Split Bregman Iteration Research Articles

Wavelet-based spatiotemporal sparse quaternion dictionary learning for reconstruction of multi-channel vibration data

Accurate reconstruction of multi-source data information plays an essential role in remote intelligent operation, and prognostic and health maintenance (RIO-PHM) of industrial systems. However, traditional signal reconstruction methods such as compressed sensing fail to capture the spatio-temporal characteristics and coupling nature of the multi-source or multi-channel data. To alleviate this bottleneck, in this paper, a new wavelet-based spatiotemporal sparse quaternion dictionary learning (WSTS-QDL) algorithm is formulated for the reconstruction of multi-channel vibration data for the first time. Specifically, the wavelet-based spatiotemporal sparse low-rank matrix (SLRM) algorithm is elaborated and the sparse coefficient matrix of the multi-channel signals can be estimated using the split Bregman iteration (SBI) technique. Then, quaternion-based dictionary learning is introduced for multi-channel data reconstruction according to the updated sparse coefficient matrix during quaternion dictionary learning. Eventually, two equipmental scenarios including run-to-failure data of rolling bearing in bearing test bench and vibration signal of the failured bearing in corn thresher, are utilized for verification. The experimental results demonstrate that the highest recovery accuracy performance with scoring function and the lowest errors are achieved by the proposed method in contrast with the state-of-the-art benchmarks such as orthogonal matching pursuit (OMP) method and spatiotemporal sparse Bayesian learning (SSBL), and the waveform of phase space trajectory and points cloud distribution of the Poincare section in the original signal are similar/same to that obtained by the proposed method.

MAP-based blind infrared spectral deconvolution via modified total variation regularization for mixture identification

Infrared (IR) spectral signals have problems with random noise and overlapping of adjacent peaks. To address these issues, we proposed a novel infrared spectral reconstruction model with improved total variation. The maximum a posteriori theory (MAP) is introduced to build the signal reconstruction model for the latent infrared spectrum. The proposed model can remove the random spectral noise and generate new peaks. In the MAP architecture, the prior probability is modeled as an improved total variation constraint, the spectral noise based on the Gaussian distribution is constructed for the likelihood probability distribution. Then, the proposed infrared spectral signal model is optimized by the famous split Bregman iteration approach. The high-quality infrared spectrum and instrument function can be estimated from the simulated and real spectral signals using the proposed model. The compared experiments show the good performance in suppressing spectral noise and splitting overlap peaks.

Infrared spectrum resolution enhancement model via Gabor transform regularization for object detection

In this paper, we proposed a novel resolution enhancement model for the unknown instrument function and infrared spectral signal estimation. The Gabor transform can be utilized on the degraded spectrum to save the proposed resolution enhancement model from converging the mistake spectral signal. In the proposed model, the spatial random noises are regularized by the total variation regularization, as well as the spectral local smoothness is reduced by the Gabor coefficient distribution regularization. Then, the split Bregman iteration scheme is introduced to alternately optimize the instrument function and latent spectrum, which shown excellent convergence and stability. After those steps, the high-resolution spectral signals can be produced by our proposed model. Comparing with the existing resolution enhancement algorithms, the proposed model can produce the comparable quality even if the observed spectrum exists the low contrast.

RISIR: Rapid Infrared Spectral Imaging Restoration Model for Industrial Material Detection in Intelligent Video Systems

Material detection by industrial infrared imaging spectrometer (IRIS) is a key technique in multiple industrial applications, including garbage collection, material analysis, and robot vision. However, IRIS often suffers from overlapped bands and random noises, which limit the precision of subsequent processing. In this article, we propose a novel Gabor transform-based mid-wave infrared (MWIR) spectrum restoration model by successfully exploring the intrinsic structure of the clean MWIR spectrum from the degraded one. First, a total variation-regularized Gabor coefficient adjustment descriptor is designed and incorporated into the spectrum restoration model. In addition to adjusting the Gabor coefficient distribution by total variation-norm, the L2-norm of gradient is leveraged to regulate the smoothness of the instrument degradation function. Then, the proposed model is inferred using an efficient optimization approach based on split Bregman iteration method and alternating minimization algorithm. Quantitative and qualitative experimental results demonstrate that the proposed model favorably outperforms the state-of-the-art approaches. The restored high-resolution MWIR spectrum can be used to rapidly detect different materials in intelligent video systems.

A Novel Imaging Method Based on Reweighted Total Variation for an Interferometer Array on Lunar Orbit

Ground-based radio observations below 30 MHz are susceptible to the ionosphere of the Earth and the radio frequency interference. Compared with other space mission concepts, making low frequency observations using an interferometer array on lunar orbit is one of the most feasible ones due to a number of technical and economic advantages. Different from traditional interferometer arrays, the interferometer array on lunar orbit faces some complications such as the three-dimensional distribution of baselines and the changing sky blockage by the Moon. Although the brute-force method based on the linear mapping relationship between the visibilities and the sky temperature can produce satisfactory results in general, there are still large residual errors on account of the loss of the edge information. To obtain the full-sky maps with higher accuracy, in this paper we propose a novel imaging method based on reweighted total variation (RTV) for a lunar orbit interferometer array. Meanwhile, a split Bregman iteration method is introduced to optimize the proposed RTV model so as to decrease the computation time. The simulation results show that, compared with the traditional brute-force method, the RTV regularization method can effectively reduce the reconstruction errors and obtain more accurate sky maps, which proves the effectiveness of the proposed method.

희박한 최소 절대 편차 지지벡터기계

The support vector machine solves a quadratic programming problem with linear inequality and equality constraints. However, it is not trivial to solve the quadratic problem. The least squares support vector machine(LS-SVM) solves a linear system by equality constraints instead of inequality constraints. LS-SVM is a popular method in regression and classification problems, because it effectively solves simple linear systems. There are two issues with the LS-SVM solution : the lack of robustness to outliers and the absence of sparseness. In this paper, we propose a sparse and robust support vector machine for regression problems using the least absolute deviation support vector machine (LAD-SVM) and recursive reduced LS-SVM (RR-LS-SVM). The split-Bregman iteration gives the exact solution for the LAD-SVM problem, while RR-LS-SVM gives a sparse solution with a much smaller number of all support vectors. Numerical experiments with simulation and benchmark data demonstrate that the proposed algorithm can achieve comparable performance to other methods in terms of robustness and sparseness.

Improved TV Image Denoising over Inverse Gradient

Noise in an image can affect one’s extraction of image information, therefore, image denoising is an important image pre-processing process. Many of the existing models have a large number of estimated parameters, which increases the time complexity of the model solution and the achieved denoising effect is less than ideal. As a result, in this paper, an improved image-denoising algorithm is proposed based on the TV model, which effectively solves the above problems. The L1 regularization term can make the solution generated by the model sparser, thus facilitating the recovery of high-quality images. Reducing the number of estimated parameters, while using the inverse gradient to estimate the regularization parameters, enables the parameters to achieve global adaption and improves the denoising effect of the model in combination with the TV regularization term. The split Bregman iteration method is used to decouple the model into several related subproblems, and the solutions of the coordinated subproblems are derived as optimal solutions. It is also shown that the solution of the model converges to a Karush–Kuhn–Tucker point. Experimental results show that the algorithm in this paper is more effective in both preserving image texture structure and suppressing image noise.

Improved Low-Rank Tensor Approximation for Seismic Random Plus Footprint Noise Suppression

Random plus footprint noise provokes severe seismic image deterioration and makes it challenging for interpreters to recognize and analyze accurate subsurface responses. Thus, as an elementary and indispensable preprocessing step, diverse footprint removal approaches, including filtering in the frequency or time-frequency domain and dictionary learning (DL), have been documented to achieve promising results in tackling this challenge. However, the prevailing denoising methods tend to treat 3-D seismic data as images for processing, but such flattening or matricization operations inevitably obliterate the three-dimensional image structures concealed in noisy observational seismic data, which hinders the removal performance of these approaches. To resolve this issue, this article proposes a new tensor model for 3-D seismic random plus footprint noise suppression, and this model is based on unidirectional total variation regularized low-rank tensor approximation (UTV-LRTA). In this model, UTV regularization is imposed to obtain the innately structural and directional behavior of the acquisition footprint. In this way, the footprint is removed by effectively decomposing the footprint-contaminated seismic image into a footprint-free image and a footprint component by UTV. In contrast, random noise is mitigated by regularizing the low-rankness of the third-order seismic tensors using the tensor nuclear norm. Moreover, a simple and powerful optimization algorithm based on the split Bregman iteration is introduced to resolve the proposed UTV-LRTA model. The suggested model is thoroughly assessed on synthetic and field datasets and significantly surpasses the state-of-the-art approaches quantitatively and qualitatively evaluated in the analyzed field examples.

Video Transmission Secrecy Improvement Based on Fractional Order Hyper Chaotic System

In the Digital World scenario, the confidentiality of information in video transmission plays an important role. Chaotic systems have been shown to be effective for video signal encryption. To improve video transmission secrecy, compressive encryption method is proposed to accomplish compression and encryption based on fractional order hyper chaotic system that incorporates Compressive Sensing (CS), pixel level, bit level scrambling and nucleotide Sequences operations. The measurement matrix generates by the fractional order hyper chaotic system strengthens the efficiency of the encryption process. To avoid plain text attack, the CS measurement is scrambled to its pixel level, bit level scrambling decreases the similarity between the adjacent measurements and the nucleotide sequence operations are done on the scrambled bits, increasing the encryption. Two stages are comprised in the reconstruction technique, the first stage uses the intra-frame similarity and offers robust preliminary retrieval for each frame, and the second stage iteratively improves the efficiency of reconstruction by integrating inter frame Multi Hypothesis (MH) estimation and weighted residual sparsity modeling. In each iteration, the residual coefficient weights are modified using a mathematical approach based on the MH predictions, and the Split Bregman iteration algorithm is defined to resolve weighted l1 regularization. Experimental findings show that the proposed algorithm provides good compression of video coupled with an efficient encryption method that is resistant to multiple attacks.

Seismic inversion with L2,0-norm joint-sparse constraint on multi-trace impedance model

Impedance inversion of post-stack seismic data is a key technology in reservoir prediction and characterization. Compared to the common used single-trace impedance inversion, multi-trace impedance simultaneous inversion has many advantages. For example, it can take lateral regularization constraint to improve the lateral stability and resolution. We propose to use the L2,0-norm of multi-trace impedance model as a regularization constraint in multi-trace impedance inversion in this paper. L2,0-norm is a joint-sparse measure, which can not only measure the conventional vertical sparsity with L0-norm in vertical direction, but also measure the lateral continuity with L2-norm in lateral direction. Then, we use a split Bregman iteration strategy to solve the L2,0-norm joint-sparse constrained objective function. Next, we use a 2D numerical model and a real seismic data section to test the efficacy of the proposed method. The results show that the inverted impedance from the L2,0-norm constraint inversion has higher lateral stability and resolution compared to the inverted impedance from the conventional sparse constraint impedance inversion.

A mixed finite element discretisation of linear and nonlinear multivariate splines using the Laplacian penalty based on biorthogonal systems

We consider a mixed finite element method for a linear multivariate spline using the Laplacian penalty. Our discretisation is based on biorthogonal systems leading to a very simple and efficient finite element scheme. We also extend our approach to a nonlinear case and describe a split Bregman iteration scheme for the resulting nonlinear equations. We apply our numerical schemes to remove the mixture of Gaussian and impulsive noise for some test images.•This paper presents a method of discretising a multivariate spline using a finite element method.•The method uses a biorthogonal system to achieve an efficient finite element method.•The method is extended to cover a discretisation scheme for a nonlinear case, including an adaptation of the split Bregman method for the nonlinear case.

Image compressive sensing via hybrid regularization combining centralized group sparse representation and deep denoiser prior

To effectively solve the ill-posed image compressive sensing (CS) reconstruction problem, it is essential to properly exploit image prior knowledge. In this paper, we propose an efficient hybrid regularization approach for image CS reconstruction, which can simultaneously exploit both internal and external image priors in a unified framework. Specifically, a novel centralized group sparse representation (CGSR) model is designed to more effectively exploit internal image sparsity prior by suppressing the group sparse coding noise (GSCN), i.e., the difference between the group sparse coding coefficients of the observed image and those of the original image. Meanwhile, by taking advantage of the plug-and-play (PnP) image restoration framework, a state-of-the-art deep image denoiser is plugged into the optimization model of image CS reconstruction to implicitly exploit external deep denoiser prior. To make our hybrid internal and external image priors regularized image CS method (named as CGSR-D-CS) tractable and robust, an efficient algorithm based on the split Bregman iteration is developed to solve the optimization problem of CGSR-D-CS. Experimental results demonstrate that our CGSR-D-CS method outperforms some state-of-the-art image CS reconstruction methods (either model-based or deep learning-based methods) in terms of both objective quality and visual perception.

Two Highly Accurate Electromagnetic Map Reconstruction Methods

An electromagnetic map (EM) can provide movable base stations with information to optimize the communication quality of temporary communication systems in disaster areas, such as areas suffering from earthquakes. In this paper, a low-cost and effective communication optimization system model that uses sensing nodes and EMs is proposed. Moreover, two EM reconstruction methods, which serve as the keys to the model, are proposed to reconstruct EMs to provide information for communication optimization according to different demands. One method is KGA-GAN-SBI, which combines the kriging algorithm, generative adversarial network and split bregman iterations, and the other is APCA-KGA-DPA, which combines the affinity propagation clustering algorithm, kriging algorithm and domain mapping algorithm. The former can satisfy the demand of high-accuracy EMs. The latter can reconstruct an EM faster than KGA-GAN-SBI. The simulation results show that both low-cost methods can reconstruct more accurate EMs than several existing algorithms; they can provide an effective way to optimize the communication quality of temporary communication and fill the gap in the study of EM applications.

Accelerating MR Parameter Mapping Using Nonlinear Compressive Manifold Learning and Regularized Pre-Imaging.

In this study, we present a novel method to reconstruct the MR parametric maps from highly undersampled k-space data. Specifically, we utilize a nonlinear model to sparsely represent the unknown MR parameter-weighted images in high-dimensional feature space. Each image at a specific time point is assumed to belong to a low-dimensional manifold which is learned from training images created based on the parametric model. The final reconstruction is carried out by venturing the sparse representation of the images in the feature space back to the input space, using the pre-imaging technique. Particularly, among an infinite number of solutions that satisfy the data consistency, the one that is closest to the manifold is selected as the desired solution. The underlying optimization problem is solved using kernel trick, sparse coding, and split Bregman iteration algorithm. In addition, both spatial and temporal regularizations are utilized to further improve the reconstruction quality. The proposed method is validated on both phantom and in vivo human brain T2 mapping data. Results suggest that the proposed method is superior to the conventional linear model-based reconstruction methods, in terms of artifact removal and quantitative estimation accuracy. The proposed method could be potentially beneficial for quantitative MR applications.

Fast Terahertz Imaging Model Based on Group Sparsity and Nonlocal Self-Similarity.

In order to solve the problems of long-term image acquisition time and massive data processing in a terahertz time domain spectroscopy imaging system, a novel fast terahertz imaging model, combined with group sparsity and nonlocal self-similarity (GSNS), is proposed in this paper. In GSNS, the structure similarity and sparsity of image patches in both two-dimensional and three-dimensional space are utilized to obtain high-quality terahertz images. It has the advantages of detail clarity and edge preservation. Furthermore, to overcome the high computational costs of matrix inversion in traditional split Bregman iteration, an acceleration scheme based on conjugate gradient method is proposed to solve the terahertz imaging model more efficiently. Experiments results demonstrate that the proposed approach can lead to better terahertz image reconstruction performance at low sampling rates.

Assimilation of Images via Dictionary Learning-Based Sparsity Regularization Strategy: An Application for Retrieving Fluid Flows

In this work, we propose a structure sparsity regularization strategy in the framework of 4-D variational data assimilation (4-D Var). In meteorology and oceanography, the number of unknown model variables is far fewer than that of image observations, often leading to solve an underdetermined nonlinear inverse problem. In recent years, the l¹-norm-based sparsity regularization approach has attracted great attention in the field of 4-D Var because of its data structure preservation and noise suppression. To avoid little underlying physical priors considered, we introduce a widely used dictionary learning (DL) method to adaptively derive an efficient sparse approximation via learning a basis from a given dataset. For our target application of estimating sea surface flows, we consider a DL sparsity constraint on the variable of flow vorticity due to its rich spatial variation related to flows evolution. A novel anisotropic regularization method combined with fluid dynamics characteristics could overcome magnitude underestimation and staircase artifacts appearing in the gradient regularization-based 4-D Var method. The split Bregman iteration with fast convergence property is employed to solve the l¹+l² nonsmooth minimization problem. The promising fluid flows estimation performance in real test cases (assimilation of image sequences collected from CORIOLIS experimental turntable) demonstrates the efficiency of our approach.

Real-Time Multi-Convex Model Predictive Control for Occlusion-Free Target Tracking With Quadrotors

This paper proposes a Model Predictive Control (MPC) algorithm for target tracking amongst static and dynamic obstacles. Our main contribution lies in improving the computational tractability and reliability of the underlying non-convex trajectory optimization. The result is an MPC algorithm that runs real-time on laptops and embedded hardware devices such as Jetson TX2. Our approach relies on novel reformulations for the tracking, collision, and occlusion constraints that induce a multi-convex structure in the resulting trajectory optimization. We exploit these mathematical structures using the split Bregman Iteration technique, eventually reducing our MPC to a series of convex Quadratic Programs solvable in a few milliseconds. The fast re-planning of our MPC allows for occlusion and collision-free tracking in complex environments even while considering a simple constant-velocity prediction for the target trajectory and dynamic obstacles. We perform extensive bench-marking in a realistic physics engine and show that our MPC outperforms the state-of-the-art algorithms in visibility, smoothness, and computation-time metrics.

Efficient infrared imaging–blur kernel estimation with multi-scale feature learning for online learning video source

To enhance the infrared images resolution, a novel infrared imaging–blur kernel estimation model is proposed, which is based on multiscale deconvolution and total variation regularization. The blur kernel can be refined by the deconvolution algorithm with increasing scale level. Furthermore, the split Bregman iteration algorithm is used to optimize the proposed cost functions. The major novelty of the study is that the proposed model can recover the high-resolution image and an accurate blur kernel from a degraded image simultaneously. Qualitative and quantitative results on simulated and actual images demonstrate that the proposed method can estimate the infrared blur function accurately and produce high-resolution image. The enhanced infrared images can be applied to the application for the learning video quality improvement.

Compressively sampled magnetic resonance imaging reconstruction based on split Bregman iteration with general non-uniform threshold shrinkage

PurposeK-space under-sampling reconstruction technology is an effective means to improve the speed of magnetic resonance imaging. Among its many reconstruction algorithms, split Bregman iteration is an effective method to solve multi-constrained models. This model often contains TV variational regularization terms, the generalized threshold shrinkage operator often used to solve TV constraints subproblem. However, when the generalized threshold shrinkage operator is performing the shrinking operation, it does not consider the inconsistency of the elements in the image matrix, which will cause the loss of image details. MethodsIn response to this problem, in this paper, a non-uniform threshold shrinkage operator was proposed to solve above TV constraints subproblem, which can dynamically adjust the shrinkage threshold by the residuals of each image element. And introduce this operator when performing Split Bregman iteration to improve the performance of generalized threshold shrinkage. ResultsAfter qualitative and quantitative analysis during the experiments, it can be concluded that compared with the other three methods, the proposed method has better performance in terms of Peak Signal to Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), Transferred Edge Information(TEI) and Normalized Mutual Information(NMI), and the visual perception is better. Then we also did denoising performance analysis at different noise levels, this method also showed good robustness. ConclusionsThe proposed method can improve the reconstruction performance of TV constrained subproblem in split Bregman iteration, and then improve the overall performance of reconstruction algorithm. Moreover, this method also shows good denoising performance at different noise levels.

Spatial Domain Terahertz Image Reconstruction Based on Dual Sparsity Constraints.

Terahertz time domain spectroscopy imaging systems suffer from the problems of long image acquisition time and massive data processing. Reducing the sampling rate will lead to the degradation of the imaging reconstruction quality. To solve this issue, a novel terahertz imaging model, named the dual sparsity constraints terahertz image reconstruction model (DSC-THz), is proposed in this paper. DSC-THz fuses the sparsity constraints of the terahertz image in wavelet and gradient domains into the terahertz image reconstruction model. Differing from the conventional wavelet transform, we introduce a non-linear exponentiation transform into the shift invariant wavelet coefficients, which can amplify the significant coefficients and suppress the small ones. Simultaneously, the sparsity of the terahertz image in gradient domain is used to enhance the sparsity of the image, which has the advantage of edge preserving property. The split Bregman iteration scheme is utilized to tackle the optimization problem. By using the idea of separation of variables, the optimization problem is decomposed into subproblems to solve. Compared with the conventional single sparsity constraint terahertz image reconstruction model, the experiments verified that the proposed approach can achieve higher terahertz image reconstruction quality at low sampling rates.