Seismic interpretation is often limited by low resolution and strong noise data. To deal with this issue, we propose to leverage deep convolutional neural network (CNN) to achieve seismic image super-resolution and denoising simultaneously. To train the CNN, we simulate a lot of synthetic seismic images with different resolutions and noise levels to serve as training data sets. To improve the perception quality, we use a loss function that combines the $\ell _{1}$ loss and multiscale structural similarity loss. Extensive experimental results on both synthetic and field seismic images demonstrate that the proposed workflow can significantly improve the perception of quality of original data. Compared to conventional methods, the network obtains better performance in enhancing detailed structural and stratigraphic features, such as thin layers and small-scale faults. From the seismic images super-sampled by our CNN method, a fault detection method can compute more accurate fault maps than from the original seismic images.

Without any prior structure information, nuclear norm minimization (NNM), a convex relaxation for rank minimization (RM), is a widespread tool for matrix completion and relevant low-rank approximation problems. Nevertheless, the result derivated by NNM generally deviates the solution we desired, because NNM ignores the difference between different singular values. In this paper, we present a non-convex regularizer and utilize it to construct two matrix completion models. In order to solve the constructed models efficiently, we develop an efficient optimization method with convergence guarantee, which can achieve faster convergence speed compared to conventional approaches. Particularly, we show that the proposed regularizer as well as the optimization method are suitable for other RM problems, such as subspace clustering based on low-rank representation. Extensive experimental results on real images demonstrate that the constructed models provide significant advantages over several state-of-the-art matrix completion algorithms. In addition, we implement numerous experiments to investigate the convergence speed of the developed optimization method.

In the field of data mining, how to deal with high-dimensional data is a fundamental problem. If they are used directly, it is not only computationally expensive but also difficult to obtain satisfactory results. Unsupervised feature selection is designed to reduce the dimension of data by finding a subset of features in the absence of labels. Many unsupervised methods perform feature selection by exploring spectral analysis and manifold learning, such that the intrinsic structure of data can be preserved. However, most of these methods ignore a fact: due to the existence of noise features, the intrinsic structure directly built from original data may be unreliable. To solve this problem, a new unsupervised feature selection model is proposed. The graph structure, feature weights, and projection matrix are learned simultaneously, such that the intrinsic structure is constructed by the data that have been feature weighted and projected. For each data point, its nearest neighbors are acquired in the process of graph construction. Therefore, we call them adaptive neighbors. Besides, an additional constraint is added to the proposed model. It requires that a graph, corresponding to a similarity matrix, should contain exactly $c$ connected components. Then, we present an optimization algorithm to solve the proposed model. Next, we discuss the method of determining the regularization parameter $\gamma $ in our proposed method and analyze the computational complexity of the optimization algorithm. Finally, experiments are implemented on both synthetic and real-world datasets to demonstrate the effectiveness of the proposed method.