Low-rank Matrix Recovery Model Research Articles

Salient Object Detection Based on Optimization of Feature Computation by Neutrosophic Set Theory.

In recent saliency detection research, too many or too few image features are used in the algorithm, and the processing of saliency map details is not satisfactory, resulting in significant degradation of the salient object detection result. To overcome the above deficiencies and achieve better object detection results, we propose a salient object detection method based on feature optimization by neutrosophic set (NS) theory in this paper. First, prior object knowledge is built using foreground and background models, which include pixel-wise and super-pixel cues. Simultaneously, the feature maps are selected and extracted for feature computation, allowing the object and background features of the image to be separated as much as possible. Second, the salient object is obtained by fusing the features decomposed by the low-rank matrix recovery model with the object prior knowledge. Finally, for salient object detection, we present a novel mathematical description of neutrosophic set theory. To reduce the uncertainty of the obtained saliency map and then obtain good saliency detection results, the new NS theory is proposed. Extensive experiments on five public datasets demonstrate that the results are competitive and superior to previous state-of-the-art methods.

Optic disc detection based on fully convolutional network and weighted matrix recovery model.

Eye diseases often affect human health. Accurate detection of the optic disc contour is one of the important steps in diagnosing and treating eye diseases. However, the structure of fundus images is complex, and the optic disc region is often disturbed by blood vessels. Considering that the optic disc is usually a saliency region in fundus images, we propose a weakly-supervised optic disc detection method based on the fully convolution neural network (FCN) combined with the weighted low-rank matrix recovery model (WLRR). Firstly, we extract the low-level features of the fundus image and cluster the pixels using the Simple Linear Iterative Clustering (SLIC) algorithm to generate the feature matrix. Secondly, the top-down semantic prior information provided by FCN and bottom-up background prior information of the optic disc region are used to jointly construct the prior information weighting matrix, which more accurately guides the decomposition of the feature matrix into a sparse matrix representing the optic disc and a low-rank matrix representing the background. Experimental results on the DRISHTI-GS dataset and IDRiD dataset show that our method can segment the optic disc region accurately, and its performance is better than existing weakly-supervised optic disc segmentation methods. Graphical abstract of optic disc segmentation.

Low-rank matrix factorization with nonconvex regularization and bilinear decomposition

Low-rank matrix factorization (LRMF) is a powerful approach that can recover useful information with low-rank features from corrupted data and has been broadly applied in various scenarios such as computer vision and statistics. Existing convex relaxation-based LRMF models' performance and solutions are often limited by unsatisfied recovery accuracy and prolonged execution time due to excessive relaxation bias and heavy computational burden. In this paper, we first explore one class of parameterized non-convex penalty function and generalize it as a non-convex relaxation substitution term for the original rank function in the LRMF, which can effectively enhance the recovery capability for low-rank data. In order to reduce the computational burden of the nuclear-norm-based optimization scheme and make LRMF applicable to large-scale data. We propose to perform bilinear decomposition on the low-rank matrix and derive the bilinear factorization formula under the parameterized non-convex alternative. With the above considering, a low-rank matrix recovery model via bilinear decomposition and non-convex regularization, denoted as NCBF, is formulated. Further, the optimal solution algorithm for the NCBF model is developed in the framework of the block coordinate descent, combining simultaneously three strategies of decoupling, proximal gradient descent, and block prox-linear. Also, the convergence condition for the proposed algorithm has been given. We perform extensive experiments using synthetic data and real-world image datasets. The synthetic data test results demonstrate the dual superiority of the bilinear decomposition scheme in terms of operation time and estimation accuracy. Application of denoising to both generic and CT image datasets, experimental results show that NCBF outperforms several existing methods under both subjective and objective metrics evaluations.

The effect of perturbation and noise folding on the recovery performance of low-rank matrix via the nuclear norm minimization

• The completely perturbed low rank matrix recovery model takes in consideration the perturbations in the measurement map and the measurement matrix. • The perturbation on the measurement map result in a multiplicative noise. • The completely perturbed model is equivalent to the partially perturbed model. • The impact of the multiplicative noise on the Signal-to-Noise Ratio (SNR) is different than the additive noise. Previous works in low-rank matrix recovery literature focused on the study of the partially perturbed low-rank matrix recovery model y = A ( X ) + ω , where y ∈ R M is the observed vector, A : R m × n → R M is the measurement operator, X ∈ R m × n is the matrix to be recovered, and ω ∈ R M is the additive noise. However in practice A may only represent a perturbed version of the measurement operator since it models a physical phenomena and there is no guarantee that the desired conditions such as the restricted isometry property (RIP) hold. Similar to the measurement matrix X ∈ R m × n , in a variety of application scenarios, it may also be corrupted by noise. In this paper we introduce the completely perturbed low-rank matrix model by incorporating to the partially perturbed model a non zero perturbation E : R m × n → R M into the measurement operator A which results in a multiplicative noise, and a noise Z ∈ R m × n into the measurement matrix X . First by extending the results of Zhou et al. (2016) we explore the RIP constants of our new proposed model. Then based on the RIP we establish a sufficient condition for robust and stable recovery of low-rank matrices and give an upper bound estimation of the recovery error in the completely perturbed context. The analysis has shown that our model after whitening is equivalent to the partially perturbed model the only distinction is noise variance increase which has a sever impact on the Signal-to-Noise Ratio (SNR).

Topological Interference Management With Inaccurate Topology of Network

In this letter, we investigate the topological interference management (TIM) problem in the presence of measurement error of the network topology. We formulate the TIM problem as a low-rank matrix recovery problem and then solve it through an alternating algorithm to recover the true network topology. Our numerical results demonstrate that the proposed low-rank matrix recovery model can significantly improve the achievable degrees of freedom of the network.

A Smoothness Regularized Low-Rank Completion Method for Power Grid Middle Platform Data

Currently, the construction of power middle platform plays a vitally important role in the evolution of the smart grid. However, due to sensor failures or network delays, the sampled power middle platform data is often inevitably missing. To address this challenge, in this paper, we propose a smoothness regularized low-rank completion method for power middle platform missing data. Technically, the acquired middle platform data are formed to a time-series data matrix. Then, the low-rank matrix recovery model is applied to complete the missing data. Since the middle platform data is time-continuous, we adopt a total variation term to use this piece-wise smoothness. Finally, the proposed model is efficiently solved by the distributed alternating direction method of multipliers. Experimental evaluations on a real middle platform dataset validate the performance of the proposed method.

Saliency detection via double nuclear norm maximization and ensemble manifold regularization

In recent years, salient object detection via robust principal component analysis (RPCA) has received a significant amount of attention. Existing methods generally replace the rank function by the nuclear norm to obtain low-rank and sparse matrices, ignores the heavy-tailed distributions of singular values and over-penalizes large singular values of low rank matrices. In addition, although the manifold regularization is introduced into RPCA to obtain satisfactory low-rank representation of an original image, the graph hyperparameters selection lacks the ability to approximate the optimal solution for intrinsic manifold estimation. To solve these issues, we propose a novel low-rank matrix recovery model for salient object detection, which integrates double nuclear norm maximization with ensemble manifold regularization and can be formulated as a tractable optimization problem. By virtue of the alternating direction method (ADM), we develop an efficient algorithm to optimize the proposed model, which not only effectively fits the heavy-tailed distribution of singular values of low-rank matrices, but automatically learns the optimal linear combination of a set of predefined graph Laplacians. Experimental results on five challenging datasets show that our model achieves better performance than state-of-the-art unsupervised methods.

Hyper-Laplacian regularized nonlocal low-rank matrix recovery for hyperspectral image compressive sensing reconstruction

Sparsity prior is a powerful tool for compressive sensing reconstruction (CSR) of hyperspectral image (HSI). However, conventional HSI-CSR strategies are not tuned to extracting refine spatial and spectral sparsity prior. Moreover, these CSR techniques are weak in preserving edges and suppressing artifacts. To alleviate these issues, this paper represents a first effort to characterize the spatial and spectral knowledge using the structure-based sparsity prior. Specifically, we introduce the nonlocal low-rank matrix recovery model and the hyper-Laplacian prior to encode the spatial and spectral structured sparsity, respectively. The key advantage of the proposed method, termed as hyper-Laplacian regularized nonlocal low-rank matrix recovery (HyNLRMR), is to adopt insightful property, namely the nonlocal self-similarity across the spatial domain and the consistency along the spectral domain. Then, the alternative direction multiplier method (ADMM) is designed to effectively implement the proposed algorithm. Experimental results on various HSI datasets verify that the proposed algorithm can significantly outperform existing state-of-the-art HSI-CSR methods.

RGBD Salient Object Detection by Structured Low-Rank Matrix Recovery and Laplacian Constraint

A structured low-rank matrix recovery model for RGBD salient object detection is proposed. Firstly, the problem is described by a low-rank matrix recovery, and the hierarchical structure of RGB image is added to the sparsity term. Secondly, the depth information is fused into the model by a Laplacian regularization term to ensure that the image regions which share similar depth value will be allocated to similar saliency value. Thirdly, a variation of alternating direction method is proposed to solve the proposed model. Finally, both quantitative and qualitative experimental results on NLPR1000 and NJU400 show the advantage of the proposed RGBD salient object detection model.

Double Low Rank Matrix Recovery for Saliency Fusion.

In this paper, we address the problem of fusing various saliency detection methods such that the fusion result outperforms each of the individual methods. We observe that the saliency regions shown in different saliency maps are with high probability covering parts of the salient object. With image regions being represented by the saliency values of multiple saliency maps, the object regions have strong correlation and thus lie in a low-dimensional subspace. Meanwhile, most of background regions tend to have lower saliency values in various saliency maps. They are also strongly correlated and lie in a lowdimensional subspace that is independent of the object subspace. Therefore, an image can be represented as the combination of two low rank matrices. To obtain a unified low rank matrix that represents the salient object, this paper presents a double low rank matrix recovery model for saliency fusion. The inference process is formulated as a constrained nuclear norm minimization problem, which is convex and can be solved efficiently with the alternating direction method of multipliers (ADMM). Furthermore, to reduce the computational complexity of the proposed saliency fusion method, a saliency model selection strategy based on the sparse representation is proposed. Experiments on five datasets show that our method consistently outperforms each individual saliency detection approach and other state-of-the-art saliency fusion methods.

Localizing scene texts by fuzzy inference systems and low rank matrix recovery model

In this paper a framework is proposed to localize both Farsi/Arabic and Latin scene texts with different sizes, fonts and orientations. First, candidate text regions are extracted via an MSER detector enhanced by weighted median filtering to adopt the low resolution texts. At the same time based on fuzzy inference system (FIS), the input image is classified into images with a focused text content and incidental scene text images which the image does not focus on the text content. For the focused scene text images the non-text candidates are filtered via an FIS. On the other hand, for the incidental scene text images apart from the FIS, an extra filtering algorithm based on low rank matrix recovery is proposed. Finally, a new approach based on the clustering, minimum area rectangle and radon transform techniques is proposed to create the single arbitrarily oriented text lines from the remaining text regions. To evaluate the proposed algorithm, we created a collection of natural images containing both Farsi/Arabic and Latin texts. Compared with the state-of-the-art methods, the proposed method achieves the best performance on our and Epshtein datasets and competitive performances on the ICDAR dataset.

Unsupervised Joint Salient Region Detection and Object Segmentation.

This paper presents a novel unsupervised algorithm to detect salient regions and to segment out foreground objects from background. In contrast to previous unidirectional saliency-based object segmentation methods, in which only the detected saliency map is used to guide the object segmentation, our algorithm mutually exploits detection/segmentation cues from each other. To achieve this goal, an initial saliency map is generated by the proposed segmentation driven low-rank matrix recovery model. Such a saliency map is exploited to initialize object segmentation model, which is formulated as energy minimization of Markov random field. Mutually, the quality of saliency map is further improved by the segmentation result, and serves as a new guidance for the object segmentation. The optimal saliency map and the final segmentation are achieved by jointly optimizing the defined objective functions. Extensive evaluations on MSRA-B and PASCAL-1500 datasets demonstrate that the proposed algorithm achieves the state-of-the-art performance for both the salient region detection and the object segmentation.

Supervised Low-Rank Matrix Recovery for Traffic Sign Recognition in Image Sequences

Correlations in image sequences can be potentially useful for recovering feature representation and subsequently prompting classification performance, which are often neglected by traditional classification approaches. In this letter, we present a supervised low-rank matrix recovery model to leverage these correlations for classification tasks by introducing a supervised penalty term to the classic low-rank matrix recovery model. This allows us to not only exploit these correlations to recover the underlying feature representation from corrupted observation, but also preserve discriminative information for classification. Our model is evaluated on both real-world data and synthetic data, and experimental results show that our model obtains highly competitive performance with state-of-the-art algorithms and is especially robust to different levels of corruptions.