Owing to the limitations of the imaging principle as well as the properties of imaging systems, infrared images often have some drawbacks, including low resolution, a lack of detail, and indistinct edges. Therefore, it is essential to improve infrared image quality. Considering the information of neighbors, a description of sparse edges, and by avoiding staircase artifacts, a new super-resolution reconstruction (SRR) method is proposed for infrared images, which is based on fractional order total variation (FTV) with quaternion total variation and the $L_p$ quasinorm. Our proposed method improves the sparsity exploitation of FTV, and efficiently preserves image structures. Furthermore, we adopt the plug-and-play alternating direction method of multipliers (ADMM) and the fast Fourier transform (FFT) theory for the proposed method to improve the efficiency and robustness of our algorithm; in addition, an accelerated step is adopted. Our experimental results show that the proposed method leads to excellent performances in terms of an objective evaluation and the subjective visual effect.

Thermal infrared (TIR) target tracking is a challenging task as it entails learning an effective model to identify the target in the situation of poor target visibility and clutter background. The sparse representation, as a typical appearance modeling approach, has been successfully exploited in the TIR target tracking. However, the discriminative information of the target and its surrounding background is usually neglected in the sparse coding process. To address this issue, we propose a mask sparse representation (MaskSR) model, which combines sparse coding together with high-level semantic features for TIR target tracking. We first obtain the pixel-wise labeling results of the target and its surrounding background in the last frame, and then use such results to train target-specific deep networks using a supervised manner. According to the output features of the deep networks, the high-level pixel-wise discriminative map of the target area is obtained. We introduce the binarized discriminative map as a mask template to the sparse representation and develop a novel algorithm to collaboratively represent the reliable target part and unreliable target part partitioned with the mask template, which explicitly indicates different discriminant capabilities by label 1 and 0. The proposed MaskSR model controls the superiority of the reliable target part in the reconstruction process via a weighted scheme. We solve this multi-parameter constrained problem by a customized alternating direction method of multipliers (ADMM) method. This model is applied to achieve TIR target tracking in the particle filter framework. To improve the sampling effectiveness and decrease the computation cost at the same time, a discriminative particle selection strategy based on kernelized correlation filter is proposed to replace the previous random sampling for searching useful candidates. Our proposed tracking method was tested on the VOT-TIR2016 benchmark. The experiment results show that the proposed method has a significant superiority compared with various state-of-the-art methods in TIR target tracking.

The anisotropic total variation with overlapping group sparsity (ATV_OGS) regularisation term is an improvement on the anisotropic total variation (ATV) regularisation term. It has been employed successfully in seismic impedance inversion as it can enhance the boundary information and relieve the staircase effect by exploring the structured sparsity of seismic impedance. However, because ATV_OGS constrains only the structured sparsity of the impedance's first-order difference and ignores the structured sparsity of the second-order difference, the staircase effect still occurs in an inversion result based on ATV_OGS. To further fit the structured sparsity of the impedance's second-order gradients, we introduce the overlapping group sparsity into the second-order difference of the impedance and propose a novel second-order ATV with overlapping group sparsity (SATV_OGS) seismic impedance inversion method. The proposed method reduces the interference of the large amplitude noise and further mitigates the staircase effect of the ATV_OGS. Furthermore, the accelerated alternating direction method of multipliers (A-ADMM) framework applied to this novel method. It can increase the efficiency of inversion. The experiments are carried out on a general model data and field data. Based on the experimental results, the proposed method can obtain higher resolution impedance than some impedance inversion methods based on total variation.

Seismic acoustic impedance (AI) inversion is widely used in geophysics as AI can indicate rock characteristics and facilitate stratigraphic analysis. However, traditional AI inversion suffers from a multi-solution problem. To overcome this barrier, anisotropic total p-variation (ATpV) regularization has been applied in inversion as it can improve the accuracy by Lp quasi-norm. Nevertheless, this regularization results in the staircase effect and the scattering effect. To reduce these two effects, we introduced the mixed second-order variations and the fractional difference in AI inversion based on ATpV and proposed a novel AI inversion method using mixed second-order fractional anisotropic total p-variation (MSFATpV) regularization. Moreover, the alternating direction method of multipliers (ADMM) algorithm is used to build the inversion framework. Numerical experiments demonstrate that the fractional difference and the mixed second-order variant can reduce the staircase and scattering effects. The proposed method reduces the multiplicity and improves the accuracy than some state-of-the-art methods based on anisotropic total variation (ATV).

Rolling bearings are important components of rotating machines. For their preventive maintenance, it is not enough to know whether there is any fault or the fault type. For an effective maintenance, a fault severity monitoring needs to be conducted. Currently, the bearing fault diagnosis method based on time–frequency image (TFI) recognition is attracting increasing attention. This paper contributes to the ongoing investigation by proposing a new approach for the fault severity monitoring of rolling bearings based on the texture feature extraction of sparse TFIs. The first and main step is to obtain accurate TFIs from the vibration signals of rolling bearings. Traditional time–frequency analysis methods have disadvantages such as low resolution and cross-term interference. Therefore, the TFIs obtained cannot satisfactorily express the time–frequency characteristics of bearing vibration signals. To solve this problem, a sparse time–frequency analysis method based on the first-order primal-dual algorithm (STFA-PD) was developed in this paper. Unlike traditional time–frequency analysis methods, the time–frequency analysis model of the STFA-PD method is based on the theory of sparse representation, and is solved using the first-order primal-dual algorithm. For employing the sparse constraint in the frequency domain, the STFA-PD obtains a higher time–frequency resolution and is free from cross-term interference, as the model is based on a linear time–frequency analysis method. The gray level co-occurrence matrix is then employed to extract texture features from the sparse TFIs as input features for classifiers. Vibration signals of rolling bearings with different fault severity degrees are used to validate the proposed approach. The experimental results show that the developed STFA-PD outperforms traditional time–frequency analysis methods in terms of the accuracy and effectiveness for the fault severity monitoring of rolling bearings.