similar algorithms, and its reconstruction time is reduced by more than 50% compared with BIHT.

Bilinear pairings computation is one of the basic operations of public key cryptography algorithm, which is widely used in the identity-based encryption and attributed-based encryption schemes. However, all of the efficient outsourcing algorithms of bilinear pairings are based on two untrusted servers, which is difficult to be realized in practical applications. In order to solve the problem, a secure outsourcing algorithm of bilinear pairings with single server was proposed. The input of users' device was took for blind treatment, which could protect the input and output confidentiality and verify the correctness of the server output by a small amount of pre-computations. The experimental results show that the proposed algorithm reduces the computation of the users' device just by several point additions and multiplications, and its verifiability probability is 2/5. Compared with the previous schemes, the proposed scheme is based on one single untrusted server and easier to be realized in reality.

Outdoor images captured in bad weather often have poor qualities in terms of visibility and contrast. A simple and effective algorithm was designed to remove haze. Firstly, the spatial high-pass filtering was used to suppress the low-frequency component and enhance the edge detail, and then the contrast-stretching transformation was used to acquire an image with high dynamic range. Finally, the exposure fusion method based on Laplacian pyramid was utilized to fuse the two results above and get the defogged image. The experimental results show that the proposed method has a good performance on enhancing images that are degraded by fog, dust or underwater and it is appropriate for real-time applications.