Gaussian Scale Research Articles

Probabilistic robust regression with adaptive weights — a case study on face recognition

Robust regression plays an important role in many machine learning problems. A primal approach relies on the use of Huber loss and an iteratively reweighted l2 method. However, because the Huber loss is not smooth and its corresponding distribution cannot be represented as a Gaussian scale mixture, such an approach is extremely difficult to handle using a probabilistic framework. To address those limitations, this paper proposes two novel losses and the corresponding probability functions. One is called Soft Huber, which is well suited for modeling non-Gaussian noise. Another is Nonconvex Huber, which can help produce much sparser results when imposed as a prior on regression vector. They can represent any lq loss ($${1 \over 2}$$ ⩽ q < 2) with tuning parameters, which makes the regression model more robust. We also show that both distributions have an elegant form, which is a Gaussian scale mixture with a generalized inverse Gaussian mixing density. This enables us to devise an expectation maximization (EM) algorithm for solving the regression model. We can obtain an adaptive weight through EM, which is very useful to remove noise data or irrelevant features in regression problems. We apply our model to the face recognition problem and show that it not only reduces the impact of noise pixels but also removes more irrelevant face images. Our experiments demonstrate the promising results on two datasets.

Yet another note on the arithmetic-geometric mean inequality

It was shown by E. Gluskin and V.D. Milman in [GAFA Lecture Notes in Math. 1807, 2003] that the classical arithmetic-geometric mean inequality can be reversed (up to a multiplicative constant) with high probability, when applied to coordinates of a point chosen with respect to the surface unit measure on a high-dimensional Euclidean sphere. We present here two asymptotic refinements of this phenomenon in the more general setting of the surface probability measure on a high-dimensional $\ell_p$-sphere, and also show that sampling the point according to either the cone probability measure on $\ell_p$ or the uniform distribution on the ball enclosed by $\ell_p$ yields the same results. First, we prove a central limit theorem, which allows us to identify the precise constants in the reverse inequality. Second, we prove the large deviations counterpart to the central limit theorem, thereby describing the asymptotic behavior beyond the Gaussian scale, and identify the rate function.

Robust Gaussian process regression with G-confluent likelihood

For robust Gaussian process regression problems where the measurements are contaminated by outliers, a likelihood/measurement noise model with heavy-tailed distributions should be used to improve the prediction performance. In this paper, we propose to use a G-confluent distribution as the measurement noise model and a coordinate ascent variational inference method to infer the overall statistical model. In contrast with the commonly used Student’s t distribution, the G-confluent distribution can also be written as a Gaussian scale mixture, but its inverse scale follows a Beta distribution rather than a Gamma distribution, and its main advantage is that it is more flexible for modeling outliers while being equally suitable for variational inference. Numerical simulations based on benchmark data show that the G-confluent distribution performs better than or as well as the Student’s t distribution.

Sparse Bayesian DOA Estimation Using Hierarchical Synthesis Lasso Priors for Off-Grid Signals

Within the conventional sparse Bayesian learning (SBL) framework, only Gaussian scale mixtures have been adopted to model sparsity-inducing priors that guarantee the exact inverse recovery. In light of the relative scarcity of formal SBL tools in enforcing a proper sparsity profile of signal vectors, we explore the use of hierarchical synthesis lasso (HSL) priors for representing the same small subset of features among multiple responses. We outline a viable approximation to this particular choice of sparse prior, leading to tractable marginalization over all weights and hyperparameters. We then discuss how the statistical variables of the hierarchical Bayesian model can be estimated via an adaptive updating formula, and include a refined one dimensional searching procedure to extraordinarily improve the direction of arrival (DOA) estimation performance when take the off-grid DOAs into account. Using these modifications, we show that exploiting HSL priors are very helpful in encouraging sparseness. Numerical simulations also verify the superiority of the proposal in terms of convergence speed and root mean squared estimation error, as compared to the traditional and more recent sparse Bayesian algorithms.

Grading of Metacarpophalangeal Rheumatoid Arthritis on Ultrasound Images Using Machine Learning Algorithms

The grading evaluation of metacarpophalangeal rheumatoid arthritis (RA) ultrasonic images is a diagnostic challenge that heavily relies on the expertise of trained sonographers. This study presents a grading method for detecting and estimating the geometric and texture features of synovium thickening and bone erosion. Unlike previous studies in this area, this work uses the metrics and texture features of region of interest (ROI). The highlighted feature of metacarpophalangeal bone and the dark feature of the synovial thickening are extracted simultaneously by the segmented method based on the Gaussian scale space. The segmented results are analyzed to extract three quantitative geometric parameters, which are combined with gray-level co-occurrence matrix (GLCM) statistic texture features to describe the ultrasonic image of metacarpophalangeal RA. To obtain the preferable ability of classification, we applied a support vector machine (SVM) and various feature descriptors, including GLCM, local binary patterns (LBP), and GLCM + LBP, to grade the ultrasonic image of metacarpophalangeal RA. Results show that the SVM, based on our feature descriptor, provides the highest accuracy of up to 92.50%, of the four descriptors. The SVM based on GLCM+LBP descriptor shows better accuracy (86.55%) than either SVM + LBP (85.43%) or SVM+GLCM (82.51%) for discriminating among four grade RA ultrasonic images. Overall, this methodology points to a significant grading of metacarpophalangeal RA ultrasound images without medical expert analysis or blood sample analysis, such as detecting C-reactive protein, measuring erythrocyte sedimentation rate, and testing rheumatoid factor.

Research on the Calibration of Binocular Camera Based on BP Neural Network Optimized by Improved Genetic Simulated Annealing Algorithm

The Back Propagation (BP) neural network has the problems of low accuracy and poor convergence in the process of binocular camera calibration. A method based on BP neural network optimized by improved genetic simulated annealing algorithm (IGSAA-BP) is proposed to solve these problems to complete the binocular camera calibration. The method of combining Gaussian scale space and Harris corner detection operator is used for corner detection. A matched algorithm of homonymous corner is proposed by combining point-to-point spatial mapping and grid motion statistics. The pixel values of the homonymous corner and three-dimensional coordinate values are taken as the input and output of BP neural network respectively. The crossover and mutation probability of genetic simulated annealing algorithm and the annealing criterion are improved, the IGSAA-BP neural network is used to calibrate the binocular camera. The average calibration accuracy of BP neural network and IGSAA-BP neural network is 0.71mm and 0.03mm, respectively. The average calibration accuracy of binocular camera is improved by 96%. The iteration speed is increased by 20 times and global optimization ability is improved. It can be seen that the IGSAA-BP neural network can improve the calibration accuracy of binocular camera and accelerate convergence speed.

Pig Ear Extraction Based on an Improved Active Contour Model

Abstract.With the integration and scale of pig breeding, the frequency of some diseases is also increasing. To automatically detect porcine reproductive and respiratory syndrome (PRRS) during the pig cultivation process, this article proposes an improved method for pig ear extraction that is based on the active contour model. Firstly, we use the Gaussian scale space filtering and piecewise linear transformation algorithm to highlight the target zones of interest. Secondly, we use a randomly picked ear image point to reconstruct the image region and combine the active contour model to coarse segment the ear image. Finally, by taking advantage of the modified active contour model, the method precisely extracts the pig ear image. The experimental result shows that the proposed method can achieve better segmentation results. The segmentation accuracy of the image of pig contains only one ear can exceed 90%, and the accuracy of the image of pig contains two ears is greater than 85%. Keywords: Active contour model, Ear extraction, Image enhancement, Spline interpolation.

An image NSCT-HMT model based on copula entropy multivariate Gaussian scale mixtures

As an important multiscale geometric analysis tool, the nonsubsampled contourlet transform (NSCT) has a strong ability in capturing anisotropy and directional features of images. This paper proposes a copula entropy multivariate Gaussian scale mixtures based nonsubsampled contourlet transform hidden Markov tree model (CE-NSCT-HMT). First, we study the probability density distribution of the NSCT coefficients and observe that they exhibit a sharp peak at the zero amplitude and two heavy tails on both sides of the peak. Second, we redefine the generalized neighborhood relationship of the NSCT coefficients and then analyze the joint statistical property among them. We get that the NSCT coefficients have the strongest correlation with their newly defined ‘four neighborhood’ coefficients. Third, we use the Gaussian copula function to model the NSCT coefficients with their ‘four neighborhood’ coefficients. Based on the copula entropy value, the copula entropy multivariate Gaussian scale mixtures distribution is proposed, the application of copula entropy helps the contourlet a lot in localizing textures. In addition, we combine these studies with the hidden Markov tree model and propose the CE-NSCT-HMT model. Finally, the proposed model is applied to image denoising and achieve a good performance. The copula entropy is first applied to the correlation measurement of multiscale decomposition coefficients in this paper, which provides a way to further extend the application of copula entropy to other image processing area.

Bi‐ISAR sparse imaging algorithm with complex Gaussian scale mixture prior

The performance of both autofocusing and imaging resolution degrades using the traditional autofocusing and range–Doppler algorithm for bistatic inverse synthetic aperture radar (Bi-ISAR) with sparse apertures. A Bi-ISAR sparse imaging algorithm based on complex Gaussian scale mixture (CGSM) prior is proposed to jointly achieve the high-resolution imaging and autofocusing. First, a sparse basis matrix with the time-varying bistatic angle is constructed to represent the sparse echo data and the Bi-ISAR joint with autofocusing imaging model is established based on compressed sensing from sparse apertures. Second, the elements of the target image and the noise are assumed to be a CGSM prior with Gaussian distribution, respectively. Finally, the sparse image reconstruction and phase autofocusing are accomplished by the variational Bayesian expectation maximisation method. The proposed algorithm with the full Bayesian inference can obtain a well-focused image without manual adjustments of regularisation parameters. Meanwhile, it can avoid the local minimum and structural errors, due to utilising the statistical information of a posterior. Simulated results of electromagnetic numerical data verify the superiority of the algorithm in autofocusing, sparse imaging and noise suppression performance.

Detection of splicing forgery using differential evolution and wavelet decomposition

Abstract In this paper, we have proposed a computationally efficient algorithm to detect splicing (copy-create) forgery, our proposed method is developed by using differential evolution and wavelet decomposition, the differential evolution algorithm automatically generates customized parameter values of tampered images, and wavelet decomposition is used to process large-size images under block-based framework. Our proposed method is resilient to distortions, such as the addition of Gaussian noise, scaling and compression of the forged images.

A Full-Reference Image Quality Assessment for Multiply Distorted Image based on Visual Mutual Information

Abstract A full-reference image quality assessment (FR-IQA) method for multi-distortion based on visual mutual information (MD-IQA) is proposed to solve the problem that the existing FR-IQA methods are mostly applicable to single-distorted images, but the assessment result for multiply distorted images is not ideal. First, the reference image and the distorted image are preprocessed by steerable pyramid decomposition and contrast sensitivity function (CSF). Next, a Gaussian scale mixture (GSM) model and an image distorted model are respectively constructed for the reference images and the distorted images. Then, visual distorted models are constructed both for the reference images and the distorted images. Finally, the mutual information between the processed reference image and the distorted image is calculated to obtain the full-reference quality assessment index for multiply distorted images. The experimental results show that the proposed method has higher accuracy and better performance for multiply distorted images.

Image-Based Copy-Paste Tamper Detection Technology Based on Improved Surf

Aiming at the problem that the existing copy-paste tamper detection algorithm has poor detection effect on the image area, and the speed is slow, an image region copy-paste tampering detection algorithm based on improved SURF is proposed. The detected image extracts feature points by improving the fast Hessian matrix, and uses k-g2NN method to match the feature points, then estimates the affine transformation parameters between the matching points, and combines the R-RANSAC and SPRT to eliminate the mismatch and finally obtain the copy-paste area. The experimental results show that the proposed algorithm can accurately locate the image copy-paste tampering region, and has strong robustness to Gaussian blur, rotation and scaling operations, and the detection speed is greatly improved.

Robust Kalman Filters Based on Gaussian Scale Mixture Distributions With Application to Target Tracking

In this paper, a new robust Kalman filtering framework for a linear system with non-Gaussian heavy-tailed and/or skewed state and measurement noises is proposed through modeling one-step prediction and likelihood probability density functions as Gaussian scale mixture (GSM) distributions. The state vector, mixing parameters, scale matrices, and shape parameters are simultaneously inferred utilizing standard variational Bayesian approach. As the implementations of the proposed method, several solutions corresponding to some special GSM distributions are derived. The proposed robust Kalman filters are tested in a manoeuvring target tracking example. Simulation results show that the proposed robust Kalman filters have a better estimation accuracy and smaller biases compared to the existing state-of-the-art Kalman filters.

Copy‐for‐duplication forgery detection in colour images using QPCETMs and sub‐image approach

Most of the existing copy-move forgery detection (CMFD) methods utilised time-consuming overlapped block-based approach. Here, a novel sub-image approach is proposed for extremely fast and highly accurate detecting of the duplicated forged objects in colour images. The proposed approach consists of few steps. The input coloured images are converted into the hue-saturation-value (HSV) colour model. Then, the edges of all objects in the forged image are detected using the Sobel operator. Morphological opening operator and median filter are used in removing unnecessary small objects. The boundaries of the duplicated objects are accurately detected. A bounding rectangle is drawn around the detected object to form a sub-image. The features of this sub-image are extracted by using the quaternion polar complex exponential transform moments (QPCETMs) and their invariants to rotation, scaling, and translation. Finally, the duplicated regions are matched via calculating the Euclidian distances and the correlation between the feature vectors. Experiments are performed using different types of duplicated regions. The obtained results of the proposed method are much accurate when compared with the results of the existing methods. Also, the proposed method exhibits high robustness against different attacks such as additive white Gaussian noise, JPEG compression, scaling, and rotation.

Robust Rauch–Tung–Striebel Smoothing Framework for Heavy-Tailed and/or Skew Noises

A novel robust Rauch–Tung–Striebel smoothing framework is proposed based on a generalized Gaussian scale mixture (GGScM) distribution for a linear state-space model with heavy-tailed and/or skew noises. The state trajectory, mixing parameters, and unknown distribution parameters are jointly inferred using the variational Bayesian approach. As such, a major contribution of this paper is unifying results within the GGScM distribution framework. Simulation and experimental results demonstrate that the proposed smoother has better accuracy than existing smoothers.

Improvement of Harris Algorithm Based on Gaussian Scale Space

Improvement of Harris Algorithm Based on Gaussian Scale Space

Toward Flotation Process Operation-State Identification via Statistical Modeling of Biologically Inspired Gabor Filtering Responses

This paper presents a froth image statistical modeling-based online flotation process operation-state identification method by introducing a biologically inspired Gabor wavelet transform in accordance with the physiological findings in the biological vision system. It derived the latent probabilistic density models of these biologically inspired Gabor filtering responses (GFRs) based on a versatile intermediate probability modeling frame, Gaussian scale mixture model. It has demonstrated that both the real and the imaginary representation of GFR obey a Laplace distribution. Accordingly, the amplitude representation of GFR obeys a Gamma distribution. Whereas the phase representation of GFR is an important yet frequently ignored aspect in Gabor-based signal analysis; it is demonstrated to be a periodic distribution and can be expressed by a von Mises-like distribution model. Successively, a local spline regression (LSR)-based classifier that the maps scattered statistical feature points of froth images directly to the operation-state labels smoothly is introduced for the operation-state recognition. Extensive confirmatory and comparative experiments on an industrial-scale bauxite flotation process demonstrate the effectiveness and superiority of the proposed method. Performance effects on different parameter settings, e.g., parameters of Gabor kernel and dimensionalities of multivariate statistical models, are further discussed.

Significance Tests for Boosted Location and Scale Models with Linear Base-Learners.

Generalized additive models for location scale and shape (GAMLSS) offer very flexible solutions to a wide range of statistical analysis problems, but can be challenging in terms of proper model specification. This complex task can be simplified using regularization techniques such as gradient boosting algorithms, but the estimates derived from such models are shrunken towards zero and it is consequently not straightforward to calculate proper confidence intervals or test statistics. In this article, we propose two strategies to obtain p-values for linear effect estimates for Gaussian location and scale models based on permutation tests and a parametric bootstrap approach. These procedures can provide a solution for one of the remaining problems in the application of gradient boosting algorithms for distributional regression in biostatistical data analyses. Results from extensive simulations indicate that in low-dimensional data both suggested approaches are able to hold the type-I error threshold and provide reasonable test power comparable to the Wald-type test for maximum likelihood inference. In high-dimensional data, when gradient boosting is the only feasible inference for this model class, the power decreases but the type-I error is still under control. In addition, we demonstrate the application of both tests in an epidemiological study to analyse the impact of physical exercise on both average and the stability of the lung function of elderly people in Germany.

Structured Graph Dictionary Learning and Application on the Seismic Denoising

Sparse coding method has been used for seismic denoising, as the data can be sparsely represented by the sparse transform and dictionary learning (DL) methods. DL methods have attracted wide attention because the learned dictionary is adaptive. However, for seismic denoising, the dictionary learned from the noise data is a mix of atoms representing seismic data patterns and atoms representing noise patterns. To make the dictionary contain more atoms to represent seismic data, we consider adding to the dictionary the local and nonlocal similarities of the data via the structured graph and propose a new DL method, namely, the structured graph dictionary learning (SGDL). The atoms of dictionary learned by the SGDL are smooth, which implies smoothness of any signal represented over this dictionary. In addition, in the dictionary domain, we use the nonlocal model, namely, SSC-GSM that connects Gaussian scale mixture (GSM) with simultaneous sparse coding (SSC), to represent the seismic data. We apply the method to the synthetic data and two kinds of field data. Results show that our method can better remove strong noise and retain the seismic weak events also.

Variational Bayesian inference based robust multiple measurement sparse signal recovery

This work concentrates on not only probing into a novel Bayesian probabilistic model to formulate a general type of robust multiple measurement vectors sparse signal recovery problem with impulsive noise, but also developing an improved variational Bayesian method to recover the original joint row sparse signals. In the design of the model, two three-level hierarchical Bayesian estimation procedures are designed to characterize impulsive noise and joint row sparse source signals by means of Gaussian scale mixtures and multivariate generalized t distribution. Those hidden variables, included in signal and measurement models are estimated based on a variational Bayesian framework, in which multiple kinds of probability distributions are adopted to express their features. In the design of the algorithm, the proposed algorithm is a full Bayesian inference approach related to variational Bayesian estimation. It is robust to impulsive noise, since the posterior distribution estimation can be effectively approached through estimating unknown parameters. Extensive simulation results show that the proposed algorithm significantly outperforms the compared robust sparse signal recovery approaches under different kinds of impulsive noises.