Seismic data are inevitably polluted by noise, which has a significant impact on subsequent applications. Currently, regularization-based methods that utilize interpretable data priors are widely used for eliminating seismic data noise. However, many existing methods are merely direct linear weighted combinations of regularization terms, resulting in the introduction of a series of balancing parameters. Moreover, these methods may fail to fully capture the complex curved structures that exist in seismic data. To handle the above problems, we propose a merged approach based on nonlocal enhanced low-rankness and second-order gradient smoothness (ELGS). The ELGS method simultaneously encodes multiple dimensional features of seismic data within a single term, including temporal evolution characteristics, geological spatial structural information, and self-repeating redundancy of seismic profiles, which minimizes the introduction of balancing parameters while effectively capturing the curved geological structures of seismic data. Specifically, the ELGS method maps low-dimensional seismic data to high-dimensional structural tensors by using a similar patch matching framework and applies low-rank constraints to the second-order gradient tensors along each direction for each high-dimensional structural tensor. To solve the optimization problem faced by the developed ELGS approach, we design an algorithm based on the alternating direction multiplier method. Numerous numerical experiments conducted on both synthetic and field seismic data show that our approach outperforms the related approaches in both quantitative measures and visual performance.

Spatialtemporal traffic data are collected by a wide array of data collection devices deployed in intelligent transportation systems, which play crucial roles in data-driven intelligent transportation systems. However, hardware malfunctions or software system errors can lead to the inability to collect accurate data. Incomplete data in intelligent transportation systems can cause difficulties for subsequent applications, such as traffic flow anomaly detection and forecasting. Recently, low-rank tensor-based methods that characterize the global correlation of high-dimensional data have achieved superior performance. However, the majority of tensor-based approaches primarily account for the global correlation within the target traffic data, which is not sufficient to recover some challenging missing scenarios, such as fiber missing and slice missing that often occur in real situations. In this manuscript, we suggest a flexible method to explore the global correlation, local smoothness, and nonlocal self-similar redundancy in traffic data to improve recovery accuracy. Specifically, we utilize the multidimensional tensor nuclear norm to characterize the correlation structure, the multidimensional total variation to maintain smoothness detail, and the plug-and-play term to promote nonlocal self-similarity. The primary merits of this model lie in the fact that these priors characterize data features from different perspectives and complement each other. We develop an alternating direction method of multipliers to achieve efficient optimization for each variable. The proposed method is comprehensively evaluated through experiments across seven missing scenarios. Extensive experiments demonstrate that the suggested method with the aid of different priors outperforms many state-of-the-art approaches, especially structured missing scenarios.

Spatiotemporal traffic data is vitally important in intelligent transportation systems, but traffic data values are inevitably missing due to malfunctions in sensing devices or transmission networks. This will cause trouble for the subsequent traffic flow prediction work. Low-rank tensor imputation methods have recently received increasing attention to traffic data imputation due to their ability to capture the spatial-temporal information in the way of multi-dimension. However, traffic data often encounters challenging multimodal missing scenarios, including random missing, fiber missing, and slice missing. Thus, only accounting for the global low-rankness of traffic data is less sufficient to recover missing data. Motivated by the local smoothness of traffic data, we introduce the hybrid total variation into spatiotemporal traffic data imputation framework. The proposed model consists of the tensor nuclear norm, the first-order and the second-order total variation, which presents the global low-rankness and local smoothness prior, respectively. We utilize the ADMM to effectively solve the proposed model and establish the theoretical guarantee. Numerous experiments on two real-world datasets under three multimodal missing scenarios indicate that we proposed method outperforms some state-of-the-art traffic data imputation methods, especially for fiber missing and slice missing.

Seismic data contain a lot of information in both spatial (t-x) and frequency domains. In order to make full use of the effective information in multiple domains, this letter proposes a low-rank tensor minimization method for seismic data denoising. This model first uses variational mode decomposition (VMD) to decompose the seismic data in the frequency domain and constructs a seismic tensor to highlight the frequency information of the seismic data; then to make use of the spatial similarity and frequency correlation of the seismic tensor, a low rank seismic tensor is built through block matching and a low-rank tensor minimization model is established to attenuate the noise. Finally, the denoised seismic tensor is reconstructed into a seismic section. Experimental results show that compared with several denoising methods, the method proposed in this letter can obtain higher signal-to-noise ratio (SNR) and structural similarity (SSIM) and achieve better denoising effects.

Seismic data denoising is an important part of seismic data processing and has attracted much attention in recent years. With the rapid development of neural networks, convolutional neural network (CNN)-based denoising methods have been widely studied and used in seismic data denoising due to their unique convolutional layer and weight sharing characteristics. However, the existing CNN-based seismic data denoising methods mainly use fixed-size convolution kernels in a certain layer, which forces the different kernels to extract features from areas of the same size and fails to extract features from various granularities. To overcome this limitation, we make full use of the local similarity of seismic sections, use different sizes of convolution kernels to parallelly extract features from different granularities, and propose a multigranularity feature fusion CNN (MFFCNN) method to remove random noise from seismic data. This method uses convolution kernels with different sizes to extract features from various granularities and uses feature fusion structures to fuse the extracted features. Experimental results show that the MFFCNN proposed in this article can better deal with details and texture information than the compared methods.

In order to remove random noise in seismic data, this letter proposes a seismic data denoising method based on tensor decomposition and total variation (TDTV). Based on the self-similarity of seismic data, this method first groups similar patches into a stack, then utilizes the low-rank tensor approximation strategy to restore the structural effective information of the seismic section. Considering that the approximate seismic section obtained after CANDECOMP/PARAFAC (CP) decomposition and patch aggregation is unsmooth, this letter introduces the total variation (TV) constraint to perform anisotropic diffusion, and protects edge information while smoothing. Finally, the gradient descent method is used to solve the whole model. The TDTV method proposed in this letter can not only effectively denoise synthetic and field seismic section but also restore structural and edge information. Experimental results show that the proposed method outperforms many state-of-the-art denoising methods.

In this letter, we combine anisotropic and isotropic diffusion models and establish a combined energy variational model for seismic denoising. We propose a dynamic threshold to separate seismic sections into different feature areas and to choose different diffusion methods more precisely according to the characteristics of the seismic sections. Multilevel noise and multilevel edges can be treated automatically. Denoised results from a synthetic model and from field seismic sections demonstrate that our proposed model can suppress random noise and preserve the features of seismic sections efficiently.

Reconstruction from only a limited number of projections is an important problem in medical imaging. In this paper, a novel kernel-based limited-view CT reconstruction method is proposed. First based on the classical FDK algorithm, we derive the reconstruction kernel. Then the FDK kernel is truncated to reduce the noises aroused by the oscillations of the kernel. And a novel anisotropic diffusion model is introduced to suppress the artifacts and noise. Finally, several reconstruction experiments are presented to verify the efficiency and accuracy of proposed method.