Deep learning performs remarkably well on many time series analysis tasks recently. The superior performance of deep neural networks relies heavily on a large number of training data to avoid overfitting. However, the labeled data of many real-world time series applications may be limited such as classification in medical time series and anomaly detection in AIOps. As an effective way to enhance the size and quality of the training data, data augmentation is crucial to the successful application of deep learning models on time series data. In this paper, we systematically review different data augmentation methods for time series. We propose a taxonomy for the reviewed methods, and then provide a structured review for these methods by highlighting their strengths and limitations. We also empirically compare different data augmentation methods for different tasks including time series classification, anomaly detection, and forecasting. Finally, we discuss and highlight five future directions to provide useful research guidance.

Decomposing complex time series into trend, seasonality, and remainder components is an important task to facilitate time series anomaly detection and forecasting. Although numerous methods have been proposed, there are still many time series characteristics exhibiting in real-world data which are not addressed properly, including 1) ability to handle seasonality fluctuation and shift, and abrupt change in trend and reminder; 2) robustness on data with anomalies; 3) applicability on time series with long seasonality period. In the paper, we propose a novel and generic time series decomposition algorithm to address these challenges. Specifically, we extract the trend component robustly by solving a regression problem using the least absolute deviations loss with sparse regularization. Based on the extracted trend, we apply the the non-local seasonal filtering to extract the seasonality component. This process is repeated until accurate decomposition is obtained. Experiments on different synthetic and real-world time series datasets demonstrate that our method outperforms existing solutions.

Extracting the underlying trend signal is a crucial step to facilitate time series analysis like forecasting and anomaly detection. Besides noise signal, time series can contain not only outliers but also abrupt trend changes in real-world scenarios. To deal with these challenges, we propose a robust trend filtering algorithm based on robust statistics and sparse learning. Specifically, we adopt the Huber loss to suppress outliers, and utilize a combination of the first order and second order difference on the trend component as regularization to capture both slow and abrupt trend changes. Furthermore, an efficient method is designed to solve the proposed robust trend filtering based on majorization minimization (MM) and alternative direction method of multipliers (ADMM). We compared our proposed robust trend filter with other nine state-of-the-art trend filtering algorithms on both synthetic and real-world datasets. The experiments demonstrate that our algorithm outperforms existing methods.

Convolutional neural networks (CNN) have successfully been employed to tackle several remote sensing tasks such as image classification and show better performance than previous techniques. For the radar imaging community, a natural question is: Can CNN be introduced to radar imaging and enhance its performance? This letter gives an affirmative answer to this question. We first propose a processing framework by which a complex-valued CNN (CV-CNN) is used to enhance radar imaging. Then we introduce two modifications to the CV-CNN to adapt it to radar imaging tasks. Subsequently, the method to generate training data is shown and some implementation details are presented. Finally, simulations and experiments are carried out, and both results show the superiority of the proposed method on imaging quality and computational efficiency.

Recently, millimeter-wave (MMW) 3D holography techniques employing a scanning 1D multiple input multiple output (MIMO) array have shown several superiorities for short-range applications than traditional single input single output (SISO) ones. However, current imaging algorithms for this emerging regime are not satisfied, either too slow as a back projection (BP) manner is used or of poor quality since several steps of approximations are introduced. In this paper, two fast fully-focused imaging algorithms are developed towards fixing these drawbacks. Both algorithms are based on the assumption that the receivers are evenly distributed. The first algorithm further hypothesizes that the transmitters are also evenly located, while the second algorithm needs looser restrictions that the transmitters can be arbitrarily positioned. The frequency domain expressions of the modified Kirchhoff method are also derived and used to promote the precision of the proposed algorithms. In addition, several implementation issues including resolution, sampling criteria and computational complexity are discussed. Finally, both simulation and experimental results validate the effectiveness of the proposed methods on reconstruction quality and computational efficiency.

A novel 3-D surface imaging method based on terahertz (THz) dual-frequency interferometry is proposed for the detection and imaging of metal objects. The interferometer is formed first in the range direction with two azimuth–elevation images at different THz frequencies. Then, the 3-D surface image can be obtained by interference processing of two azimuth–elevation imaging results. Compared with the traditional wideband 3-D imaging, the proposed method can avoid the nonlinear error caused by the signal nonlinearity. In addition, the image registration for the interference processing is evitable, when the frequency difference satisfies certain conditions. Based on the electromagnetic calculation data, the 3-D surface imaging results of both rough cone and rough cube validate the effectiveness of the proposed method. Furthermore, the reconstruction error increases slightly with the increasing of the error of frequency difference, which indicates that the proposed method has a good tolerance with respect to frequency instability.