Jigen Peng

Junxiong Jia, Jigen Peng, Jinghuai Gao et al.

In this paper, we consider a backward problem for a time-space fractional diffusion process. For this problem, we propose to construct the initial data by minimizing data residual error in fourier space domain and variable total variation (TV) regularizing term which can protect the edges as TV regularizing term and reduce staircasing effect. The well-posedness of this optimization problem is studied under a very general setting. Actually, we write the time-space fractional diffusion equation as an abstract fractional differential equation and get our results by using fractional semigroup theory, so our results can be applied to other backward problems for more general fractional differential equations. Then a modified Bregman iterative algorithm is proposed to approximate the minimizer. The new features of this algorithm is that the regularizing term changed in each step and we need not to solve the complexed Euler-Lagrange equations of variable TV regularizing term (just need to solve a simpler Euler-Lagrange equations). The convergence of this algorithm and the strategy of choosing parameters are also obtained. Numerical implementations are given to support our analysis to show the flexibility of our minimization model.

Hongxin Wang, Zhiyan Zhong, Fang Lei et al.

Feedback is crucial to motion perception in animals' visual systems where its spatial and temporal dynamics are often shaped by movement patterns of surrounding environments. However, such spatio-temporal feedback has not been deeply explored in designing neural networks to detect small moving targets that cover only one or a few pixels in image while presenting extremely limited visual features. In this paper, we address small target motion detection problem by developing a visual system with spatio-temporal feedback loop, and further reveal its important roles in suppressing false positive background movement while enhancing network responses to small targets. Specifically, the proposed visual system is composed of two complementary subnetworks. The first subnetwork is designed to extract spatial and temporal motion patterns of cluttered backgrounds by neuronal ensemble coding. The second subnetwork is developed to capture small target motion information and integrate the spatio-temporal feedback signal from the first subnetwork to inhibit background false positives. Experimental results demonstrate that the proposed spatio-temporal feedback visual system is more competitive than existing methods in discriminating small moving targets from complex dynamic environment.

Junxiong Jia, Bangyu Wu, Jigen Peng et al.

This paper is concerned with the modeling errors appeared in the numerical methods of inverse medium scattering problems (IMSP). Optimization based iterative methods are wildly employed to solve IMSP, which are computationally intensive due to a series of Helmholtz equations need to be solved numerically. Hence, rough approximations of Helmholtz equations can significantly speed up the iterative procedure. However, rough approximations will lead to instability and inaccurate estimations. Using the Bayesian inverse methods, we incorporate the modelling errors brought by the rough approximations. Modelling errors are assumed to be some complex Gaussian mixture (CGM) random variables, and in addition, well-posedness of IMSP in the statistical sense has been established by extending the general theory to involve CGM noise. Then, we generalize the real valued expectation-maximization (EM) algorithm used in the machine learning community to our complex valued case to learn parameters in the CGM distribution. Based on these preparations, we generalize the recursive linearization method (RLM) to a new iterative method named as Gaussian mixture recursive linearization method (GMRLM) which takes modelling errors into account. Finally, we provide two numerical examples to illustrate the effectiveness of the proposed method.

Mingshuo Xu, Hao Luan, Zhou Daniel Hao et al.

Recognizing motions of tiny targets - only few dozen pixels - in cluttered backgrounds remains a fundamental challenge when standard feature-based or deep learning methods fail under scarce visual cues. We propose STMDNet, a model-based computational framework to Recognize motions of tiny targets at variable velocities under low-sampling frequency scenarios. STMDNet designs a novel dual-dynamics-and-correlation mechanism, harnessing ipsilateral excitation to integrate target cues and leakage-enhancing-type contralateral inhibition to suppress large-object and background motion interference. Moreover, we develop the first collaborative directional encoding-decoding strategy that determines the motion direction from only one correlation per spatial location, cutting computational costs to one-eighth of prior methods. Further, simply substituting the backbone of a strong STMD model with STMDNet raises AUC by 24%, yielding an enhanced STMDNet-F. Evaluations on real-world low sampling frequency datasets show state-of-the-art results, surpassing the deep learning baseline. Across diverse speeds, STMDNet-F improves mF1 by 19%, 16%, and 8% at 240Hz, 120Hz, and 60Hz, respectively, while STMDNet achieves 87 FPS on a single CPU thread. These advances highlight STMDNet as a next-generation backbone for tiny target motion pattern recognition and underscore its broader potential to revitalize model-based visual approaches in motion detection.

Ziyan Qin, Jigen Peng, Shigang Yue et al.

Compared to human vision, locust visual systems excel at rapid and precise collision detection, despite relying on only hundreds of thousands of neurons organized through a few neuropils. This efficiency makes them an attractive model system for developing artificial collision-detecting systems. Specifically, researchers have identified collision-selective neurons in the locust's optic lobe, called lobula giant movement detectors (LGMDs), which respond specifically to approaching objects. Research upon LGMD neurons began in the early 1970s. Initially, due to their large size, these neurons were identified as motion detectors, but their role as looming detectors was recognized over time. Since then, progress in neuroscience, computational modeling of LGMD's visual neural circuits, and LGMD-based robotics have advanced in tandem, each field supporting and driving the others. Today, with a deeper understanding of LGMD neurons, LGMD-based models have significantly improved collision-free navigation in mobile robots including ground and aerial robots. This review highlights recent developments in LGMD research from the perspectives of neuroscience, computational modeling, and robotics. It emphasizes a biologically plausible research paradigm, where insights from neuroscience inform real-world applications, which would in turn validate and advance neuroscience. With strong support from extensive research and growing application demand, this paradigm has reached a mature stage and demonstrates versatility across different areas of neuroscience research, thereby enhancing our understanding of the interconnections between neuroscience, computational modeling, and robotics. Furthermore, this paradigm would shed light upon the modeling and robotic research into other motion-sensitive neurons or neural circuits.

Qinbing Fu, Tian Liu, Xuelong Sun et al.

Visual dynamic complexity is a ubiquitous, hidden attribute of the visual world that every dynamic vision system is faced with. However, it is implicit and intractable which has never been quantitatively described due to the difficulty in defending temporal features correlated to spatial image complexity. To fill this vacancy, we propose a novel bio-robotic approach to profile visual dynamic complexity which can be used as a new metric. Here we apply a state-of-the-art brain-inspired motion detection neural network model to explicitly profile such complexity associated with spatial-temporal frequency (SF-TF) of visual scene. This model is for the first time implemented in an autonomous micro-mobile robot which navigates freely in an arena with visual walls displaying moving sine-wave grating or cluttered natural scene. The neural dynamic response can make reasonable prediction on surrounding complexity since it can be mapped monotonically to varying SF-TF of visual scene. The experiments show this approach is flexible to different visual scenes for profiling the dynamic complexity. We also use this metric as a predictor to investigate the boundary of another collision detection visual system performing in changing environment with increasing dynamic complexity. This research demonstrates a new paradigm of using biologically plausible visual processing scheme to estimate dynamic complexity of visual scene from both spatial and temporal perspectives, which could be beneficial to predicting input complexity when evaluating dynamic vision systems.

Hongxin Wang, Jiannan Zhao, Huatian Wang et al.

Small target motion detection within complex natural environments is an extremely challenging task for autonomous robots. Surprisingly, the visual systems of insects have evolved to be highly efficient in detecting mates and tracking prey, even though targets occupy as small as a few degrees of their visual fields. The excellent sensitivity to small target motion relies on a class of specialized neurons called small target motion detectors (STMDs). However, existing STMD-based models are heavily dependent on visual contrast and perform poorly in complex natural environments where small targets generally exhibit extremely low contrast against neighbouring backgrounds. In this paper, we develop an attention and prediction guided visual system to overcome this limitation. The developed visual system comprises three main subsystems, namely, an attention module, an STMD-based neural network, and a prediction module. The attention module searches for potential small targets in the predicted areas of the input image and enhances their contrast against complex background. The STMD-based neural network receives the contrast-enhanced image and discriminates small moving targets from background false positives. The prediction module foresees future positions of the detected targets and generates a prediction map for the attention module. The three subsystems are connected in a recurrent architecture allowing information to be processed sequentially to activate specific areas for small target detection. Extensive experiments on synthetic and real-world datasets demonstrate the effectiveness and superiority of the proposed visual system for detecting small, low-contrast moving targets against complex natural environments.

Hongxin Wang, Huatian Wang, Jiannan Zhao et al.

Discriminating small moving objects within complex visual environments is a significant challenge for autonomous micro robots that are generally limited in computational power. By exploiting their highly evolved visual systems, flying insects can effectively detect mates and track prey during rapid pursuits, even though the small targets equate to only a few pixels in their visual field. The high degree of sensitivity to small target movement is supported by a class of specialized neurons called small target motion detectors (STMDs). Existing STMD-based computational models normally comprise four sequentially arranged neural layers interconnected via feedforward loops to extract information on small target motion from raw visual inputs. However, feedback, another important regulatory circuit for motion perception, has not been investigated in the STMD pathway and its functional roles for small target motion detection are not clear. In this paper, we propose an STMD-based neural network with feedback connection (Feedback STMD), where the network output is temporally delayed, then fed back to the lower layers to mediate neural responses. We compare the properties of the model with and without the time-delay feedback loop, and find it shows preference for high-velocity objects. Extensive experiments suggest that the Feedback STMD achieves superior detection performance for fast-moving small targets, while significantly suppressing background false positive movements which display lower velocities. The proposed feedback model provides an effective solution in robotic visual systems for detecting fast-moving small targets that are always salient and potentially threatening.

Hongxin Wang, Jigen Peng, Xuqiang Zheng et al.

Monitoring small objects against cluttered moving backgrounds is a huge challenge to future robotic vision systems. As a source of inspiration, insects are quite apt at searching for mates and tracking prey -- which always appear as small dim speckles in the visual field. The exquisite sensitivity of insects for small target motion, as revealed recently, is coming from a class of specific neurons called small target motion detectors (STMDs). Although a few STMD-based models have been proposed, these existing models only use motion information for small target detection and cannot discriminate small targets from small-target-like background features (named as fake features). To address this problem, this paper proposes a novel visual system model (STMD+) for small target motion detection, which is composed of four subsystems -- ommatidia, motion pathway, contrast pathway and mushroom body. Compared to existing STMD-based models, the additional contrast pathway extracts directional contrast from luminance signals to eliminate false positive background motion. The directional contrast and the extracted motion information by the motion pathway are integrated in the mushroom body for small target discrimination. Extensive experiments showed the significant and consistent improvements of the proposed visual system model over existing STMD-based models against fake features.

Huatian Wang, Qinbing Fu, Hongxin Wang et al.

Insects use visual cues to control their flight behaviours. By estimating the angular velocity of the visual stimuli and regulating it to a constant value, honeybees can perform a terrain following task which keeps the certain height above the undulated ground. For mimicking this behaviour in a bio-plausible computation structure, this paper presents a new angular velocity decoding model based on the honeybee's behavioural experiments. The model consists of three parts, the texture estimation layer for spatial information extraction, the motion detection layer for temporal information extraction and the decoding layer combining information from pervious layers to estimate the angular velocity. Compared to previous methods on this field, the proposed model produces responses largely independent of the spatial frequency and contrast in grating experiments. The angular velocity based control scheme is proposed to implement the model into a bee simulated by the game engine Unity. The perfect terrain following above patterned ground and successfully flying over irregular textured terrain show its potential for micro unmanned aerial vehicles' terrain following.

Hongxin Wang, Jigen Peng, Qinbing Fu et al.

The robust detection of small targets against cluttered background is important for future artificial visual systems in searching and tracking applications. The insects' visual systems have demonstrated excellent ability to avoid predators, find prey or identify conspecifics - which always appear as small dim speckles in the visual field. Build a computational model of the insects' visual pathways could provide effective solutions to detect small moving targets. Although a few visual system models have been proposed, they only make use of small-field visual features for motion detection and their detection results often contain a number of false positives. To address this issue, we develop a new visual system model for small target motion detection against cluttered moving backgrounds. Compared to the existing models, the small-field and wide-field visual features are separately extracted by two motion-sensitive neurons to detect small target motion and background motion. These two types of motion information are further integrated to filter out false positives. Extensive experiments showed that the proposed model can outperform the existing models in terms of detection rates.

Angang Cui, Meng Wen, Haiyang Li et al.

In this paper, we develop a nonconvex approach to the problem of low-rank and sparse matrix decomposition. In our nonconvex method, we replace the rank function and the $l_{0}$-norm of a given matrix with a non-convex fraction function on the singular values and the elements of the matrix respectively. An alternative direction method of multipliers algorithm is utilized to solve our proposed nonconvex problem with the nonconvex fraction function penalty. Numerical experiments on some low-rank and sparse matrix decomposition problems show that our method performs very well in recovering low-rank matrices which are heavily corrupted by large sparse errors.

Hongxin Wang, Jigen Peng, Shigang Yue

Small target motion detection is critical for insects to search for and track mates or prey which always appear as small dim speckles in the visual field. A class of specific neurons, called small target motion detectors (STMDs), has been characterized by exquisite sensitivity for small target motion. Understanding and analyzing visual pathway of STMD neurons are beneficial to design artificial visual systems for small target motion detection. Feedback loops have been widely identified in visual neural circuits and play an important role in target detection. However, if there exists a feedback loop in the STMD visual pathway or if a feedback loop could significantly improve the detection performance of STMD neurons, is unclear. In this paper, we propose a feedback neural network for small target motion detection against naturally cluttered backgrounds. In order to form a feedback loop, model output is temporally delayed and relayed to previous neural layer as feedback signal. Extensive experiments showed that the significant improvement of the proposed feedback neural network over the existing STMD-based models for small target motion detection.

Hongxin Wang, Jigen Peng, Shigang Yue

A class of specialized neurons, called lobula plate tangential cells (LPTCs) has been shown to respond strongly to wide-field motion. The classic model, elementary motion detector (EMD) and its improved model, two-quadrant detector (TQD) have been proposed to simulate LPTCs. Although EMD and TQD can percept background motion, their outputs are so cluttered that it is difficult to discriminate actual motion direction of the background. In this paper, we propose a max operation mechanism to model a newly-found transmedullary neuron Tm9 whose physiological properties do not map onto EMD and TQD. This proposed max operation mechanism is able to improve the detection performance of TQD in cluttered background by filtering out irrelevant motion signals. We will demonstrate the functionality of this proposed mechanism in wide-field motion perception.

Hongxin Wang, Jigen Peng, Shigang Yue

Discriminating targets moving against a cluttered background is a huge challenge, let alone detecting a target as small as one or a few pixels and tracking it in flight. In the fly's visual system, a class of specific neurons, called small target motion detectors (STMDs), have been identified as showing exquisite selectivity for small target motion. Some of the STMDs have also demonstrated directional selectivity which means these STMDs respond strongly only to their preferred motion direction. Directional selectivity is an important property of these STMD neurons which could contribute to tracking small targets such as mates in flight. However, little has been done on systematically modeling these directional selective STMD neurons. In this paper, we propose a directional selective STMD-based neural network (DSTMD) for small target detection in a cluttered background. In the proposed neural network, a new correlation mechanism is introduced for direction selectivity via correlating signals relayed from two pixels. Then, a lateral inhibition mechanism is implemented on the spatial field for size selectivity of STMD neurons. Extensive experiments showed that the proposed neural network not only is in accord with current biological findings, i.e. showing directional preferences, but also worked reliably in detecting small targets against cluttered backgrounds.

Yingtong Chen, Jigen Peng

The letter presents a method for the reduction in the mutual coherence of an overcomplete Gaussian or Bernoulli random matrix, which is fairly small due to the lower bound given here on the probability of the event that the aforesaid mutual coherence is less than any given number in (0, 1). The mutual coherence of the matrix that belongs to a set which contains the two types of matrices with high probability can be reduced by a similar method but a subset that has Lebesgue measure zero. The numerical results are provided to illustrate the reduction in the mutual coherence of an overcomplete Gaussian, Bernoulli or uniform random dictionary. The effect on the third type is better than a former result.