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The option butterfly portfolio is the commonly option arbitrage strategy. In reality, because the distribution of the option state price density (SPD) function is not normal and unknown, so the nonparametric deep learning methods to estimate option butterfly portfolio returns are proposed. This paper constructs the single-index nonparametric option pricing model which contains multiple influencing factors and presents the nonparametric estimation form for option butterfly portfolio returns. The empirical analysis shows that the SPD function estimated by using single-index nonparametric option model can effectively calculate the option butterfly portfolio returns with the minimum option strike price interval and provide an effective reference tool for risk-averse investors with limited risk preferences. [ABSTRACT FROM AUTHOR]

At present, the traditional phase unwrapping algorithm is difficult to balance the accuracy and unwrapping efficiency. The traditional phase unwrapping algorithm is difficult to balance the accuracy and efficiency in the phase unwrapping experiments of simulated and measured topographic interferograms. In this paper, the phase unwrapping technology will be studied under the framework of deep learning theory according to the development trend of InSAR intelligence. A phase unwrapping algorithm based on deep GAN is proposed. The model structure includes dense convolution layer blocks and series structure, so that the network can achieve a better balance between feature extraction and detail preservation of interferogram. This is helpful to improve the phase unwrapping accuracy and training efficiency of the network. The experimental results show that the algorithm has a good expansion effect on the interferogram with high signal-to-noise ratio. The synthesis algorithm makes full use of the advantages of the branch cutting method and the finite element method. The phase reliable region and unreliable region are determined, and the transmission of phase error from the unreliable region to reliable region is effectively avoided. The accuracy of the phase unwrapping results in the reliable region is ensured, and the overall phase unwrapping convergence accuracy is greatly improved. [ABSTRACT FROM AUTHOR]

As a complex machine learning algorithm, deep learning can extract object shape information and more complex and advanced information in images by using a deep learning model. In order to solve some problems of deep learning in image feature extraction and classification, this paper designs a modeling method of multifocus image segmentation algorithm based on deep learning. The acceleration effect of FPGA (field programmable gate array) on deep learning and weight sharing is analyzed. By introducing deep learning, the trouble of determining the weight coefficient is eliminated, and the energy function is simplified. Therefore, the relevant parameters of multifocus image segmentation can be easily set, and better results can be obtained. The multifocus image segmentation algorithm based on deep learning can not only obtain closed and smooth segmentation curves but also adaptively deal with topology changes due to high segmentation accuracy and stable algorithm. The results show that the model effectively combines the local and global information of the image, so that the model has good robustness. The depth learning algorithm is used to calculate the average value of local inner and outer pixels of an image. Even for complex images, relatively simple contour curves can be obtained. [ABSTRACT FROM AUTHOR]