In this paper, we study the minimization problem of a non-convex sparsity-promoting penalty function, i.e., fraction function, in compressed sensing. First, we discuss the equivalence of ℓ₀ minimization and fraction function minimization. It is proved that the optimal solution to fraction function minimization solves ℓ₀ minimization and the optimal solution to the regularization problem also solves fraction function minimization if the certain conditions are satisfied, which is similar to the regularization problem in a convex optimization theory. Second, we study the properties of the optimal solution to the regularization problem, including the first-order and second-order optimality conditions and the lower and upper bounds of the absolute value for its nonzero entries. Finally, we derive the closed-form representation of the optimal solution to the regularization problem and propose an iterative FP thresholding algorithm to solve the regularization problem. We also provide a series of experiments to assess the performance of the FP algorithm, and the experimental results show that the FP algorithm performs well in sparse signal recovery with and without measurement noise.

In this paper, the cross-flow vortex-induced vibration (VIV) response of a top tension riser under different flow fields are comprehensively studied using a numerical simulation model based on time domain analysis. A semi-empirical time-domain analysis model that considers the fluid-structure interaction problem in the riser vibration process is proposed and verified by comparison with the previous experimental results. The influence of the flow velocity, the spanwise length of the flow field, and other factors on the VIV amplitude and frequency characteristics of the riser is analyzed in detail. The results show that the VIV response of the riser exhibits obvious multi-modal characteristics, which are accompanied by modal transition, lock-in vibration, synchronous vibration, etc., and the region where the lock-in or synchronous vibration occurs is exactly the region where the crest of the amplitude curve locates. Besides, the VIV intensity of the riser in the stepped flow and uniform flow fields show a tendency of fluctuating increase with the increase of the flow velocity and spanwise length of the flow field, while the VIV intensity of the riser in shear flow is positively correlated with the flow velocity and spanwise length of the flow field. The present study may provide a reference for the prediction of VIV of marine riser in the complex current environment.

Recently there have been renewed interests in high order neural networks (HONNs) for its powerful mapping capability. Ridge polynomial neural network (RPNN) is an important kind of HONNs, which always occupies a key position as an efficient instrument in the tasks of classification or regression. In order to make the convergence speed faster and the network generalization ability stronger, we introduce a regularization model for RPNN with Group Lasso penalty, which deals with the structural sparse problem at the group level in this paper. Nevertheless, there are two main obstacles for introducing the Group Lasso penalty, one is numerical oscillation and the other is convergence analysis challenge. In doing so, we adopt smoothing function to approximate the Group Lasso penalty to overcome these drawbacks. Meanwhile, strong and weak convergence theorems, and monotonicity theorems are provided for this novel algorithm. We also demonstrate the efficiency of our proposed algorithm by numerical experiments, and compare it to the no regularizer, L2 regularizer, L1/2 regularizer, smoothing L1/2 regularizer, and the Group Lasso regularizer, and also the relevant theoretical analysis has been verified.

Introduction: Lobular giant motion detector (LGMD) neurons, renowned for their distinctive response to looming stimuli, inspire the development of visual neural network models for collision prediction. However, the existing LGMD-based models could not yet incorporate the invaluable feature of depth distance and still suffer from the following two primary drawbacks. Firstly, they struggle to effectively distinguish the three fundamental motion patterns of approaching, receding, and translating, in contrast to the natural abilities of LGMD neurons. Secondly, due to their reliance on a general determination process employing an activation function and fixed threshold for output, these models exhibit dramatic fluctuations in prediction effectiveness across different scenarios.Methods: To address these issues, we propose a novel LGMD-based model with a binocular structure (Bi-LGMD). The depth distance of the moving object is extracted by calculating the binocular disparity facilitating a clear differentiation of the motion patterns, after obtaining the moving object's contour through the basic components of the LGMD network. In addition, we introduce a self-adaptive warning depth-distance, enhancing the model's robustness in various motion scenarios.Results: The effectiveness of the proposed model is verified using computer-simulated and real-world videos.Discussion: Furthermore, the experimental results demonstrate that the proposed model is robust to contrast and noise.

Building an efficient and reliable small target motion detection visual system is challenging for artificial intelligence robotics because a small target only occupies few pixels and hardly displays visual features in images. Biological visual systems that have evolved over millions of years could be ideal templates for designing artificial visual systems. Insects benefit from a class of specialized neurons, called small target motion detectors (STMDs), which endow them with an excellent ability to detect small moving targets against a cluttered dynamic environment. Some bio-inspired models featured in feed-forward information processing architectures have been proposed to imitate the functions of the STMD neurons. However, feedback, a crucial mechanism for visual system regulation, has not been investigated deeply in the STMD-based neural circuits and its roles in small target motion detection remain unclear. In this paper, we propose a time-delay feedback STMD model for small target motion detection in complex backgrounds. The main contributions of this study are as follows. First, a feedback pathway is designed by transmitting information from output-layer neurons to lower-layer interneurons in the STMD pathway and the role of the feedback is analyzed from the view of mathematical analysis. Second, to estimate the feedback constant, the existence and uniqueness of solutions for nonlinear dynamical systems formed by feedback loop are analyzed via Schauder's fixed point theorem and contraction mapping theorem. Finally, an iterative algorithm is designed to solve the nonlinear problem and the performance of the proposed model is tested by experiments. Experimental results demonstrate that the feedback is able to weaken background false positives while maintaining a minor effect on small targets. It outperforms existing STMD-based models regarding the accuracy of fast-moving small target detection in visual clutter. The proposed feedback approach could inspire the relevant modeling of robust motion perception robotics visual systems.