Iteratively Reweighted Research Articles

Image Denoising and Refinement Based on an Iteratively Reweighted Least Squares Filter

This paper presents a method to reduce noise and refine detail features of a scene based on an iteratively reweighted least squares method. The performance of the proposed filter, called the iteratively reweighted least squares filter (IRLSF), was compared with the state-of-the-art filters by checking their ability to recover simulated edge models under various degrees of noise contamination. The results of the simulation comparison show that IRLSF is superior to the other filters in terms of its ability to recover the original edge models. To apply IRLSF to real images of a scene captured by a camera, a procedure composed of corner detection, least squares matching, bilinear resampling, and iteratively reweighted least squares is proposed. The experimental results show that IRLSF produces mean images that are effectively denoised, and that its accuracy is less than one half of grey-level-quantization-unit of test images captured by a commercial camera.

Increasing efficiency of the robust deformation analysis methods using genetic algorithm and generalised particle swarm optimisation

The paper analyses the possibility of increasing efficiency of the Iterative Weighted Similarity Transformation (IWST) method, which is a prototype of classic robust methods, using global optimisation approach instead of classical one, available in the literature. For the purpose of solving the optimisation problem of the IWST method, in addition to the Iterative Reweighted Least Squares (IRLS) method, the Genetic algorithm (GA) and Generalised Particle Swarm Optimisation (GPSO) algorithm were applied, in order to overcome some flaws of IRLS method. Experimental research was performed based on the Monte Carlo simulation using the mean success rate (MSR) on the example of the geodetic control network for monitoring the Šelevrenac dam in the Republic of Serbia. By using the GA and GPSO algorithms, the overall efficiency of the IWST method has been increased by about 18% compared to the IRLS method. Also, it has been determined that the efficiency of the IRLS method significantly reduces with the increase in the number of displaced potential reference points (PRPs), while the GA and GPSO algorithms’ efficiency does not change significantly. The values of overall absolute true errors due to the increased number of displaced PRPs in the GA and GPSO algorithms did not change notably while with the IRLS method their values increased significantly.

Random Noise Attenuation of Common Offset Gathers Using Iteratively Reweighted $\ell_{2,1}$ Norm Minimization

Sparse representation (SR)-based denoising method attenuates random seismic noise trace-by-trace, which may not be able to employ the coherency between neighboring traces. To address this, we propose a multiple measurement vector (MMV)-based algorithm for robust denoising of multichannel seismic gathers. Seismic reflectors in common offset gather (COG) is characterized by horizontal events, which satisfy the common sparsity assumption, making it ideal for the MMV approach. $\ell _{2,1}$ -norm regularization, which enforces two constraints on source matrix, i.e., temporal sparsity and the horizontal continuity, is then adopted in the MMV model to stabilize the lateral variation between channels. Besides, $\ell _{2,1}$ -norm regularization provides a reasonable intrinsic structure to reduce the multisolution of the algorithm. Celebrating the strengths of iteratively reweighted (IR), we present a novel MMV algorithm, IR $\ell _{2,1}$ norm minimization (IR- $\ell _{2,1}$ ), that further improves the performance. The formulated IR- $\ell _{2,1}$ can be minimized by the alternating direction method of multipliers. Both synthetic and field data applications confirm the effectiveness of the proposed denoising method.

Joint Array Diagnosis and Channel Estimation for RIS-Aided mmWave MIMO System

In this paper, we consider a reconfigurable intelligent surface (RIS) aided millimeter wave (mmWave) multiple-input multiple-output (MIMO) system. The system can obtain the huge gain via joint active beamforming at the base station (BS) and passive beamforming at the RIS. However, due to weather and atmospheric effects, outdoor RIS antenna elements are subject to full or partial blockages from a plethora of particles like dirt, salt, ice, and water droplets. These blockages can cause an approximate squared power/SNR loss for the system. Different from the conventional array diagnosis, the RIS has no signal processing capability. Thus, we propose the joint array diagnosis and channel estimation techniques containing two stages to solve the problem. At the first stage the channel parameters at user equipment (UE) and BS are estimated using an iterative reweighted (IR) method. At the second stage, the array blockage coefficient vector and the effective sparse channel parameters at RIS are jointly estimated via solving a two-timescale non-convex optimization problem. We propose two algorithms, i.e., a batch algorithm (BA) and a two-timescale online joint array diagnosis and channel estimation (TOJADCE) algorithm to solve the problem and compare the performance of these two algorithms. Finally, to speed up the convergence of long-term variable and improve estimation performance, we propose a noise reduction (NR) algorithm. The simulations verify the effectiveness of our proposed algorithms.

Multi-parameter multiplicative regularization: An application to force reconstruction problems

This paper introduces a multi-parameter multiplicative regularization for force reconstruction problems. This approach allows exploiting the local prior information available on the sources to identify, while determining the related regularization parameters in an elegant and efficient manner. The aim of this paper is to assess the applicability of a multi-parameter regularization strategy compared to a single parameter formulation for reconstructing the external sources acting on a mechanical structure. A particular attention is also paid to the practical resolution of the regularization problem by implementing an original Iteratively Reweighted algorithm derived from the direct application of the first-order optimality condition. The performance of the proposed algorithm in terms of solution accuracy is compared with a more classical implementation based on an Iteratively Reweighted Least-Squares procedure. The interest of the proposed multi-parameter strategy is assessed numerically. Obtained results demonstrates that consistent reconstructions are obtained for high and moderate measurement noise level whatever the formulation considered (i.e. single or multi-parameter) provided that the suitable resolution algorithm is implemented. For very and extremely noisy input data, the single parameter strategy is more robust than the multi-parameter approach.

Infrared with Visual Image Fusion Based on Two-Scale Decomposition and Sturdy Guided Filtering Technique

Several Infrared (IR) and Visual (VIS) image fusion techniques have been widely used to acquire a novel image which may characterize the image accurately, completely and reliably. This process can serve an essential part in image processing applications. In this article, an enhanced IR and VIS image fusion technique is proposed by Two-Scale Decomposition (TSD) and Sturdy Guided Filtering (SGF) together to further increase the robustness of fusion process. Initially, IR and VIS images are decomposed for creating the base and detail layers. Then, Phase Congruency (PC) and Sum Modified Laplacian(SML) are applied to get saliency maps of base and detail layers, respectively. Also, Iteratively Reweighted Least Squares (IRLS) algorithm with GF, namely SGF is included instead of GF method in an efficient manner to properly smooth the weighting maps by preserving the depth edges that correspond to weak color edges and small structures. In this SGF technique, Enhanced Preconditioned Conjugate Gradient (EPCG) method is applied to optimize the RLS iteratively and select the conjugate paths for each iteration efficiently. This SGF can achieve high convergence rate and handle the structure inconsistency while properly preserving the edges. Experimental outcomes exhibit that the proposed TSD-PS-SGF based image fusion technique has higher performance over state-of-the-art techniques in terms of image feature-based, information theory-based and image structure-based metrics.

TRANSFORMATION BASED ALGORITHMS FOR CHANGE DETECTION IN FULL POLARIMETRIC REMOTE SENSING IMAGES

Abstract. Thanks to the recent advances in the development of polarimetric synthetic aperture radar (SAR) sensors, this remote sensing field attracts many applications. Among the different applications of these data, change detection is one of the most important applications. PolSAR images, due to interactions between electromagnetic waves and the target, could be used to study changes in the Earth's surface. This paper is a type of transformation-based method for polarimetric change detection (CD) purpose. For this purpose, we use full polarimetry imaging radar and extracted 138 features based on decomposition. The CD methods are the principal component analysis (PCA), the Multivariate Alteration Detection (MAD), the Iteratively Reweighted Multivariate Alteration Detection (IR-MAD), the Covariance Equalization (CE), and the Cross-Covariance (CRC). Assessment of the incorporated methods performed using most common criteria as quantity and quality assessment, such as overall accuracy (OA), kappa coefficient, and as visual analysis. The results of the experiments show that CC has better performance compared with other algorithms.

A nonlinear acceleration method for iterative algorithms

Iterative methods have led to better understanding and solving problems such as missing sampling, deconvolution, inverse systems, and impulsive and Salt and Pepper noise removal problems. However, the challenges regarding the speed of convergence and or the accuracy of the answer still remain. In order to improve the existing iterative algorithms, a non-linear method is discussed in this paper. The mentioned method is analyzed from different aspects, including its convergence and its ability to accelerate recursive algorithms. We show that this method is capable of improving Iterative Method (IM) as a non-uniform sampling reconstruction algorithm and some other iterative sparse recovery algorithms such as Iterative Reweighted Least Squares (IRLS), Iterative Method with Adaptive Thresholding (IMAT), Smoothed ℓ0 (SL0) and Alternating Direction Method of Multipliers (ADMM) for solving LASSO problem family (including LASSO itself, LASSO-LSQR and Group-LASSO). It is also capable of both accelerating and stabilizing the well-known Chebyshev Acceleration (CA) method. Furthermore, the proposed algorithm can extend the stability range by reducing the sensitivity of iterative algorithms to the changes of adaptation rate.

Total Variation Regularization Based on Iteratively Reweighted Least-Squares Method for Electrical Resistance Tomography

The regularization method has been utilized to address the ill-posed inverse problem of electrical resistance tomography (ERT). As one of the regularization methods, the total variation (TV) regularization method has the advantage of edge-preserving. A majority of research has been focused on the study of the penalty term in the TV method. In this article, a novel TV regularization based on iteratively reweighted least squares (TV-IRLS) method is proposed, in which, $L_{1}$ -norm is applied to the fidelity term, and a weighting matrix is applied to convert the $L_{1}$ -norm to $L_{2}$ -norm when calculating the objective function, which reduces the difficulty of solving the $L_{1}$ -norm. An improved generalized cross-validation method is adopted to determine the optimal regularization parameter (RP) automatically, and an automatic method is presented for the selection of the threshold value in the weighting matrix to guarantee the accuracy and speed of the solution. Meanwhile, a scaling factor is introduced to constrain the solution and ensure the stability of the solution. For verifying the performance of the proposed TV-IRLS regularization method, both numerical simulation and static experiments are carried out in the image reconstruction of ERT through qualitative and quantitative analysis. The results demonstrate that the proposed TV-IRLS regularization method performs well in improving the quality and resolution of the reconstructed images in ERT. Besides, it is more robust to data noises compared with the Tikhonov regularization method and TV regularization method.

SAR 3D sparse imaging based on CLA

A novel method for synthetic aperture radar (SAR) three-dimensional (3D) sparse imaging based on a coprime linear array (CLA) is proposed. To reduce the geometric resolution loss caused by under-sampled sparse SAR, a jointed sparse imaging approach is used. In this scheme, the coprime sampled data of CLA is separately processed via the iterative reweight least-squares approach, and their recovered results are combined to cancel the false targets and grating-lobes to improve the imaging quality. Both simulated and experimented results demonstrate the effectiveness of the method. It shows that the exploiting of CLA and sparse recovery can significantly reduce the linear array antenna amount and the geometric resolution loss compared with the conventional uniform linear array SAR.

A Robust Statistical Approach to Distributed Power System State Estimation With Bad Data

This paper presents a robust statistical approach to distributed power system state estimation (DPSSE) under bad data based on iterative reweight least squares (IRWLS) method and an improved alternating direction method of multipliers (ADMM) framework. In particular, the Hampel’s redescending and the Schweppe–Huber generalized M-estimators (SHGM) are studied for mitigating the adverse effect of outliers with large magnitude. Moreover, a new robust weight smoothing scheme is proposed for improving the numerical stability and convergence speed of the algorithm. The proposed approach is further extended to recursive monitoring of measurement devices and inpainting of missing data by utilizing prior information provided in previous state estimation. The resultant algorithm is solved using the Levenberg–Marquardt (LM) solver, which helps to maintain numerical stability under unexpected adverse situations. Experimental results show that the proposed approach outperforms conventional approaches using the ADMM with L1 outlier detection in state estimation accuracy and convergence speed. Moreover, it maintains numerical stability and good performance under missing data. As state estimation will be performed more frequently in future smart grid due to the increased penetration of renewables, the proposed methods and investigations offer much insight in addressing the missing data and outlier problems in DPSSE.

Alternating Iteratively Reweighted Least Squares Minimization for Low-Rank Matrix Factorization

Nowadays, the availability of large-scale data in disparate application domains urges the deployment of sophisticated tools for extracting valuable knowledge out of this huge bulk of information. In that vein, low-rank representations (LRRs), which seek low-dimensional embeddings of data have naturally appeared. In an effort to reduce computational complexity and improve estimation performance, LRR has been viewed via a matrix factorization (MF) perspective. Recently, low-rank MF (LRMF) approaches have been proposed for tackling the inherent weakness of MF, i.e., the unawareness of the dimension of the low-dimensional space where data reside. Herein, inspired by the merits of iterative reweighted schemes for sparse recovery and rank minimization, we come up with a generic low-rank promoting regularization function. Then, focusing on a specific instance of it, we propose a regularizer that imposes column-sparsity jointly on the two matrix factors that result from MF, thus promoting low-rankness on the optimization problem. The low-rank promoting properties of the resulting regularization term are brought to light by mathematically showing that it is actually a tight upper bound of a specific version of the weighted nuclear norm. The problems of denoising and matrix completion are redefined according to the new LRMF formulation and solved via efficient alternating iteratively reweighted least squares type algorithms. Theoretical analysis of the algorithms regarding the convergence and the rates of convergence to stationary points is provided. The effectiveness of the proposed algorithms is verified in diverse simulated and real data experiments.

Combining Binary and Post-Classification Change Analysis of Augmented ALOS Backscatter for Identifying Subtle Land Cover Changes

This research aims to detect subtle changes by combining binary change analysis, the Iteratively Reweighted Multivariate Alteration Detection (IRMAD), over dual polarimetric Advanced Land Observing Satellite (ALOS) backscatter with augmented data for post-classification change analysis. The accuracy of change detection was iteratively evaluated based on thresholds composed of mean and a range constant of standard deviation. Four datasets were examined for post-classification change analysis including the dual polarimetric backscatter as the benchmark and its augmented data with indices, entropy alpha decomposition and selected texture features. Variable importance was then evaluated to build a best subset model employing seven classifiers, including Bagged Classification and Regression Tree (CAB), Extreme Learning Machine Neural Network (ENN), Bagged Multivariate Adaptive Regression Spline (MAB), Regularised Random Forest (RFG), Original Random Forest (RFO), Support Vector Machine (SVM), and Extreme Gradient Boosting Tree (XGB). The best accuracy was 98.8%, which resulted from thresholding MAD variate-2 with constants at 1.7. The highest improvement of classification accuracy was obtained by amending the grey level co-occurrence matrix (GLCM) texture. The identification of variable importance (VI) confirmed that selected GLCM textures (mean and variance of HH or HV) were equally superior, while the contribution of index and decomposition were negligible. The best model produced similar classification accuracy at about 90% for both years 2007 and 2010. Tree-based algorithms including RFO, RFG and XGB were more robust than SVM and ENN. Subtle changes indicated by binary change analysis were somewhat hidden in post-classification analysis. Reclassification by combining all important variables and adding five classes to include subtle changes assisted by Google Earth yielded an accuracy of 82%.

Continuous Iteratively Reweighted Least Squares Algorithm for Solving Linear Models by Convex Relaxation

In this paper, we present continuous iteratively reweighted least squares algorithm (CIRLS) for solving the linear models problem by convex relaxation, and prove the convergence of this algorithm. Under some conditions, we give an error bound for the algorithm. In addition, the numerical result shows the efficiency of the algorithm.

Super-Resolution Channel Estimation for MmWave Massive MIMO With Hybrid Precoding

Channel estimation is challenging for millimeter-wave (mmWave) massive MIMO with hybrid precoding, since the number of radio frequency (RF) chains is much smaller than that of antennas. Conventional compressive sensing based channel estimation schemes suffer from severe resolution loss due to the channel angle quantization. To improve the channel estimation accuracy, we propose an iterative reweight (IR)-based super-resolution channel estimation scheme in this paper. By optimizing an objective function through the gradient descent method, the proposed scheme can iteratively move the estimated angle of arrivals/departures (AoAs/AoDs) towards the optimal solutions, and finally realize the super-resolution channel estimation. In the optimization, a weight parameter is used to control the tradeoff between the sparsity and the data fitting error. In addition, a singular value decomposition (SVD)-based preconditioning is developed to reduce the computational complexity of the proposed scheme. Simulation results verify the better performance of the proposed scheme than conventional solutions.

Study on baseline correction methods for the Fourier transform infrared spectra with different signal-to-noise ratios.

Removing the baseline from the spectra, which are measured by a Fourier transform infrared spectrometer (FTIR), is an important preprocessing step for further spectra analysis such as quantitative and qualitative analysis. An automatic baseline correction method named iterative averaging, which is based on the basic knowledge of moving average, is presented. We also compared it to other methods, such as rubber band, adaptive iterative reweight penalized least squares, automatic iterative moving average, and morphological weighted penalized least squares, using simulated and experimental spectra with different signal-to-noise ratios (SNRs) to evaluate the performance of these methods by performance metrics and to select an appropriate method to analyze FTIR spectra. Performance metrics such as root-mean-square error, goodness-of-fit coefficient, and chi-square are calculated. The iterative averaging method achieves the best results, which are judged by performance metrics values, when it is applied to the FTIR spectra with different SNRs. It also can correct the baseline of the FTIR spectra automatically, and improve the capability and adaptability of the unsupervised online analysis of the FTIR system effectively.

Relative radiometric normalization of bitemporal very high-resolution satellite images for flood change detection

Change-detection analysis using bitemporal satellite imagery is a reliable method for providing and assessing information about flood-induced changes over a wide area in a timely and cost-effective manner. Accurate radiometric normalization between bitemporal imagery is a critical component in the application of change-detection techniques to flood mapping because the accuracy of the change detection is directly affected by the quality of radiometric normalization. A methodology based on multivariate alteration detection (MAD) is introduced as an approach that enables reliable radiometric normalization of bitemporal very high-resolution (VHR) images for detecting flood-induced changes. The method uses a weighting function to adaptively identify weights based on open water features, which are estimated by the normalized difference water index, in the computation of the covariance matrices of the MAD transform. To quantitatively evaluate and test the performance of the proposed method, a comparison is made between it and the iteratively reweighted (IR)-MAD method based on statistical tests and the accuracy of flood change detection. Change vector analysis- and MAD-based change-detection methods were used for the comparison of the proposed and IR-MAD methods. Experimental results on KOMPSAT-2 bitemporal VHR images prove that the proposed method produced better results than the IR-MAD method in the statistical tests and also increased the overall accuracy of flood change detection by 1.8% and 12.6% for the two study sites.

PRIM: An Efficient Preconditioning Iterative Reweighted Least Squares Method for Parallel Brain MRI Reconstruction.

The most recent history of parallel Magnetic Resonance Imaging (pMRI) has in large part been devoted to finding ways to reduce acquisition time. While joint total variation (JTV) regularized model has been demonstrated as a powerful tool in increasing sampling speed for pMRI, however, the major bottleneck is the inefficiency of the optimization method. While all present state-of-the-art optimizations for the JTV model could only reach a sublinear convergence rate, in this paper, we squeeze the performance by proposing a linear-convergent optimization method for the JTV model. The proposed method is based on the Iterative Reweighted Least Squares algorithm. Due to the complexity of the tangled JTV objective, we design a novel preconditioner to further accelerate the proposed method. Extensive experiments demonstrate the superior performance of the proposed algorithm for pMRI regarding both accuracy and efficiency compared with state-of-the-art methods.

The Iterative Reweighted Alternating Direction Method of Multipliers for Separating Structural Layovers in SAR Tomography

Layover scatterers of tall building structures can be separated by synthetic aperture radar tomography (SAR-tomo). An iterative reweighted L1 minimization (IRL1) has been applied to enhance the sparsity in a tomographic inversion, where the basis pursuit (BP) technique was adopted to search for the solution. However, the IRL1 with BP is highly time-consuming, which may prevent its real application to large-scale data sets. In this letter, we propose the iterative reweighted alternating direction method of multipliers (IR-ADMM) for fast SAR-tomo imaging. We demonstrate and validate the enhanced sparsity and fast convergence of our IR-ADMM algorithm with experiments using both simulated data and TerraSAR-X Stripmap images of tall urban buildings. The experimental results show that compared with conventional IR-BP, the IR-ADMM greatly reduces the computation time without substantial performance degradation.

Relative Radiometric Normalisation - performance testing of selected techniques and impact analysis on vegetation and water bodies

In this paper, six image-based Relative Radiometric Normalization (RRN) techniques were applied to normalize the bi-temporal Landsat 5 TM data-set. RRN techniques do not require any atmospheric and ground information at the time of image acquisition. The target image for the year 2009 was normalized in such a way that it resembled the atmospheric and sensor conditions similar to those under which the reference image of the same season for the year 1990 was acquired. Among the selected methods applied, it was found that the Iteratively Reweighted Multivariate Alteration Detection (IR-MAD) method performed better, based on the error statistic. The IR-MAD technique was found to be advantageous as it identified a large set of true time-invariant pixels automatically from the change background using iterative canonical component analysis. The technique also stretches the values of Normalized Difference Vegetation Index and Normalized Difference Water Index and may help to distinguish different vegetation and water bodies better.