Group Sparse Model Research Articles

Multi-component group sparse RPCA model for motion object detection under complex dynamic background

Abstract Robust PCA model and its variants are promising tools for motion object detection, which decompose video or image sequences matrix into a low rank background component and a sparse moving object component. Although they can handle static background well, the background motion is usually mixed in the sparse components under the condition of complex dynamic background, such as fountains, ripples, and shaking leaves, etc. Meanwhile, the detected boundaries of foreground objects are usually inaccurate and incomplete. In this paper, a multi-component group sparse RPCA model is proposed to cope with all the difficulties mentioned above. With the aiming to separate foreground motion object from dynamic background, our model represents the observed video or image sequences as three components, i.e., a low-rank static background, a group sparse foreground, and a dynamic background. In order to integrate the object boundary prior, each frame is over-segmented into super-pixels which are taken as the group information to define a group sparse norm. Accordingly, the group sparse norm takes each super-pixels as a whole to measure the sparse foreground. Furthermore, an incoherence term is introduced to enhance the separability of sparse foreground motion from dynamic background component. We further apply alternating direction method of multipliers algorithm to solve the proposed model. Extensive experiment results demonstrate the superiority of our method over some representative methods.

Object-Oriented Hierarchy Radiation Consistency for Different Temporal and Different Sensor Images.

In the paper, we propose a novel object-oriented hierarchy radiation consistency method for dense matching of different temporal and different sensor data in the 3D reconstruction. For different temporal images, our illumination consistency method is proposed to solve both the illumination uniformity for a single image and the relative illumination normalization for image pairs. Especially in the relative illumination normalization step, singular value equalization and linear relationship of the invariant pixels is combined used for the initial global illumination normalization and the object-oriented refined illumination normalization in detail, respectively. For different sensor images, we propose the union group sparse method, which is based on improving the original group sparse model. The different sensor images are set to a similar smoothness level by the same threshold of singular value from the union group matrix. Our method comprehensively considered the influence factors on the dense matching of the different temporal and different sensor stereoscopic image pairs to simultaneously improve the illumination consistency and the smoothness consistency. The radiation consistency experimental results verify the effectiveness and superiority of the proposed method by comparing two other methods. Moreover, in the dense matching experiment of the mixed stereoscopic image pairs, our method has more advantages for objects in the urban area.

Adaptive group sparse representation in fetal echocardiogram segmentation

This paper present a novel group sparse representation model to segment four cardiac chambers in fetal echocardiograms. By incorporating the group reconstruction error, sparsity and distinctive term in a unified framework, the model is able to exploit the inherent structure of echocardiograms, constructing a discriminative group dictionary. A novel adaptive group dictionary learning approach is developed to obtain a compact dictionary with high atoms’ utilization and low complexity. With the learned dictionary, the reconstruction residue is employed to discriminate the initial location of four chambers. The local appearances are used to regionally refine the final contours. Extensive experiments have been conducted to evaluate the performance of our proposed AGDL and its application in the fetal echocardiogram segmentation. The results demonstrate both representation and discriminative power of our approach and its superior performances to other competing state-of-the-art sparse representation methods and general intensity models. Our approach is capable of learning a more compact and discriminative group dictionary, providing robust and accurate four-chamber segmentation results.

A method of infrared nephogram super-resolution based on structural group sparse representation

For the problems of low-resolution and poor visual effect of infrared cloud images, a super-resolution method based on structural group sparse representation was proposed. In consideration of the self similarity of infrared image, a structural group sparse representation model was first established. In the training stage, the Gauss mixture model is used to study the prior information of the image structure group, and then to cluster it, using principal component analysis to get a compact classification dictionary. In the reconstruction phase, the best matching dictionary of each structure group is selected, adaptively reweighted l1-norm sparsity is introduced to effectively obtain sparse coefficient. Experimental results demonstrate that our method can achieve better reconstruction effect in both subjective visual effect and objective evaluation criteria compared with ScSR, Zeyde and NARM methods.

Super-resolution in sound field recording and reproduction based on sparse representation

Sound field recording and reproduction enables us to construct more realistic audio systems. In practical systems, sound pressure is obtained with microphones in a recording area, and then the sound field is reproduced with loudspeakers in a target area. Therefore, a signal conversion algorithm for obtaining the driving signals of the loudspeakers from the signals received by the microphones is necessary. Most of the current methods are based on the sound field analysis and synthesis in the spatial frequency domain. Although these methods make it possible for stable and efficient signal conversion, artifacts originating from spatial aliasing notably occur, which depends on the intervals of microphones and loudspeakers. We have proposed a signal conversion method based on sparse sound field decomposition, which enables sound field recording and reproduction above the spatial Nyquist frequency. By using sparse decomposition algorithms, the sound pressure distribution can be represented using a small number of fundamental solutions of the Helmholtz equation, such as Green's functions. Group sparse signal models are also required for accurate and robust decomposition. In this presentation, we reports on comparisons between several group sparse signal models and decomposition algorithms as well as their relation to reproduction performances.

Image denoising via adaptive eigenvectors of graph Laplacian

An image denoising method via adaptive eigenvectors of graph Laplacian (EGL) is proposed. Unlike the trivial parameter setting of the used eigenvectors in the traditional EGL method, in our method, the eigenvectors are adaptively selected in the whole denoising procedure. In detail, a rough image is first built with the eigenvectors from the noisy image, where the eigenvectors are selected by using the deviation estimation of the clean image. Subsequently, a guided image is effectively restored with a weighted average of the noisy and rough images. In this operation, the average coefficient is adaptively obtained to set the deviation of the guided image to approximately that of the clean image. Finally, the denoised image is achieved by a group-sparse model with the pattern from the guided image, where the eigenvectors are chosen in the error control of the noise deviation. Moreover, a modified group orthogonal matching pursuit algorithm is developed to efficiently solve the above group sparse model. The experiments show that our method not only improves the practicality of the EGL methods with the dependence reduction of the parameter setting, but also can outperform some well-developed denoising methods, especially for noise with large deviations.

Discriminative Dictionary Learning With Two-Level Low Rank and Group Sparse Decomposition for Image Classification.

Discriminative dictionary learning (DDL) framework has been widely used in image classification which aims to learn some class-specific feature vectors as well as a representative dictionary according to a set of labeled training samples. However, interclass similarities and intraclass variances among input samples and learned features will generally weaken the representability of dictionary and the discrimination of feature vectors so as to degrade the classification performance. Therefore, how to explicitly represent them becomes an important issue. In this paper, we present a novel DDL framework with two-level low rank and group sparse decomposition model. In the first level, we learn a class-shared and several class-specific dictionaries, where a low rank and a group sparse regularization are, respectively, imposed on the corresponding feature matrices. In the second level, the class-specific feature matrix will be further decomposed into a low rank and a sparse matrix so that intraclass variances can be separated to concentrate the corresponding feature vectors. Extensive experimental results demonstrate the effectiveness of our model. Compared with the other state-of-the-arts on several popular image databases, our model can achieve a competitive or better performance in terms of the classification accuracy.

A time-varying group sparse additive model for genome-wide association studies of dynamic complex traits.

Despite the widespread popularity of genome-wide association studies (GWAS) for genetic mapping of complex traits, most existing GWAS methodologies are still limited to the use of static phenotypes measured at a single time point. In this work, we propose a new method for association mapping that considers dynamic phenotypes measured at a sequence of time points. Our approach relies on the use of Time-Varying Group Sparse Additive Models (TV-GroupSpAM) for high-dimensional, functional regression. This new model detects a sparse set of genomic loci that are associated with trait dynamics, and demonstrates increased statistical power over existing methods. We evaluate our method via experiments on synthetic data and perform a proof-of-concept analysis for detecting single nucleotide polymorphisms associated with two phenotypes used to assess asthma severity: forced vital capacity, a sensitive measure of airway obstruction and bronchodilator response, which measures lung response to bronchodilator drugs. Source code for TV-GroupSpAM freely available for download at http://www.cs.cmu.edu/~mmarchet/projects/tv_group_spam, implemented in MATLAB. epxing@cs.cmu.edu Supplementary data are available at Bioinformatics online.

Variational Bayesian image restoration with group-sparse modeling of wavelet coefficients

In this work, we present a recent wavelet-based image restoration framework based on a group-sparse Gaussian scale mixture model. A hierarchical Bayesian estimation is derived using a combination of variational Bayesian inference and a subband-adaptive majorization–minimization method that simplifies computation of the posterior distribution. We show that both of these iterative methods can converge together without needing nested loops, and thus good solutions can be found rapidly in the non-convex search space. We also integrate our method, variational Bayesian with majorization minimization (VBMM), with tree-structured modeling of the wavelet coefficients. This extension achieves significant gains in performance over the coefficient-sparse version of the algorithm. The experimental results demonstrate that the proposed method and its tree-structured extensions are effective for various imaging applications such as image deconvolution, image superresolution and compressive sensing magnetic resonance imaging (MRI) reconstruction, and that they outperform more conventional sparsity-inducing methods based on the l1-norm.

Laplace Group Sensing for Acoustic Models

This paper presents the group sparse learning for acoustic models where a sequence of acoustic features is driven by Markov chain and each feature vector is represented by groups of basis vectors. The group of common bases represents the features across Markov states within a regression class. The group of individual basis compensates the intra-state residual information. Laplace distribution is used as the sparse prior of sensing weights for group basis representation. Laplace parameter serves as regularization parameter or automatic relevance determination which controls the selection of relevant bases for acoustic modeling. The groups of regularization parameters and basis vectors are estimated from training data by maximizing the marginal likelihood over sensing weights which is implemented by Laplace approximation using the Hessian matrix and the maximum a posteriori parameters. Model uncertainty is compensated through full Bayesian treatment. The connection of Laplace group sensing to lasso regularization is illustrated. Experiments on noisy speech recognition show the robustness of group sparse acoustic models in presence of different noise types and SNRs.

Bayesian Group-Sparse Modeling and Variational Inference

In this paper, we present a general class of multivariate priors for group-sparse modeling within the Bayesian framework. We show that special cases of this class correspond to multivariate versions of several classical priors used for sparse modeling. Hence, this general prior formulation is helpful in analyzing the properties of different modeling approaches and their connections. We derive the estimation procedures with these priors using variational inference for fully Bayesian estimation. In addition, we discuss the differences between the proposed inference and deterministic inference approaches with these priors. Finally, we show the flexibility of this modeling by considering several extensions such as multiple measurements, within-group correlations, and overlapping groups.

Laplacian group sparse modeling of human actions

Recently, many local-feature based methods have been proposed for feature learning to obtain a better high-level representation of human behavior. Most of the previous research ignores the structural information existing among local features in the same video sequences, while it is an important clue to distinguish ambiguous actions. To address this issue, we propose a Laplacian group sparse coding for human behavior representation. Unlike traditional methods such as sparse coding, our approach prefers to encode a group of relevant features simultaneously and meanwhile allow as less atoms as possible to participate in the approximation so that video-level sparsity is guaranteed. By incorporating Laplacian regularization the method is capable to ensure the similar approximation of closely related local features and the structural information is successfully preserved. Thus, a compact but discriminative human behavior representation is achieved. Besides, the objective of our model is solved with a closed-form solution, which reduces the computational cost significantly. Promising results on several popular benchmark datasets prove the efficiency and effectiveness of our approach.

Infrared image super-resolution via locality-constrained group sparse model

Aiming at the problems of low-resolution and poor visual quality of infrared images, a locality-constrained group sparsity based infrared image super-resolution algorithm is proposed. Firstly with considering the texture self-similarity of infrared images and group structural sparsity of atom coefficients, a locality-constrained group sparse (LCGS) model is proposed. Secondly, under LCGS and K-singular value decomposition, a pair of group structural dictionaries is learned. The dictionary pair can well capture and preserve the intrinsic geometrical manifold of low and high resolution data. Finally, the high-resolution infrared images are recovered by the high-resolution dictionary and the corresponding low-resolution group sparse coefficients. Experimental results show that the proposed method obtains excellent performance in objective evaluation and subjective visual effect.

Robust sparse bounding sphere for 3D face recognition

A robust sparse bounding sphere representation (RSBSR) is proposed to analyze 3D facial data. There are many obstacles to distinguishing facial differences, such as large pose and expression variations, hair occlusions and noise corruptions. In our framework, 3D point clouds are first preprocessed to remove the irrelevant areas and to align with a frontal neutral face model for overcoming the influence of large pose variations based on axis-angle representation. Then, 3D facial models are projected on the bounding spheres to describe both the depth and 3D geometric shape information, referred to as bounding sphere representation (BSR). This descriptor has the potential of decreasing the influence of large expression and pose variations on each normalized face within the corresponding spherical domain. Next, a robust group sparse regression model (RGSRM) is proposed to estimate the regression matrix, which preserves the intrinsic discriminant information. By embedding the descriptors into the low dimensional regression matrix, hair occlusions and artifacts can be treated as corruptions and can be patched. Under the constraints of Spectral Regression and corruptions, noise corruptions can be removed and the remaining small variations can be further corrected. FRGC v2.0 and CASIA 3D face databases are introduced to examine the performance of our framework and the previous algorithms with different schemes, and the experimental results show our proposed framework has the performance of simple implementation, high accuracy and low computational complexity.