It has been widely concerned to apply fractional partial differential equations in image processing, especially in the image denoising and image Super Resolution (SR) reconstruction. The current research results have shown the advantages and effects of fractional order applications. The theory and model of fractional partial differential equations in image denoising and image super-resolution reconstruction were introduced and discussed. The simulation results show that the methods based on fractional partial differential equations has more advantages than the methods based on integer order partial differential equations in terms of denoising and reducing the staircase effect. Finally, the related research problems were pointed out.

College enrollment consultation service usually relies on artificial reply or keyword matching Question and Answer (Q&A) system, which exists the problems of low efficiency and irrelevant answers. In addition, a consultation text is often a short statement, therefore its vectorized representation may easily lead to the high-dimensional sparse problem. To solve the problems mentioned above, an enrollment consultation algorithm based on Stacked Denoising Sparse AutoEncoders (SDSAE) was proposed. First of all, to improve generalization ability of the algorithm, an autoencoder network was used to extract features and reduce the data dimension; at the same time, dataset enhancement technique and noise-adding technique were introduced to solve the problems of small training sample set and uneven classification. After low dimensional representation of short texts being obtained, a text classification was conducted afterwards by using Back Propagation (BP) algorithm. The experimental results show that the proposed algorithm has a better classification performance over BP, Support Vector Machine (SVM), Extreme Learning Machine (ELM) algorithm and etc., and it significantly improves the classification effect of enrollment consultant texts.

Concerning the limitations that the accuracy of prediction is low and the classification on box-office is not significant in application, this paper proposed a new model to predict box-revenue of movie, based on the movie market in reality. The algorithm could be summarized as follows. Firstly, the factors that affected the box and format of the output were determined. Secondly, these factors should be analyzed and quantified within [0, 1]. Then, the number of neurons was also determined, aiming to build up the architecture of the neural network according to input and output. The algorithm and procedure were improved before finishing the prediction model. Finally, the model was trained with denoised historical movie data, and the output of model was optimized to dispel the randomness so that the result could reflect box more reliably. The experimental results demonstrate that the model based on back propagation neural network algorithm performs better on prediction and classification (For the first five weeks, the average relative error is 43.2% while the average accuracy rate achieves 93.69%), so that it can provide a more comprehensive and reliable suggestion for publicity and risk assessment before the movie is on, which possesses a better application value and research prospect in the prediction field.

In this paper, a new image encryption algorithm was presented based on the fractional-order Chen chaotic system, for fractional-order chaotic dynamical systems have more complex dynamical behaviors than those of integer-order systems and can provide more freedom for image encryption schemes. In the transmitter, the positions of the image pixels were scrambled by the chaotic signal generated by the driving system firstly. Then the disturbed image was embedded into the chaotic signal and the encrypted image for transmission was obtained. In the receiver, the chaotic signal was removed by the synchronization system. Then the inverse process of pixel scrambling was carried out and the original image was recovered. The security of the proposed algorithm was analyzed in the end. The experimental results demonstrate that the encryption algorithm is of high security and has good research value and application prospects.