arXiv subjects

Jigen Peng

Publications and source records attributed to Jigen Peng.

At least 37 records · Page 2Linked to original sources

arXiv2019

An adaptive augmented regularization method and its applications

Regularization method and Bayesian inverse method are two dominating ways for solving inverse problems generated from various fields, e.g., seismic exploration and medical imaging. The two methods are related with each other by the MAP estimates of posterior probability distributions. Considering this connection, we construct a prior probability distribution with several hyper-parameters and provide the relevant Bayes' formula, then we propose a corresponding adaptive augmented regularization model (AARM). According to the measured data, the proposed AARM can adjust its form to various regularization models at each discrete point of the estimated function, which makes the characterization of local smooth properties of the estimated function possible. By proposing a modified Bregman iterative algorithm, we construct an alternate iterative algorithm to solve the AARM efficiently. In the end, we provide some numerical examples which clearly indicate that the proposed AARM can generates a favorable result for some examples compared with several Tikhonov and Total-Variation regularization models.

math.NA↗

arXiv2019

Nonconvex fraction function recovery sparse signal by convex optimization algorithm

In this paper, we will generate a convex iterative FP thresholding algorithm to solve the problem $(FP^λ_{a})$. Two schemes of convex iterative FP thresholding algorithms are generated. One is convex iterative FP thresholding algorithm-Scheme 1 and the other is convex iterative FP thresholding algorithm-Scheme 2. A global convergence theorem is proved for the convex iterative FP thresholding algorithm-Scheme 1. Under an adaptive rule, the convex iterative FP thresholding algorithm-Scheme 2 will be adaptive both for the choice of the regularized parameter $λ$ and parameter $a$. These are the advantages for our two schemes of convex iterative FP thresholding algorithm compared with our previous proposed two schemes of iterative FP thresholding algorithm. At last, we provide a series of numerical simulations to test the performance of the convex iterative FP thresholding algorithm-Scheme 2, and the simulation results show that our convex iterative FP thresholding algorithm-Scheme 2 performs very well in recovering a sparse signal.

math.OC↗

arXiv2019

A non-convex approach to low-rank and sparse matrix decomposition

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.

math.OC↗

arXiv2019

A Robust Visual System for Small Target Motion Detection Against Cluttered Moving Backgrounds

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.

cs.CV↗

arXiv2019

Constant Angular Velocity Regulation for Visually Guided Terrain Following

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.

cs.RO↗

arXiv2019

Angular Velocity Estimation of Image Motion Mimicking the Honeybee Tunnel Centring Behaviour

Insects use visual information to estimate angular velocity of retinal image motion, which determines a variety of flight behaviours including speed regulation, tunnel centring and visual navigation. For angular velocity estimation, honeybees show large spatial-independence against visual stimuli, whereas the previous models have not fulfilled such an ability. To address this issue, we propose a bio-plausible model for estimating the image motion velocity based on behavioural experiments of the honeybee flying through patterned tunnels. The proposed model contains mainly three parts, the texture estimation layer for spatial information extraction, the delay-and-correlate layer for temporal information extraction and the decoding layer for angular velocity estimation. This model produces responses that are largely independent of the spatial frequency in grating experiments. And the model has been implemented in a virtual bee for tunnel centring simulations. The results coincide with both electro-physiological neuron spike and behavioural path recordings, which indicates our proposed method provides a better explanation of the honeybee's image motion detection mechanism guiding the tunnel centring behaviour.

q-bio.NC↗

arXiv2019

Visual Cue Integration for Small Target Motion Detection in Natural Cluttered Backgrounds

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.

cs.CV↗

arXiv2019

Recursive linearization method for inverse medium scattering problems with complex mixture Gaussian error learning

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.

math.NA↗

arXiv2018

A New Nonconvex Strategy to Affine Matrix Rank Minimization Problem

The affine matrix rank minimization (AMRM) problem is to find a matrix of minimum rank that satisfies a given linear system constraint. It has many applications in some important areas such as control, recommender systems, matrix completion and network localization. However, the problem (AMRM) is NP-hard in general due to the combinational nature of the matrix rank function. There are many alternative functions have been proposed to substitute the matrix rank function, which lead to many corresponding alternative minimization problems solved efficiently by some popular convex or nonconvex optimization algorithms. In this paper, we propose a new nonconvex function, namely, $TL_α^ε$ function (with $0\leqα<1$ and $ε>0$), to approximate the rank function, and translate the NP-hard problem (AMRM) into the $TL_{p}^ε$ function affine matrix rank minimization (TLAMRM) problem. Firstly, we study the equivalence of problem (AMRM) and (TLAMRM), and proved that the uniqueness of global minimizer of the problem (TLAMRM) also solves the NP-hard problem (AMRM) if the linear map $\mathcal{A}$ satisfies a restricted isometry property (RIP). Secondly, an iterative thresholding algorithm is proposed to solve the regularization problem (RTLAMRM) for all $0\leqα<1$ and $ε>0$. At last, some numerical results on low-rank matrix completion problems illustrated that our algorithm is able to recover a low-rank matrix, and the extensive numerical on image inpainting problems shown that our algorithm performs the best in finding a low-rank image compared with some state-of-art methods.

math.OC↗

arXiv2018

A Directionally Selective Small Target Motion Detecting Visual Neural Network in Cluttered Backgrounds

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.

cs.CV↗

arXiv2018

A Feedback Neural Network for Small Target Motion Detection in Cluttered Backgrounds

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.

cs.NE↗

arXiv2018

Exact recovery low-rank matrix via transformed affine matrix rank minimization

The goal of affine matrix rank minimization problem is to reconstruct a low-rank or approximately low-rank matrix under linear constraints. In general, this problem is combinatorial and NP-hard. In this paper, a nonconvex fraction function is studied to approximate the rank of a matrix and translate this NP-hard problem into a transformed affine matrix rank minimization problem. The equivalence between these two problems is established, and we proved that the uniqueness of the global minimizer of transformed affine matrix rank minimization problem also solves affine matrix rank minimization problem if some conditions are satisfied. Moreover, we also proved that the optimal solution to the transformed affine matrix rank minimization problem can be approximately obtained by solving its regularization problem for some proper smaller $λ>0$. Lastly, the DC algorithm is utilized to solve the regularization transformed affine matrix rank minimization problem and the numerical experiments on image inpainting problems show that our method performs effectively in recovering low-rank images compared with some state-of-art algorithms.

math.OC↗

arXiv2018

Modified lp-norm regularization minimization for sparse signal recovery

In numerous substitution models for the $ł_{0}$-norm minimization problem $(P_{0})$, the $ł_{p}$-norm minimization $(P_{p})$ with $0 0$, this modified function would like to interpolate the $ł_{p}$-norm $\|x\|_{p}^{p}$. By this transformation, we translated the $ł_{p}$-norm regularization minimization $(P_{p}^λ)$ into a modified $ł_{p}$-norm regularization minimization $(P_{p}^{λ,ε})$. Then, we develop the thresholding representation theory of the problem $(P_{p}^{λ,ε})$, and based on it, the IT algorithm is proposed to solve the problem $(P_{p}^{λ,ε})$ for all $0<p<1$. Indeed, we could get some much better results by choosing proper $p$, which is one of the advantages for our algorithm compared with other methods. Numerical results also show that, for some proper $p$, our algorithm performs the best in some sparse signal recovery problems compared with some state-of-art methods.

math.OC↗

arXiv2018

Iterative thresholding algorithm based on non-convex method for modified lp-norm regularization minimization

Recently, the $ł_{p}$-norm regularization minimization problem $(P_{p}^λ)$ has attracted great attention in compressed sensing. However, the $ł_{p}$-norm $\|x\|_{p}^{p}$ in problem $(P_{p}^λ)$ is nonconvex and non-Lipschitz for all $p\in(0,1)$, and there are not many optimization theories and methods are proposed to solve this problem. In fact, it is NP-hard for all $p\in(0,1)$ and $λ>0$. In this paper, we study two modified $ł_{p}$ regularization minimization problems to approximate the NP-hard problem $(P_{p}^λ)$. Inspired by the good performance of Half algorithm and $2/3$ algorithm in some sparse signal recovery problems, two iterative thresholding algorithms are proposed to solve the problems $(P_{p,1/2,ε}^λ)$ and $(P_{p,2/3,ε}^λ)$ respectively. Numerical results show that our algorithms perform effectively in finding the sparse signal in some sparse signal recovery problems for some proper $p\in(0,1)$.

math.OC↗

arXiv2018

Generalized singular value thresholding operator to affine matrix rank minimization problem

It is well known that the affine matrix rank minimization problem is NP-hard and all known algorithms for exactly solving it are doubly exponential in theory and in practice due to the combinational nature of the rank function. In this paper, a generalized singular value thresholding operator is generated to solve the affine matrix rank minimization problem. Numerical experiments show that our algorithm performs effectively in finding a low-rank matrix compared with some state-of-art methods.

math.OC↗

arXiv2018

Sparse Portfolio Selection via Non-convex Fraction Function

In this paper, a continuous and non-convex promoting sparsity fraction function is studied in two sparse portfolio selection models with and without short-selling constraints. Firstly, we study the properties of the optimal solution to the problem $(FP_{a,λ,η})$ including the first-order and the second optimality condition and the lower and upper bound of the absolute value for its nonzero entries. Secondly, we develop the thresholding representation theory of the problem $(FP_{a,λ,η})$. Based on it, we prove the existence of the resolvent operator of gradient of $P_{a}(x)$, calculate its analytic expression, and propose an iterative fraction penalty thresholding (IFPT) algorithm to solve the problem $(FP_{a,λ,η})$. Moreover, we also prove that the value of the regularization parameter $λ>0$ can not be chosen too large. Indeed, there exists $\barλ>0$ such that the optimal solution to the problem $(FP_{a,λ,η})$ is equal to zero for any $λ>\barλ$. At last, inspired by the thresholding representation theory of the problem $(FP_{a,λ,η})$, we propose an iterative nonnegative fraction penalty thresholding (INFPT) algorithm to solve the problem $(FP_{a,λ,η}^{\geq})$. Empirical results show that our methods, for some proper $a>0$, perform effective in finding the sparse portfolio weights with and without short-selling constraints.

math.OC↗

arXiv2018

An Improved LPTC Neural Model for Background Motion Direction Estimation

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.

cs.CV↗

arXiv2018

Seismic Wave Equations in Tight Oil/Gas Sandstone Media

The paper is devoted to the derivation of a combined system of motion equations for solid and fluid in isotropic tight oil/gas sandstone media through volume averaging theorems (VAT). Based on the features of the media, four physical assumptions are proposed as the foundation for our derivation. More precisely, volume averaging theorems are applied to the micro-scale motion equations for both the solid and the fluid as well as to the stress-strain relations, resulting in a combined system of macro-scale equations for the tight oil/gas sandstone media. It is worth noting that the four assumptions may not be satisfied in the whole region. Nevertheless, since the characteristic diameter for applying VAT ranges between $10^{-6}$ meters and dozens of meters, we may split the entire domain into several sub-domains such that the four physical assumptions are satisfied in each sub-domain. By choosing a proper characteristic diameter of an averaging volume, we derive a formula for the fluid average pressure in terms of the divergence of the average displacement from the continuity equation of the fluid. As a result, the motion equations derived in this paper are simpler than the Biot equations, and are more suitable for inversion of porous medium parameters. When the fluid is gas and the compressional wave is considered, the derived motion equations can be simplified to the diffusive-viscous wave equation. Moreover, the explicit relationship between the coefficients in this equation and medium parameters is very important for gas detection in tight gas sandstone.

physics.geo-ph↗