scholarly journals New Robust PCA for Outliers and Heavy Sparse Noises’ Detection via Affine Transformation, the L ∗ , w and L 2,1 Norms, and Spatial Weight Matrix in High-Dimensional Images: From the Perspective of Signal Processing

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Peidong Liang ◽  
Habte Tadesse Likassa ◽  
Chentao Zhang ◽  
Jielong Guo
Keyword(s):  
Signal Processing ◽  
Extreme Values ◽  
Weight Matrix ◽  
High Dimensional ◽  
Affine Transformations ◽  
Spatial Weight Matrix ◽  
Art Works ◽  
Spatial Weight ◽  
Recursive Equations

In this paper, we propose a novel robust algorithm for image recovery via affine transformations, the weighted nuclear, L ∗ , w , and the L 2,1 norms. The new method considers the spatial weight matrix to account the correlated samples in the data, the L 2,1 norm to tackle the dilemma of extreme values in the high-dimensional images, and the L ∗ , w norm newly added to alleviate the potential effects of outliers and heavy sparse noises, enabling the new approach to be more resilient to outliers and large variations in the high-dimensional images in signal processing. The determination of the parameters is involved, and the affine transformations are cast as a convex optimization problem. To mitigate the computational complexity, alternating iteratively reweighted direction method of multipliers (ADMM) method is utilized to derive a new set of recursive equations to update the optimization variables and the affine transformations iteratively in a round-robin manner. The new algorithm is superior to the state-of-the-art works in terms of accuracy on various public databases.

scholarly journals Research on the Spatial Correlation and Spatial Lag of COVID-19 Infection Based on Spatial Analysis

2021 ◽  
Vol 13 (21) ◽  
pp. 12013
Author(s):  
Keqiang Dong ◽  
Liao Guo
Keyword(s):  
Spatial Analysis ◽  
Spatial Correlation ◽  
Lagrange Multiplier ◽  
Weight Matrix ◽  
Primary Data ◽  
Lagrange Multiplier Test ◽  
Spatial Lag ◽  
Spatial Weight Matrix ◽  
The World ◽  
Spatial Weight

COVID-19 has spread throughout the world since the virus was discovered in 2019. Thus, this study aimed to identify the global transmission trend of the COVID-19 from the perspective of the spatial correlation and spatial lag. The research used primary data collected of daily increases in the amount of COVID-19 in 14 countries, confirmed diagnosis, recovered numbers, and deaths. Findings of the Moran index showed that the propagation of infection was aggregated between 9 May and 21 May based on the composite spatial weight matrix. The results from the Lagrange multiplier test indicated the COVID-19 patients can infect others with a lag.

scholarly journals Spatial weight matrix in dimensionality reduction reconstruction for micro-electromechanical system-based photoacoustic microscopy

2020 ◽  
Vol 3 (1) ◽  
Author(s):  
Yuanzheng Ma ◽  
Chang Lu ◽  
Kedi Xiong ◽  
Wuyu Zhang ◽  
Sihua Yang
Keyword(s):  
Image Reconstruction ◽  
Dimensionality Reduction ◽  
Optical Resolution ◽  
Distortion Correction ◽  
Electromechanical System ◽  
Weight Matrix ◽  
Photoacoustic Microscopy ◽  
Spatial Weight Matrix ◽  
Spatial Weight ◽  
Micro Electromechanical System

AbstractA micro-electromechanical system (MEMS) scanning mirror accelerates the raster scanning of optical-resolution photoacoustic microscopy (OR-PAM). However, the nonlinear tilt angular-voltage characteristic of a MEMS mirror introduces distortion into the maximum back-projection image. Moreover, the size of the airy disk, ultrasonic sensor properties, and thermal effects decrease the resolution. Thus, in this study, we proposed a spatial weight matrix (SWM) with a dimensionality reduction for image reconstruction. The three-layer SWM contains the invariable information of the system, which includes a spatial dependent distortion correction and 3D deconvolution. We employed an ordinal-valued Markov random field and the Harris Stephen algorithm, as well as a modified delay-and-sum method during a time reversal. The results from the experiments and a quantitative analysis demonstrate that images can be effectively reconstructed using an SWM; this is also true for severely distorted images. The index of the mutual information between the reference images and registered images was 70.33 times higher than the initial index, on average. Moreover, the peak signal-to-noise ratio was increased by 17.08% after 3D deconvolution. This accomplishment offers a practical approach to image reconstruction and a promising method to achieve a real-time distortion correction for MEMS-based OR-PAM.

scholarly journals On Misspecification of Spatial Weight Matrix for Small Area Estimation in Longitudinal Analysis

2013 ◽  
Vol 15 (4) ◽  
pp. 305-318
Author(s):  
Tomasz Żądło
Keyword(s):  
Sample Size ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Weight Matrix ◽  
Random Sample Size ◽  
Monte Carlo Simulation Study ◽  
Spatial Weight Matrix ◽  
First Case ◽  
Spatial Weight ◽  
Random Components

The problem of prediction of subpopulation (domain) total is studied as in Rao (2003). Considerations are based on spatially correlated longitudinal data. The domain of interest can be defined after sample selection what implies its random sample size. The special case of the General Linear Mixed Model is proposed where two random components obey assumptions of spatial and temporal moving average process respectively. Moreover, it is assumed that the population may change in time and elements’ affiliations to subpopulation may change in time as well. The proposed model is a generalization of longitudinal models studied by e.g. Verbeke, Molenberghs (2000) and Hedeker, Gibbons (2006). The best linear unbiased predictor (BLUP) is derived. It may be used even if the sample size in the subpopulation of interest in the period of interest is zero. In the Monte Carlo simulation study the accuracy of the empirical version of the BLUP will be studied in the case of correct and incorrect specification of the spatial weight matrix. Two cases of model misspecification are studied. In the first case the misspecified spatial weight is used. In the second case independence of random components is assumed but the variable which is used to compute elements of spatial weight matrix in the correct case will be used as auxiliary variable in the model.

scholarly journals New Robust Regularized Shrinkage Regression for High-Dimensional Image Recovery and Alignment via Affine Transformation and Tikhonov Regularization

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Habte Tadesse Likassa ◽  
Wen Xian ◽  
Xuan Tang
Keyword(s):  
Tikhonov Regularization ◽  
Affine Transformation ◽  
State Of The Art ◽  
High Dimensional ◽  
Affine Transformations ◽  
Regularization Term ◽  
Alternating Direction ◽  
Art Works ◽  
Programming Techniques ◽  
Public Datasets

In this work, a new robust regularized shrinkage regression method is proposed to recover and align high-dimensional images via affine transformation and Tikhonov regularization. To be more resilient with occlusions and illuminations, outliers, and heavy sparse noises, the new proposed approach incorporates novel ideas affine transformations and Tikhonov regularization into high-dimensional images. The highly corrupted, distorted, or misaligned images can be adjusted through the use of affine transformations and Tikhonov regularization term to ensure a trustful image decomposition. These novel ideas are very essential, especially in pruning out the potential impacts of annoying effects in high-dimensional images. Then, finding optimal variables through a set of affine transformations and Tikhonov regularization term is first casted as mathematical and statistical convex optimization programming techniques. Afterward, a fast alternating direction method for multipliers (ADMM) algorithm is applied, and the new equations are established to update the parameters involved and the affine transformations iteratively in the form of the round-robin manner. Moreover, the convergence of these new updating equations is scrutinized as well, and the proposed method has less time computation as compared to the state-of-the-art works. Conducted simulations have shown that the new robust method surpasses to the baselines for image alignment and recovery relying on some public datasets.

scholarly journals Application of economic distance for the purposes of a spatial analysis of the unemployment rate for Poland

2010 ◽  
Vol 1 (1) ◽  
pp. 79-98 ◽  
Author(s):  
Michał Bernard Pietrzak
Keyword(s):  
Spatial Analysis ◽  
Physical Properties ◽  
Unemployment Rate ◽  
Spatial Econometrics ◽  
Weight Matrix ◽  
Spatial Weight Matrix ◽  
Economic Distance ◽  
Spatial Weight ◽  
The Matrix ◽  
The Impact

The article presents the problem of the application of the spatial weigh matrix based on economic distance in spatial analysis of the unemployment rate. The spatial weight matrix expresses potential spatial interactions between the researched areas and forms a basis for the instruments applied in spatial econometrics. While identifying the neighbourhood, the following criteria are used: a common border, distance, and the k number of the nearest neighbours. The potential force of impact is identified by means of the standardisation of the matrix by rows to unity, or by means of the distance based on the physical properties of the areas. The disadvantage of the matrix standardisation is the fact of accepting the same force of impact for all the areas. It seems natural is the differentiation of the force of the impact dependent on the selected areas which should result from the differences and similarities of the areas in the scope of the researched phenomenon and its determinants. The use of the distance based on physical properties of the areas allows considering the diverse force of impact of neighbouring areas, which, in turn, allows to obtain a more precise outcome of analyses. Unfortunately, physical properties do not constitute the determinants of economic phenomena covered by a spatial analysis which means that they are not related directly to the scrutinised phenomenon. The application of economic distance for building spatial weight matrix shown in the present paper constitutes a way of determining of the force of impact for the economic spatial processes that is alternative to the distance based on physical properties of the researched areas and to the proposal of the standardisation by rows to unity.

scholarly journals W: SPATIAL WEIGHT MATRIX DIVERSITY AND ITS IMPACT ON SPATIAL ANALYSIS RESULTS

2019 ◽  
Vol 2 (1) ◽  
pp. 209-213
Author(s):  
Simona Mackova
Keyword(s):  
Spatial Analysis ◽  
Spatial Econometrics ◽  
Stochastic Matrix ◽  
Spatial Regression ◽  
Regional Analysis ◽  
Geographical Location ◽  
Spillover Effects ◽  
Weight Matrix ◽  
Spatial Weight Matrix ◽  
Spatial Weight

Spatial econometrics presents irreplaceable tool for regional analysis. Omitting additional information about geographical location of observed units could neglect some important influences. The spatial weight matrix W determining neighbourhood relations and degree of influence between observed units belongs to the main components of spatial analysis. Various specification approaches of this non-stochastic matrix could be applied. There is a commonly held belief that spatial regression models are sensitive to spatial weight structure. Some analytics consider it as a myth and points out incorrect interpretation of the model coefficients or misspecified models. Does it really matter what kind of specification is used? This contribution brings an empirical example of several approaches to neighbourhood specification and compares obtained results. According to findings of this analysis, especially spillover effects are incomparable. That confirms unequal performance of spatial structures. The W matrix should be built carefully at the beginning of each spatial analysis task.   

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