L1 Norm Estimation Research Articles

An $\ell_0$ -Norm-Based Centers Selection for Failure Tolerant RBF Networks

There are two important issues in the construction of a radial basis function (RBF) neural network. The first one is to select suitable RBF centers. The second one is that the resultant RBF network should be with good fault tolerance. This paper proposes an algorithm that is able to select RBF centers and to train fault tolerant RBF networks simultaneously. The proposed algorithm borrows the concept from sparse approximation. In our formulation, we first define a fault tolerant objective function based on all input vectors from the training samples. We then introduce the minimax concave penalty (MCP) function, which is an approximation of l 0 -norm, into the objective function. The MCP term is able to force some unimportant RBF weights to zero. Hence the RBF node selection process can be achieved during training. As the MCP function is nondifferentiable and nonconvex, traditional gradient descent based algorithms are still unable to minimize the modified objective function. Based on the alternating direction method of multipliers (ADMM) framework, we develop an algorithm, called ADMM-MCP, to minimize the modified objective function. The convergent proof of the proposed ADMM-MCP algorithm is also presented. Simulation results show that the proposed ADMM-MCP algorithm is superior to many existing center selection algorithms under the concurrent fault situation.

Performance evaluation of total variation (TV) denoising technique for dual-energy contrast-enhanced digital mammography (CEDM) with photon counting detector (PCD): Monte Carlo simulation study

The dual-energy contrast-enhanced digital mammography (CEDM) system based on a photon counting detector (PCD) is very useful providing functional information for breast cancer detection. In particular, this system can be used to solve the spectral overlap and high radiation dose problems. However, imaging noise is a big problem because of the degradation image performance and cancer detection ratio in the CEDM system. To address this problem, a total variation (TV)-based denoising technique approach has recently been studied. Thus, the aim of this study was to evaluate and confirm the image performance of our TV-based denoising technique with dual-energy CEDM with a PCD. For this purpose, we simulated a dual-energy CEDM with a PCD and breast phantom in Monte Carlo simulation using the Geant4 Application for Tomographic Emission (GATE) that is an essential open source program. We also designed a TV-based denoising technique based on the L1-norm estimation included correction and iteration steps for acquiring high edge preservation in X-ray images. To evaluate the image performance, we used evaluation parameters with a contrast-to-noise ratio (CNR) and coefficient of variation (COV) as a function of the absorbed dose levels (2.18, 1.53, 1.09, and 0.66 mGy). According to the results, the average of all iodine thicknesses and absorbed dose conditions for the CNR using our proposed TV-based denoising technique was 1.71, 1.39, and 1.13 times higher than that acquired for the noisy image, median filter and Wiener filter, respectively. We also acquired excellent COV results for the dual-energy CEDM with a PCD system (2.53 times higher than that of the noisy image). In conclusion, the results of this study suggested that a TV-based denoising technique can be achieved with an improved image performance and the effect and feasibility of the TV-based denoising technique for dual-energy CEDM with a PCD can be investigated.

Delay-Aware User Association and Power Control for 5G Heterogeneous Network

Heterogeneous network (HetNet) serves as one of the most promising technologies for the upcoming fifth-generation (5G) wireless networks. In this paper, we consider the joint design of the delay-aware user association and power control problem in an uplink HetNet. The problem of interest is to minimize the overall power consumption subject to the strict delay constraints, which is modeled as a non-convex and mixed-integer nonlinear programming (MINLP) problem. To solve this intractable problem, we first adopt the l1-norm approximation approach to convert the integer constraints into solvable forms. Then, an iterative algorithm is proposed to solve the reformulated problem based on the successive convex approximation (SCA). The proposed centralized SCA-based algorithm employs the arithmetic-geometric mean (AGM) approximation and it can be further improved by the reweighted l1-minimization technique. A distributed implementation using alternating direction method of multipliers (ADMM) is presented as well. The simulation results are provided to demonstrate the effectiveness of the proposed algorithms.

Gradient Projection with Approximate L₀ Norm Minimization for Sparse Reconstruction in Compressed Sensing.

In the reconstruction of sparse signals in compressed sensing, the reconstruction algorithm is required to reconstruct the sparsest form of signal. In order to minimize the objective function, minimal norm algorithm and greedy pursuit algorithm are most commonly used. The minimum L1 norm algorithm has very high reconstruction accuracy, but this convex optimization algorithm cannot get the sparsest signal like the minimum L0 norm algorithm. However, because the L0 norm method is a non-convex problem, it is difficult to get the global optimal solution and the amount of calculation required is huge. In this paper, a new algorithm is proposed to approximate the smooth L0 norm from the approximate L2 norm. First we set up an approximation function model of the sparse term, then the minimum value of the objective function is solved by the gradient projection, and the weight of the function model of the sparse term in the objective function is adjusted adaptively by the reconstruction error value to reconstruct the sparse signal more accurately. Compared with the pseudo inverse of L2 norm and the L1 norm algorithm, this new algorithm has a lower reconstruction error in one-dimensional sparse signal reconstruction. In simulation experiments of two-dimensional image signal reconstruction, the new algorithm has shorter image reconstruction time and higher image reconstruction accuracy compared with the usually used greedy algorithm and the minimum norm algorithm.

Vision-based relative navigation using cubature Huber-based filtering

PurposeA novel vision-based relative navigation system (VBRNS) plays an important role in aeronautics and astronautics fields, and the filter is the core of VBRNS. However, most of the existing filtering algorithms used in VBRNS are derived based on Gaussian assumption and disregard the non-Gaussianity of VBRNS. Therefore, a novel robust filtering named as cubature Huber-based filtering (CHF) is proposed and applied to VBRNS to improve the navigation accuracy in non-Gaussian noise case.Design/methodology/approachUnder the Bayesian filter framework, the third-degree cubature rule is used to compute the cubature points which are propagated through state equation, and then the predicted mean and the associated covariance are taken. A combined minimum l1 and l2-norm estimation method referred as Huber’s criterion is used to design the measurement update. After that, the vision-based relative navigation model is presented and the CHF is used to integrate the line-of-sight measurements from vision camera with inertial measurement of the follower to estimate the precise relative position, velocity and attitude between two unmanned aerial vehicles. During the design of relative navigation filter, the quaternions are used to represent the attitude and the generalized Rodrigues parameters are used to represent the attitude error. The simulation is conducted to demonstrate the effectiveness of the algorithm.FindingsBy this means, the VBRNS could perform better than traditional VBRNS whose filter is designed by Gaussian filtering algorithms. And the simulation results demonstrate that the CHF could exhibit robustness when the system is non-Gaussian. Moreover, the CHF has more accurate estimation and faster rate of convergence than extended Kalman Filtering (EKF) in face of inaccurate initial conditions.Originality/valueA novel robust nonlinear filtering algorithm named as CHF is proposed and applied to VBRNS based on cubature Kalman filtering (CKF) and Huber’s technique. The CHF could adapt to the non-Gaussian system effectively and perform better than traditional Gaussian filtering such as EKF.

Research on reconstruction of atmospheric turbulence wavefront compressed sensing measurement

Compressed sensing technology for atmospheric turbulence wavefront slope measurement can greatly improve the wavefront signal measurement speed, while reducing the pressure of wavefront measurement system hardware. Different from the existing wavefront slope measurement method, the compressed sensing wavefront measurement increase a process which from sparse measurement of wavefront slope value to the reconstruction of the wavefront slope signal. Therefore, a fast and accurate wavefront slope reconstruction algorithm is needed if the compressed sensing technology is used for wavefront measurement. Smoothed L0 Norm (SL0) algorithm is an optimized iterative reconstruction algorithm with approximate L0 norm estimation, and compared with other algorithms, it is not necessary to know the sparsity of the signal in advance, and the calculation is low and the estimation accuracy is high. Based on the SL0 algorithm, this paper implements a subregion parallel algorithm-Block-Smoothed L0 Norm (B-SL0) which can quickly and accurately reconstruct the signal by measuring the wavefront slope signal in subarea and parallel operations through theoretical analysis and experiments. The experimental results show that B-SL0 is significantly better than other existing reconstruction algorithms in the calculation time and accuracy, and explore the feasibility of compressed sensing technology for measurement of atmospheric turbulence wavefront preliminarily.

A Monte Carlo simulation study for feasibility of total variation (TV) noise reduction technique using digital mouse whole body (MOBY) phantom image

Although radiation dose based on X-ray source is becoming a concern, use of micro-computed tomography (m-CT) system continues to grow in diagnostic imaging. To address radiation dose concern in m-CT system, Monte Carlo simulation using Geant4 Application for Tomography Emission (GATE) tool and noise reduction technique have recently developed. Among these techniques, total variation (TV) noise reduction technique is well known to many researchers for X-ray imaging. Also, an important disadvantage of median filter and Wiener filter is low edge preservation compared with recently developed noise reduction methods Thus, the aim of this study was to design TV noise reduction technique based on L1-norm estimation with iterative method and compare to other techniques in m-CT system using GATE simulation. We used 4-dimension (4D) digital mouse whole body (MOBY) phantom and to clarify the feasibility of TV noise reduction technique in m-CT images, we compared the image performance using contrast-to-noise ratio (CNR) and coefficient of variation (COV). According to the results, the average for three image planes (coronal, sagittal and transverse) of CNR and COV of the TV noise reduction technique were 68.07 and 1.61%, respectively. In particular, the CNR and the COV difference between TV noise reduction technique and noisy image were maximum 5.28 and 2.89 times, respectively. In conclusion, the results of this study suggested that TV noise reduction technique can be achieved improved performance and the effect and feasibility of TV noise reduction technique for m-CT imaging can be investigated.

Source recovery of underdetermined blind source separation based on SCMP algorithm

In this study, a new algorithm subspace complementary matching pursuit (SCMP) is developed for source recovery of underdetermined blind source separation. The proposed SCMP is more simplified than the conventional complementary matching pursuit (CMP) algorithm. SCMP algorithm selects more than one atom in each iteration to reduce computational complexity, and replaces the l2 norm minimisation involved in CMP with the approximate l0 norm minimisation to ensure higher recovery accuracy. Numerical results show that, compared with the existing algorithms for source recovery, such as CMP, orthogonal CMP (OCMP), optimised OCMP and sparsity adaptive CMP, the proposed SCMP algorithm significantly reduces the computational time with improved recovery accuracy.

Robust high-degree cubature information filter and its application to trajectory estimation for ballistic missile

This paper presents a new recursive filter algorithm, the robust high-degree cubature information filter, which can provide reliable state estimation in the presence of non-Gaussian measurement noise. The novel algorithm is developed in the framework of the conventional information filter. The fifth-degree Cubature rule is utilized to improve the estimation accuracy and numerical stability during the time update, while the Huber technique is adopted in the measurements update stage. As the Huber technique is a combined minimum l1 and l2 norm estimation algorithm, the proposed algorithm could exhibit robustness to the non-Gaussian measurement noise, especially the glint noise. In addition, Monte Carlo simulation and the trajectory estimation for ballistic missile experiments demonstrate that the robust high-degree cubature information filter can provide improved state estimation performance over extended information filter and high-degree cubature information filter.

Relay Selection Algorithm for Cognitive Relay Network

In the cognitive relay network, due to the different fading characteristics of communication links, not all relay nodes have constructive impacts on the system performance. A relay selection algorithm is proposed to obtain the minimum relay transmission power while satisfying the secondary user SINR requirements and interference temperature constraints. The algorithm first introduces l1 norm as the approximation of l0 norm, then constructs a minimum relay transmission power constraint problem to select appropriate relays. Simulation results show that the algorithm can efficiently conduct relay selection with mild system transmission power increase over traditional full cooperation cognitive relay network.

Assessing the Impact of Building Volume on Land Subsidence in the Central Business District of Beijing with SAR Tomography

ABSTRACTHigh-rise buildings in the modern urban setting may have a considerable impact on land subsidence. The process of urbanization in Beijing has been found to be in direct relationship with the land subsidence. The permanent scatterers interferometric aperture radar (PSInSAR) technology is becoming a conventional tool for land subsidence monitoring. Synthetic aperture radar (SAR) tomography, as an extension of PSInSAR technology, allows a full 3D imaging, and is useful to reconstruct 3D urban building maps. In this study, a SAR tomography method “scale-down by L1 norm minimization, model selection, and estimation reconstruction” (SL1MMER) was applied to 33 TerraSAR-X images to retrieve building height. The object-oriented classification method based on the support vector machine was applied on the World View 2 image to extract geometry of building footprints and to aggregate SL1MMER derived building heights for each building. The building footprints and building heights were used to calculate the volume of buildings. The Stanford method for persistent scatterers, a PSInSAR methodology, was used to obtain land subsidence rates. The correlation coefficient between the building volumes and land subsidence showed no positive relationship for buildings that were below a certain volume. However, at local scale, with the increase of the building volumes, the correlation increased. The larger the volume of buildings, the stronger the relationship became. Once the volume of buildings became larger than 3.00 × 105 m3, the impact of building volume on land subsidence remained stable.

DOA Estimation of Time-Modulated Linear Array Based on Sparse Signal Recovery

Under the circumstances of small number of snapshots, low signal-to-noise ratio, and closely spaced sources, especially with correlated signals, the existing direction of arrival angle (DOA) estimation methods for time-modulated linear arrays (TMLAs) generally does not yield satisfactory results. To deal with those problems, a new weighted l1-norm DOA estimation algorithm is proposed for the TMLA in this letter. The proposed algorithm constructs the weighted matrix by making full use of the orthogonality of the signal subspace and the noise subspace to penalize the l1-norm constrained model. Accordingly, the reconstructed coefficient vector with better sparsity could be achieved, and the false peaks could be effectively suppressed. Simulation results have been provided to validate the effectiveness of the proposed method.

Compressing Sensing Based Source Localization for Controlled Acoustic Signals Using Distributed Microphone Arrays

In order to enhance the accuracy of sound source localization in noisy and reverberant environments, this paper proposes an adaptive sound source localization method based on distributed microphone arrays. Since sound sources lie at a few points in the discrete spatial domain, our method can exploit this inherent sparsity to convert the localization problem into a sparse recovery problem based on the compressive sensing (CS) theory. In this method, a two-step discrete cosine transform- (DCT-) based feature extraction approach is utilized to cover both short-time and long-time properties of acoustic signals and reduce the dimensions of the sparse model. In addition, an online dictionary learning (DL) method is used to adjust the dictionary for matching the changes of audio signals, and then the sparse solution could better represent location estimations. Moreover, we propose an improved block-sparse reconstruction algorithm using approximate l0 norm minimization to enhance reconstruction performance for sparse signals in low signal-noise ratio (SNR) conditions. The effectiveness of the proposed scheme is demonstrated by simulation results and experimental results where substantial improvement for localization performance can be obtained in the noisy and reverberant conditions.

Wireless backhaul resource allocation and user‐centric clustering in ultra‐dense wireless networks

Wireless backhaul is a promising technology to lower the cost for connecting a large number of densely deployed access points in the emerging fifth generation wireless system. In this study, the authors consider the joint optimisation of resource allocation in wireless backhaul links and user-centric clustering in the access links. The objective is to maximise the weighted sum rate of all users under the backhaul resource constraints. To solve this intractable problem, they first adopt the l 1 -norm approximation approach to convert the non-convex backhaul constraints into the solvable forms. They then reformulate the objective function as a set of second-order cone constraints based on the sequential parametric convex approximation method. An iterative algorithm is proposed to solve the transformed problem based on its special property. Simulation results show that the proposed algorithm outperforms other existing schemes under different network settings.

SEISMIC SPARSE INVERSION METHOD OF IMAGING DATA FOR DETECTING DISCONTINUOUS AND INHOMOGENEOUS GEOLOGIES

AbstractThe small‐scale discontinuous and inhomogeneous geologies, such as tiny faults, cavities and fractures, play an important role in reservoir analysis. However, effectively extracting them from seismic imaging data is a challenging problem, as their seismic responses are much weaker than reflections' from large‐scale structures. On the other hand, this small‐scale information is easily contaminated with noises, which will make their analysis difficult to perform if there is no strategy adopted for improving the signal‐to‐noise ratio (S/N) of their images. By combing a non‐linear filter and a sparsity constraint, a seismic sparse inversion method of imaging data is developed for detecting these small‐scale discontinuous and inhomogeneous geologies.The core of extracting discontinuous and inhomogeneous information lies in removing strong reflections and noises. The plane‐wave destruction method uses a local plane‐wave model for representing seismic structures and thus is appropriate for estimating reflections. Through subtracting the predicted reflections from seismic imaging data, the small‐scale discontinuous and inhomogeneous information will be left into the seismic residual data. Considering the sparsity property of this small‐scale information, a L1 ‐ L2 norm model is built that uses a non‐linear filter for promoting the S/N of the discontinuous and inhomogeneous inversion results. In order to guarantee the computation efficiency in solving this sparsity model, a L1 norm approximation scheme and quasi‐Newton algorithm is introduced.Numerical experiment demonstrates the effectiveness of the proposed method in extracting the small‐scale discontinuous and inhomogeneous geologies. This numerical model is composed of fractures, faults and cavities. The geological targets are four series of cavities in the shallow part and three series of cavities in the deep part. With the proposed seismic sparse inversion method, a profile with reflections eliminated and noises destroyed is obtained and the edges, faults, fractures and cavities are completely resolved. In field application, a carbonate reservoirs analysis is performed. The 3D prestack time migration profile can clearly display large‐scale layers but fails in describing discontinuous and inhomogeneous geologies. Although coherency techniques can reveal discontinuous information, the small‐scale tiny faults, fractures and cavities are beyond its detection. The proposed method succeeds in clarifying and locating the small‐scale discontinuous and inhomogeneous geologies. The seismic attribute analysis based on seismic spares inversion data also provides valuable information about the planar distribution of the tiny faults, cavities and fractures.Based on a sparsity‐constraint model, a seismic sparse inversion method of imaging data is proposed for extracting small‐scale discontinuous and inhomogeneous geologies. The method can achieve a high‐resolution image by removing strong reflections and elimination of noises. In method application, this seismic discontinuous and inhomogeneous information is required to be imaged by seismic data processing. Otherwise, some additional seismic data processing is needed. As an end, we suggest future research on individually extracting discontinuity and inhomogeneity, especially for evaluating the capacity of carbonate reservoirs.

Error analysis of a diffuse interface method for elliptic problems with Dirichlet boundary conditions

We use a diffuse interface method for solving Poisson's equation with a Dirichlet condition on an embedded curved interface. The resulting diffuse interface problem is identified as a standard Dirichlet problem on approximating regular domains. We estimate the errors introduced by these domain perturbations, and prove convergence and convergence rates in the H1-norm, the L2-norm and the L∞-norm in terms of the width of the diffuse layer. For an efficient numerical solution we consider the finite element method for which another domain perturbation is introduced. These perturbed domains are polygonal and non-convex in general. We prove convergence and convergences rates in the H1-norm and the L2-norm in terms of the layer width and the mesh size. In particular, for the L2-norm estimates we present a problem adapted duality technique, which crucially makes use of the error estimates derived for the regularly perturbed domains. Our results are illustrated by numerical experiments, which also show that the derived estimates are sharp.

Delayed Lagrange neural network for sparse signal reconstruction under compressive sampling

In this paper, two new Lagrange neural networks are proposed for compressed sensing. The first one is for the standard recovery of sparse signals. The second one is for the recovery of sparse signals with noise. By drawing into delay, we also derive two delayed Lagrange neural networks. Both the two networks are based on the l0 norm approximation. They can be implemented by circuits.

Fuzzy fault tolerant predictive control for a diesel engine air path

This paper proposes a Fuzzy Fault Tolerant Predictive Control (FFTPC) with integral action method for a class of nonlinear systems. The Takagi-Sugeno (T-S) fuzzy approach is introduced as a modelling technique in order to consider the active control methods adapted to linear models. The proposed control strategy is based on a combination between Parallel Distributed Compensation (PDC) control law and Model Predictive Control (MPC) where the T-S fuzzy aspect uses the Unmeasurable Premise Variables (UPV). A T-S fuzzy observer provides an L2 norm estimation of system state vector and faults. The controller and observer gains are obtained by solving Linear Matrix Inequalities (LMIs) derived from the Lyapunov theory. The validity of the proposed Fault Tolerant Control (FTC) strategy is illustrated through an application to a Diesel Engine Air Path (DEAP) system.

A discrete-time learning algorithm for image restoration using a novel L2-norm noise constrained estimation

This paper proposes a discrete-time learning algorithm for fast image restoration using a novel L2-norm noise constrained estimation. The noise constrained estimation approach can relax the need of the optimal regularization parameter to be estimated. Performance analysis shows that the proposed algorithm can converge globally to a robust optimal weight vector. Compared with the cooperative neural fusion (CNF) algorithm minimizing L1-norm estimation, the proposed algorithm only needs O(N) multiplication operationper iteration, instead of O(N2) multiplication operation required by the CNF algorithm. Moreover, the proposed fusion approach overcomes the difficulty of estimating the noise error set in the CNF approach. Simulation results show by comparison that under the non-optimal regularization parameter, the proposed algorithm can obtain a better restored estimate in Gaussian mixture noise and can run much faster compared to the CNF algorithm.

Sparse-view computed tomography image reconstruction via a combination of L(1) and SL(0) regularization.

Low-dose computed tomography reconstruction is an important issue in the medical imaging domain. Sparse-view has been widely studied as a potential strategy. Compressed sensing (CS) method has shown great potential to reconstruct high-quality CT images from sparse-view projection data. Nonetheless, low-contrast structures tend to be blurred by the total variation (TV, L1-norm of the gradient image) regularization. Moreover, TV will produce blocky effects on smooth and edge regions. To overcome this limitation, this study has proposed an iterative image reconstruction algorithm by combining L1 regularization and smoothed L0 (SL0) regularization. SL0 is a smooth approximation of L0 norm and can solve the problem of L0 norm being sensitive to noise. To evaluate the proposed method, both qualitative and quantitative studies were conducted on a digital Shepp-Logan phantom and a real head phantom. Experimental comparative results have indicated that the proposed L1/SL0-POCS algorithm can effectively suppress noise and artifacts, as well as preserve more structural information compared to other existing methods.