Sparse Decomposition Model Research Articles

Low-Rank and Sparse Decomposition With Mixture of Gaussian for Hyperspectral Anomaly Detection.

Recently, the low-rank and sparse decomposition model (LSDM) has been used for anomaly detection in hyperspectral imagery. The traditional LSDM assumes that the sparse component where anomalies and noise reside can be modeled by a single distribution which often potentially confuses weak anomalies and noise. Actually, a single distribution cannot accurately describe different noise characteristics. In this article, a combination of a mixture noise model with low-rank background may more accurately characterize complex distribution. A modified LSDM, by modeling the sparse component as a mixture of Gaussian (MoG), is employed for hyperspectral anomaly detection. In the proposed framework, the variational Bayes (VB) algorithm is applied to infer a posterior MoG model. Once the noise model is determined, anomalies can be easily separated from the noise components. Furthermore, a simple but effective detector based on the Manhattan distance is incorporated for anomaly detection under complex distribution. The experimental results demonstrate that the proposed algorithm outperforms the classic Reed-Xiaoli (RX), and the state-of-the-art detectors, such as robust principal component analysis (RPCA) with RX.

Smooth robust tensor principal component analysis for compressed sensing of dynamic MRI

Dynamic magnetic resonance imaging (DMRI) often requires a long time for measurement acquisition, and it is a crucial problem about the enhancement of reconstruction quality from a limited set of under-samples. The low-rank plus sparse decomposition model, which is also called robust principal component analysis (RPCA), is widely used for reconstruction of DMRI data in the model-based way. In this paper, considering that DMRI data are naturally in tensor form with block-wise smoothness, we propose a smooth robust tensor principal component analysis (SRTPCA) method for DMRI reconstruction. Compared with classical RPCA approaches, the low rank and sparsity terms are extended to tensor versions to fully exploit the spatial and temporal data structures. Moreover, a tensor total variation regularization term is used to encourage the multi-dimensional block-wise smoothness for the reconstructed DMRI data. The relaxed convex optimization model can be divided into several sub-problems by the alternating direction method of multipliers. Numerical experiments on cardiac perfusion and cine datasets demonstrate that the proposed SRTPCA method outperforms the state-of-the-art ones in terms of recovery accuracy.

A Novel Singing Voice Separation Method Based on a Learnable Decomposition Technique

In this paper, a new monaural singing voice separation algorithm is presented. This field of signal processing provides important information in many areas dealing with voice recognition, data retrieval, and singer identification. The proposed approach includes a sparse and low-rank decomposition model using spectrogram of the singing voice signals. The vocal and non-vocal parts of a singing voice signal are investigated as sparse and low-rank components, respectively. An alternating optimization algorithm is applied to decompose the singing voice frames using the sparse representation technique over the vocal and non-vocal dictionaries. Also, a novel voice activity detector is presented based upon the energy of the sparse coefficients to learn atoms related to the non-vocal data in the training step. In the test phase, the learned non-vocal atoms of the music instrumental part are updated according to the non-vocal components captured from the test signal using domain adaptation technique. The proposed dictionary learning process includes two coherence measures: atom–data coherence and mutual coherence to provide a learning procedure with low reconstruction error along with a proper separation in the test step. The simulation results using different measures show that the proposed method leads to significantly better results in comparison with the earlier methods in this context and the traditional procedures.

Multiscale Feature Extraction Based on Convolutional Sparse Decomposition for Hyperspectral Image Classification

Due to the different spatial properties presented by various ground objects in hyperspectral image (HSI), multiscale-based feature extraction approaches have been developed for HSI classification in recent years. However, the spatial features of different scales are usually acquired at the cost of obscuring the structural information of input image, which severely limits the effectiveness of multiscale strategy. In this article, a convolutional sparse decomposition (CSD) model is introduced to characterize the significant spatial structures of hyperspectral data while removing the irrelevant noise and local textures at the specific scale. Based on the CSD model, a multiscale spectral-spatial feature extraction framework is generated, which consists of the following steps. First, the spectral dimensionality of the original HSI is reduced through a segmented averaging approach. Second, spatial features at different scales are separated from the dimension-reduced data by solving the CSD model with different regularization parameters. Finally, principal component analysis is performed and the obtained multiscale spectral-spatial features are stacked together for classification. Experiments conducted on three widely used hyperspectral datasets demonstrate that the proposed method is robust in capturing effective features of ground objects at different scales and leads to better classification results than several state-of-the-art methods.

Hierarchical Coding of Convolutional Features for Scene Recognition

Convolutional neural networks (CNNs) have achieved great success in visual recognition because of the availability of large-scale image datasets, such as the ImageNet. The transfer of convolutional features to challenging scene recognition remains an open problem. Multiple non-linear transforms endow the convolutional features with abundant information. On the other side, CNNs are adept at capturing the holistic appearances of scenes, whereas the lack of some critical local details may reduce the recognition accuracy. To address these problems, we propose a novel hierarchical coding algorithm to learn effective representations. To adapt the scale variations, many useful patches with various scales sampled from the whole image are considered to provide the sufficient details. Non-negative sparse decomposition model (NNSD) based on convolutional features is proposed to learn the sharable components for each scale and further produce global signatures. Based on the global signatures, inter-class linear coding (ICLC) is proposed to learn the discriminative components and ultimate image representations. Experimental results indicate that our approach significantly improves the recognition accuracy compared with general CNN models and achieves excellent performance on five standard benchmarks.

Task-free brainprint recognition based on low-rank and sparse decomposition model

Electroencephalography (EEG)-based brainprint recognition was usually completed under a singular task, such as recognition based on visual-evoked potentials. This paper proposes a fast task-free brainprint recognition to break the restriction. We presume a task-related EEG can be divided into the background EEG (BEEG) and the residue EEG. Wherein, BEEG contains one's unique intrinsic brainprint, which was supposed to be a low-rank characteristic. To analyse more precisely, short time Fourier Transform (STFT) are exerted to expand time series EEG into time-frequency domain. Then, a Low-Rank Matrix Decomposition (LRMD)-based algorithm combined with maximum correntropy criterion (MCC) and rational quadratic kernel was designed to extract BEEG. Finally, through sparse representation, BEEG can be classified efficiently. The excellent performance under low rank and various time length scales indicates that our method does not rely on task types and provides a new direction for the application of brainprint recognition.

Efficient Dynamic Parallel MRI Reconstruction for the Low-Rank Plus Sparse Model.

The low-rank plus sparse (L+S) decomposition model enables the reconstruction of under-sampled dynamic parallel magnetic resonance imaging (MRI) data. Solving for the low-rank and the sparse components involves non-smooth composite convex optimization, and algorithms for this problem can be categorized into proximal gradient methods and variable splitting methods. This paper investigates new efficient algorithms for both schemes. While current proximal gradient techniques for the L+S model involve the classical iterative soft thresholding algorithm (ISTA), this paper considers two accelerated alternatives, one based on the fast iterative shrinkage-thresholding algorithm (FISTA), and the other with the recent proximal optimized gradient method (POGM). In the augmented Lagrangian (AL) framework, we propose an efficient variable splitting scheme based on the form of the data acquisition operator, leading to simpler computation than the conjugate gradient (CG) approach required by existing AL methods. Numerical results suggest faster convergence of the efficient implementations for both frameworks, with POGM providing the fastest convergence overall and the practical benefit of being free of algorithm tuning parameters.

Accurate vessel extraction via tensor completion of background layer in X-ray coronary angiograms

This paper proposes an effective method for accurately recovering vessel structures and intensity information from the X-ray coronary angiography (XCA) images of moving organs or tissues. Specifically, a global logarithm transformation of XCA images is implemented to fit the X-ray attenuation sum model of vessel/background layers into a low-rank, sparse decomposition model for vessel/background separation. The contrast-filled vessel structures are extracted by distinguishing the vessels from the low-rank backgrounds by using a robust principal component analysis and by constructing a vessel mask via Radon-like feature filtering plus spatially adaptive thresholding. Subsequently, the low-rankness and inter-frame spatio-temporal connectivity in the complex and noisy backgrounds are used to recover the vessel-masked background regions using tensor completion of all other background regions, while the twist tensor nuclear norm is minimized to complete the background layers. Finally, the method is able to accurately extract vessels’ intensities from the noisy XCA data by subtracting the completed background layers from the overall XCA images. We evaluated the vessel visibility of resulting images on real X-ray angiography data and evaluated the accuracy of vessel intensity recovery on synthetic data. Experiment results show the superiority of the proposed method over the state-of-the-art methods.

Regularized sparse decomposition model for speech enhancement via convex distortion measure

An important stage in speech enhancement is to estimate noise signal which is a difficult task in non-stationary and low signal-to-noise conditions. This paper presents an iterative speech enhancement approach which requires no prior knowledge of noise and is based on low-rank sparse matrix decomposition using Gammatone filterbank and convex distortion measure. To estimate noise and speech, the noisy speech is decomposed into low-rank noise and sparse-speech parts by enforcing sparsity regularization. The exact distribution of noise signals and noise estimator is not required in this approach. The experimental results demonstrate that our approach outperforms competing methods and yields better overall speech quality and intelligibility. Moreover, composite objective measure reinforced a better performance in terms of residual noise and speech distortion in adverse noisy conditions. The time-varying spectral analysis validates significant reduction of the background noise.

Knowledge-driven dictionaries for sparse representation of continuous glucose monitoring signals.

Continuous glucose monitoring (CGM) of patients with diabetes allows the effective management of the disease and reduces the risk of hypoglycemic or hyperglycemic episodes. Towards this goal, the development of reliable CGM models is essential for representing the corresponding signals and interpreting them with respect to factors and outcomes of interest. We propose a sparse decomposition model to approximate CGM time-series as a linear combination of a small set of exemplar atoms, appropriately designed through parametric functions to capture the main fluctuations of the CGM signal. Sparse decomposition is performed through the orthogonal matching pursuit (OMP). Results indicate that the proposed model provides 0.1 relative reconstruction error with 0.8 compression rate on a publicly available dataset containing 25 patients diagnosed with Type 1 diabetes. The atoms selected from the OMP procedure can be further interpreted in relation to the clinically meaningful components of the CGM signal (e.g. glucose spikes, hypoglycemic episodes, etc.

Intelligent Prognostics of Degradation Trajectories for Rotating Machinery Based on Asymmetric Penalty Sparse Decomposition Model

The ability to accurately track the degradation trajectories of rotating machinery components is arguably one of the challenging problems in prognostics and health management (PHM). In this paper, an intelligent prediction approach based on asymmetric penalty sparse decomposition (APSD) algorithm combined with wavelet neural network (WNN) and autoregressive moving average-recursive least squares algorithm (ARMA-RLS) is proposed for degradation prognostics of rotating machinery, taking the accelerated life test of rolling bearings as an example. Specifically, the health indicators time series (e.g., peak-to-peak value and Kurtosis) is firstly decomposed into low frequency component (LFC) and high frequency component (HFC) using the APSD algorithm; meanwhile, the resulting non-convex regularization problem can be efficiently solved using the majorization-minimization (MM) method. In particular, the HFC part corresponds to the stable change around the zero line of health indicators which most extensively occurs; in contrast, the LFC part is essentially related to the evolutionary trend of health indicators. Furthermore, the nonparametric-based method, i.e., WNN, and parametric-based method, i.e., ARMA-RLS, are respectively introduced to predict the LFC and HFC that focus on abrupt degradation regions (e.g., last 100 points). Lastly, the final predicted data could be correspondingly obtained by integrating the predicted LFC and predicted HFC. The proposed methodology is tested using degradation health indicator time series from four rolling bearings. The proposed approach performed favorably when compared to some state-of-the-art benchmarks such as WNN and largest Lyapunov (LLyap) methods.

Low rank sparse decomposition model based speech enhancement using gammatone filterbank and Kullback–Leibler divergence

In speech enhancement systems, the key stage is to estimate noise which generally requires prior speech or noise models. However, it is difficult to obtain such prior models sometimes. This paper presents a speech enhancement algorithm which does not require prior knowledge of speech and noise, and is based on low-rank and sparse matrix decomposition model using gammatone filterbank and Kullback–Leibler divergence to estimate noise and speech by decomposing the input noisy speech magnitude spectra into low-rank noise and sparse speech parts, respectively. According to the proposed technique, noise signals are assumed as low-rank components because noise spectra within different time frames are usually highly correlated with each other; while the speech signals are considered as sparse components because they are relatively sparse in time–frequency domain. Based on these assumptions, we have developed an alternative speech enhancement algorithm to separate the speech and noise magnitude spectra by imposing rank and sparsity constraints, with which the enhanced time-domain speech can be constructed from sparse matrix The proposed technique is significantly different from existing speech enhancement techniques as it enhances noisy speech in an uncomplicated manner, without need of noise estimation algorithm to find noise-only excerpts for noise estimation. Moreover, it can obtain improved performance in low SNR conditions, and does not need to know the exact distribution of noise signals. Experimental results have showed that proposed technique can perform better than conventional techniques in many types of strong noise conditions, in terms of yielding less residual noise, lower speech distortion and better overall speech quality. An important improvement in terms of the PESQ, SNRSeg, SIG and BAK is observed with the proposed algorithm over baseline algorithms.

Spectrally-Spatially Regularized Low-Rank and Sparse Decomposition: A Novel Method for Change Detection in Multitemporal Hyperspectral Images

Change detection (CD) for multitemporal hyperspectral images (HSI) can be approached as classification consisting of two steps, change feature extraction and change identification. This paper is focused on binary classification of the changed and the unchanged samples, which is the essential case of change detection. Meanwhile, it is challenging to extract clean change features from heavily corrupted spectral change vectors (SCV) of multitemporal HSI. The corruptions can be characterized as gross sample-specific errors, i.e., outliers, and small entry-wise noise following Gaussian distribution. To address the issue, this paper proposes a novel Spectrally-Spatially (SS) Regularized Low-Rank and Sparse Decomposition (LRSD) model, denoted by LRSD_SS. It decomposes the SCV into three components, a locally smoothed low-rank matrix for the clean change features, a sparse matrix for the outliers and an error matrix for the small Gaussian noise. The proposed method is effective in change feature extraction and robust to noise corruptions as it exploits the underlying data structures of the SCV, especially local spectral-spatial smoothness. It is also efficient since there is a closed-form solution for the feature component in the optimization problem of LRSD_SS. The experimental results in the paper show that the proposed method outperforms several classic methods which only deal with the spectral domain of image samples, as well as some state-of-the-art methods which use both spectral and spatial information

Low-Rank and Sparse Decomposition Model for Accelerating Dynamic MRI Reconstruction.

The reconstruction of dynamic magnetic resonance imaging (dMRI) from partially sampled k-space data has to deal with a trade-off between the spatial resolution and temporal resolution. In this paper, a low-rank and sparse decomposition model is introduced to resolve this issue, which is formulated as an inverse problem regularized by robust principal component analysis (RPCA). The inverse problem can be solved by convex optimization method. We propose a scalable and fast algorithm based on the inexact augmented Lagrange multipliers (IALM) to carry out the convex optimization. The experimental results demonstrate that our proposed algorithm can achieve superior reconstruction quality and faster reconstruction speed in cardiac cine image compared to existing state-of-art reconstruction methods.

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.

Nonconvex plus quadratic penalized low-rank and sparse decomposition for noisy image alignment

This paper proposes a general method for dealing with the problem of recovering the low-rank structure, in which the data can be deformed by some unknown transformations and corrupted by sparse or nonsparse noises. Nonconvex penalization method is used to remedy the drawbacks of existing convex penalization method and a quadratic penalty is further used to better tackle the nonsparse noises in the data. We exploits the local linear approximation (LLA) method for turning the resulting nonconvex penalization problem into a series of weighted convex penalization problems and these subproblems are efficiently solved via the augmented Lagrange multiplier (ALM). Besides comparing with the method of robust alignment by sparse and low-rank decomposition for linearly correlated images (RASL), we also propose a nonconvex penalized lowrank and sparse decomposition (NLSD) model as comparison. Numerical experiments are conducted on both controlled and uncontrolled data to demonstrate the outperformance of the proposed method over RASL and NLSD.

A novel speech enhancement method by learnable sparse and low-rank decomposition and domain adaptation

This paper proposes a novel speech enhancement algorithm based on a low-rank sparse decomposition model. The sparse and low-rank components of a corrupted signal are considered as speech and noise in time-frequency domain, respectively. We use a new alternating optimization algorithm for accurate decomposition of the noisy observed data using sparse coding over the speech and noise dictionaries.Adequate noise training frames with the same data size as speech data are provided by a noise estimation algorithm to learn the overcomplete noise dictionaries with low sparse approximation error. Since encountering non-stationary noises reduces the performance of speech enhancement methods, we take advantage of domain adaptation method which is a novel speech enhancement procedure to transform a learned noise dictionary to an adapted dictionary by data distribution captured in the enhancement process.Using this step, an adapted separation scheme based on the current situation of noisy space is carried out, and the main drawbacks seen in the earlier dictionary-learning-based speech enhancement methods are solved. The proposed approach results in a significant reduction of noise, especially for non-stationary noises, in comparison with the earlier methods in this context and the traditional procedures, based on different objective and subjective measures.

Quadtree structured image approximation for denoising and interpolation.

The success of many image restoration algorithms is often due to their ability to sparsely describe the original signal. Shukla proposed a compression algorithm, based on a sparse quadtree decomposition model, which could optimally represent piecewise polynomial images. In this paper, we adapt this model to the image restoration by changing the rate-distortion penalty to a description-length penalty. In addition, one of the major drawbacks of this type of approximation is the computational complexity required to find a suitable subspace for each node of the quadtree. We address this issue by searching for a suitable subspace much more efficiently using the mathematics of updating matrix factorisations. Algorithms are developed to tackle denoising and interpolation. Simulation results indicate that we beat state of the art results when the original signal is in the model (e.g., depth images) and are competitive for natural images when the degradation is high.