Optimal Sparse Representation Research Articles

Batch process monitoring based on sequential phase division multiway sparse weighted neighborhood preserving embedding

Batch processes are often characterized by multiphase and different batch durations, which vary from phase to phase presenting multiple local neighborhood features. In this paper, a sequential phase division-multiway sparse weighted neighborhood preserving embedding method is proposed for monitoring batch processes more sensitively. First, batches with uneven durations are synchronized, and the phases are automatically determined in chronological order. Secondly, the nearest neighbors are computed at each phase and the optimal sparse representation (SR) is obtained based on the nearest neighbors. This improves the robustness of the algorithm to noise and outliers, and solves the problem of computational difficulties associated with global SR based. Thirdly, the distance values of the neighbor elements are considered to fully extract the neighbor structure when the optimal SR is calculated. Finally, after dimension reduction, T 2 and squared prediction error statistics are established in feature space and residual space respectively for fault detection. The effectiveness of the method is verified by a multiphase numerical simulation example and the penicillin fermentation process.

3-D SAR Imaging via Perceptual Learning Framework With Adaptive Sparse Prior

Mathematically, three-dimensional (3D) SAR imaging is a typical inverse problem, which, by nature, can be solved by applying the theory of sparse signal recovery. However, many reconstruction algorithms are constructed by exploring the inherent sparsity of imaging space, which may cause unsatisfactory estimations in weakly sparse cases. To address this issue, we propose a new perceptual learning framework, dubbed as PeFIST-Net, for 3D SAR imaging, by unfolding the fast iterative shrinkage-thresholding algorithm (FISTA) and exploring the sparse prior offered by the convolutional neural network (CNN). We first introduce a pair of approximated sensing operators in lieu of the conventional sensing matrices, by which the computational efficiency is highly improved. Then, to improve the reconstruction accuracy in inherently non-sparse cases, a mirror-symmetric CNN structure is designed to explore an optimal sparse representation of roughly estimated SAR images. The network weights control the hyper-parameters of FISTA by elaborated regularization functions, ensuring a well-behaved updating tendency. Unlike directly using pixel-wise loss function in existing unfolded networks, we introduce the perceptual loss by defining loss term based on high-level features extracted from the pre-trained VGG-16 model, which brings higher reconstruction quality in terms of visual perception. Finally, the methodology is validated on simulations and measured SAR experiments. The experimental results indicate the proposed method can obtain well-focused SAR images from highly incomplete echoes while maintaining fast computational speed.

Feature Extraction of Bearing Weak Fault Based on Sparse Coding Theory and Adaptive EWT

In industry, early fault signals of rolling bearings are submerged in strong background noise, causing a low signal-to-noise ratio (SNR) and difficult diagnosis. This paper proposes a fault feature extraction method based on an optimized Laplacian wavelet dictionary (LWD) and the feature symbol search (FSS) algorithm to extract early fault characteristic frequencies of bearings under low SNR. As the morphological parameters of the Laplace wavelet dictionary and sparse coefficients are not easy to obtain, this method uses the adaptive empirical wavelet transform (AEWT) to determine the morphological parameters of the Laplace wavelet. Firstly, AEWT is applied to obtain the different frequency components, and the combination index is utilized for optimal component selection. Then, the morphological parameters of LWD are determined by AEWT processing, by which the overcomplete dictionary that best matches the signal can be obtained. Finally, the optimal sparse representation of the component signal in the dictionary is calculated by FSS, which helps to achieve sparse denoising and enhance the impact features. The effectiveness of the method is verified by simulation. The effectiveness and advantages of LWDFSS-AEWT are verified by experiment in comparison with methods such as fast spectral kurtosis (FSK), correlation filtering (CF), shift-invariant sparse coding (SISC), base pursuit denoising (BPDN) and wavelet packet transform Kurtogram (WPT Kurtogram).

Compressed Sensing Based RFI Mitigation and Restoration for Pulsar Signals

In pulsar signal processing, two primary difficulties are (1) radio-frequency interference (RFI) mitigation and (2) information loss due to preprocessing and mitigation itself. Linear mitigation methods have a difficulty in RFI modeling, and accommodate a limited range of RFI morphologies. Thresholding methods suffer from manual factors and adaptability. There is also a distinct lack of methods dedicated to information loss. In this paper, a novel method “CS-Pulsar” is proposed. It carries out compressed sensing (CS) on time-frequency signals to accomplish RFI mitigation and signal restoration simultaneously. Curvelets allow an optimal sparse representation for multichannel pulsar signals containing the time-of-arrival dispersion relationship. CS-Pulsar mitigation is implemented using a regularized least-squares framework that does not require the statistics of RFI to be known beforehand. CS-Pulsar implements channel restoration, and useful signal contents are retrieved from the measurement error by a morphological component analysis aided by the root-mean-square envelope. These two steps allow CS-Pulsar to provide key signal details for special astrophysical purposes. Experiments of signal restoration for pulsar data from the Nanshan 26 m radio telescope reveal the advantage of CS-Pulsar. The method successfully removes false peaks due to on-pulse RFI in multipeaked pulsar profiles. CS-Pulsar also increases the timing accuracy and signal-to-noise ratio proving its feasibilities and prospects in astrophysical measurements.

Learned iterative shrinkage and thresholding algorithm for terahertz sparse deconvolution.

Terahertz sparse deconvolution based on an iterative shrinkage and thresholding algorithm (ISTA) has been used to characterize multilayered structures with resolution equivalent to or finer than the sampling period of the measurement. However, this method was only studied on thin samples to separate the overlapped echos that can't be distinguished by other deconvolution algorithms. Besides, ISTA heavily depends on the convolution matrix consisting of delayed incident pulse, which is difficult to precisely extricate from the reference signal, and thereby fluctuations caused by noise are occasionally treated as echos. In this work, a terahertz sparse deconvolution based on a learned iterative shrinkage and thresholding algorithm (LISTA) is proposed. The method enclosed the matrix multiplication and soft thresholding in a block and cascaded multiple blocks together to form a deep network. The convolution matrices of the network were updated by stochastic gradient descent to minimize the distance between the output sparse vector and the optimal sparse representation of the signal, and subsequently the trained network made more precise estimation of the echos than ISTA. Additionally, LISTA is notably faster than ISTA, which is important for real-time tomographic-image processing. The algorithm was evaluated on terahertz tomographic imaging of a high-density poly ethylene (HDPE) sample, revealing obvious improvements in detecting defects of different sizes and depths. This technique has potential usage in nondestructive testings of thick samples, where echos reflected by minor defects are not discernible by existed deconvolution algorithms.

Improved Sparse Representation based Robust Hybrid Feature Extraction Models with Transfer and Deep Learning for EEG Classification

Numerous studies in the field of cognitive research is dependent on Electroencephalography (EEG) as it apprehends the neural correspondences of various mental activities such as memory, speech, or attention related activities with millisecond precision. In this work, initially sparse rendition is imposed on EEG signals and then sparse optimization is performed to it. For sparse representation, initially the work utilized both K-Singular Value Decomposition (K-SVD) for dictionary learning along with Orthogonal Matching Pursuit (OMP) for sparse coding. Later an advanced OMP technique was developed which made a significant improvement, and then instead of K-SVD, K-means and Method of Optimal direction (MOD) techniques were utilized with it and as a result, totally six different combinations in sparse representation optimization were developed. Then, it is modelled into clusters using seven different hybrid models developed here for the purpose of feature extraction and selection. Out of the seven models, two models are already existing such as Finite Mixture Logistic Regression Model (FMLR) and Expectation-Maximization based Gaussian Mixture Model (EM-GMM) which are widely used. The remaining five hybrid models are proposed as variations of GMM such as Variational Bayesian Matrix Factorization (VBMF) based GMM (VBMF-GMM), VBMF and Probabilistic Principal Component Analysis (PCA) with GMM (VBMF-PCA-GMM), VBMF and Partial Least Squares (PLS) with GMM (VBMF-PLS-GMM), VBMF and Canonical Correlation Analysis (CCA) with GMM (VBMF-CCA-GMM) and Empirical VBMF with GMM (EVBMF-GMM). This model is validated on two unique EEG datasets, such as epilepsy dataset and schizophrenia dataset, and the results have been classified with the standard machine learning techniques, transfer learning techniques and the proposed deep learning techniques leading to a total of twelve different classifiers and a comprehensive analysis is made in this work with very promising results in terms of classification accuracy reporting more than 95% for most of the proposed cases.

Sparse representation optimization of Gaussian mixed feature of image based on convolution neural network

With the rapid development of intelligent algorithm and image processing technology, the limitations of traditional image processing methods are more and more obvious. Based on this, this paper studies a new pattern of sparse representation optimization of image Gaussian mixture feature based on convolution neural network, and designs a sparse representation system model of vehicle detection image based on convolution neural network. The vehicle image data are collected from many aspects, and the convolution neural network is used for comprehensive analysis and evaluation. The model can extract the feature information of the vehicle detection image better by making the scheme of the real-time vehicle detection image and according to the image features and convolution neural network algorithm. The results show that the Gaussian mixture feature sparse representation optimization model based on convolution neural network has the advantages of high feasibility, high data accuracy and high response speed, which can enhance the processing efficiency of vehicle detection image and improve the utilization of local environmental information in the image.

Deep Shearlet Network for Change Detection in SAR Images

Convolutional neural networks (CNN) can extract shift-invariant features, and have been widely applied in change detection task. However, common CNN lacks noise robustness and needs supervised data, to alleviate these problems, in this paper, we propose a novel deep shearlet network (ShearNet) for change detection in SAR images. In the network, a shearlet denoising layer (SDL) is designed to enhance the representation ability of common CNN. In SDL, feature maps are decomposed into subband coefficients by shearlet transform (ST). Due to optimal sparse representation property and highly direction sensitivity of ST, the network can capture important geometric information. Then, hard-threshold shrinkage is applied to high frequency subbands to drop small coefficients that are most likely to be noise, so that reduce the effect of noise. Finally, ShearNet is trained by introducing a noise-robust loss with noisy labels. The noisy labels are obtained by deep clustering that shows more robustness than existing preclassification methods. This fine-tuning process novelly follows the paradigm of learning from noisy labels to aside the difficulty of precisely labeling samples. Our experimental results on multiple real SAR datasets show that ShearNet can boost accuracy, and have better applicability for change detection in SAR images. The source code is available at https://github.com/yizhilanmaodhh/ShearNet.

Sparse representation optimization of image Gaussian mixture features based on a convolutional neural network

Sparse representation optimization of image Gaussian mixture features based on a convolutional neural network

Robust high-dimensional seismic data interpolation based on elastic half norm regularization and tensor dictionary learning

Due to the limitations imposed by acquisition cost, obstacles, and inaccessible regions, the originally acquired seismic data are often sparsely or irregularly sampled in space, which seriously affects the ability of seismic data to image underground structures. Fortunately, compressed sensing provides theoretical support for interpolating and recovering irregularly or undersampled data. Under the framework of compressed sensing, we have adopted a robust interpolation method for high-dimensional seismic data, based on elastic half norm regularization and tensor dictionary learning. Inspired by the elastic net, we first develop the elastic half norm regularization as a sparsity constraint, and we establish a robust high-dimensional interpolation model with this technique. Then, considering the multidimensional structure and spatial correlation of seismic data, we introduce a tensor dictionary learning algorithm to train a high-dimensional adaptive tensor dictionary from the original data. This tensor dictionary is used as the sparse transform for seismic data interpolation because it can capture more detailed seismic features to achieve the optimal and fast sparse representation of high-dimensional seismic data. Finally, we solve the robust interpolation model by an efficient iterative thresholding algorithm in the transform space and perform the space conversion by a modified imputation algorithm to recover the wavefields at the unobserved spatial positions. We conduct high-dimensional interpolation experiments on model and field seismic data on a regular data grid. Experimental results demonstrate that this method has superior performance and higher computational efficiency in noise-free and noisy seismic data interpolation, compared to extensively used dictionary learning-based interpolation methods.

An Image Reconstruction Model under Poisson Noise Using multiscale Compressed Sensing

For the influence of poisson noise images, in order to get rid of poisson noise, this paper put forward image reconstruction method by using multiscale compressed sensing. the algorithm can approximate the optimal sparse representation of the image edge details such as the characteristics of theShearlet domain based multi-scale compressed sensing method. The image is decomposed into the high-frequency subbands byShearlet, and the compressed sensing is applied into each subband to reconstruct the image. In this paper, A total variation of RL iterative algorithm constructed by nonlinear projection algorithm based on closed convex set is explored as the reconstruction method, which use derivation of the nonlinear projection instead of total variation. In mathematics, Shearlet has been proved to be a better tool for edge characterization than traditional wavelet. By using the nonlinear projection scheme to constrain the residual coefficients in the Shearlet domain, a better estimation can be obtained from the Shearlet representation. Numerical examples show that the denoising effect of these methods is very good, which is better than the correlation method based on Curvelet transform. In addition, the number of iterations required by our scheme is far less than that of our competitors.

Constrained [formula omitted]-optimal sparse representation technique for face recognition

The performance of face recognition (FR) system essentially depends on the availability of training data. With limited training data available, it creates a major challenge in real world applications. This motivates researchers to investigate for such technique which generates optimum results using limited training samples or even single sample per person (SSPP). In this paper, a novel FR method is developed as Constrained L1-Optimal Sparse Representation Technique (L1-CSRT) for SSPP. An optimal sparse representation technique is formulated using the constrained Cuckoo search algorithm (CSA) for estimation of λ coefficients. Further, a novel fitness function is developed based on the L1-norm for better classification accuracy yielding better FR. The motivation behind the optimization of λ coefficients using CSA is to increase the sparsity by a better exploration of search space. The efficiency and accuracy of proposed L1-CSRT is shown based on the extensive simulations carried out on standard databases. The experimental results are compared with existing methods in terms of mean classification error. The performance of L1-CSRT is analysed with an improvement of 2--6% in terms of classification accuracy.

Road Detection Based on Shearlet for GF-3 Synthetic Aperture Radar Images

GF-3 satellite is China’s first C-band multi-polarized synthetic aperture radar (SAR) satellite with the 1-meter resolution, which has been widely used in various fields. Road detection for GF-3 SAR images is an important part of the application of GF-3, especially in fields of map update, target recognition, and image matching. However, speckle appears in GF-3 SAR images due to coherent imaging system and it hinders the interpretation of images seriously. Especially the detection of weak roads under strong speckle background becomes extremely difficult. As a representative of multiscale geometric analysis (MGA) tool, shearlet has the optimal sparse representation feature and strong directional orientation, which can effectively capture edge and other anisotropic feature information, and can accurately describe the sparse characteristics of GF-3 SAR images. Based on shearlet, a method for detecting weak roads under strong speckle interference is proposed. Firstly, the Frost filter is used for despeckling. Secondly, shearlet is used for road detection. Finally, morphological operations are adopted to obtain the final result. Road detection experiments on various types of GF-3 SAR images demonstrate that, the proposed method can effectively overcome the interference of speckle, and completely and smoothly detect road information, which is very suitable for the detection of weak roads under strong speckle interference of GF-3 SAR images.

Human Face Identification based on Optimal Sparse Features

Security of human being is an important aspect in the context of data communication. To maintain security, technology is being developed from alpha-numeric passwords to biometric scanners. Recent advancement in security is the user authentication using face recognition. But the flaws in existing face recognition systems are yet to be addressed. This paper discusses solutions to the issues encountered by face recognition systems. Sparsity based classification is performed in this work. This method can handle errors occurs due to compress in and occlusion in a robust manner. We suggest a comprehensive classification algorithm characterized by sparse representation and 1l -minimization. In this method, the feature points and selection of features are not critical. The effect of change in occlusion can be easily addressed by using this optimal sparse representation based classification (OSRC) algorithm.

Multi-Objective Sparse Subspace Clustering for Hyperspectral Imagery

Hyperspectral images (HSIs) are typical high-dimensional and complex data. As such, the clustering of HSIs is a challenging task. Out of the motivation to find the low-dimensional structure representation of the high-dimensional data, sparse subspace clustering (SSC) methods have been proposed in recent studies. Sparse representation is an important technique in SSC, which is aimed at obtaining the sparse coefficient matrix of the HSI data. Generally speaking, the acquisition of the sparse coefficient matrix is an ill-posed problem, and the existing methods introduce an extra condition as a regularization term to resolve it. However, the regularization parameter is determined manually, which is difficult and lacks self-adaptability. Hence, in this article, a multi-objective SSC method for hyperspectral imagery is proposed, which simultaneously optimizes the sparse term and the data fidelity term. In addition, the spatial structure information of the HSIs is often neglected in the processing model, and thus, a spatial prior term, as the third optimization objective function, is also tested in this article. As a result, there is no need to manually set a regularization parameter. Furthermore, by using the l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> norm as the sparse term, this reduces the error caused by the convex relaxation of the other norms. In the proposed method, a multi-objective optimization model is first used to acquire the sparse coefficient matrix, in which a strategy for constructing the dictionary is proposed for more precise and efficient multi-objective optimization. In addition, a knee point-based selection method is utilized to automatically select the optimal sparse representation solution from the Pareto front. The adjacency matrix is then constructed according to the sparse coefficient matrix. Finally, a spectral clustering method is used to obtain clustering results. Experiments undertaken with four HSI data sets confirm the effectiveness of the proposed method.

Image Fusion Technique Based on Hybrid Whale Optimization Algorithm Simulated Annealing (hWOA-SA)

Curvelet transform is a multiscale directional transformer, which allows optimal non-adaptive sparse representation of object with edge. In this paper, a new image fusion technique has been developed by combination of whale optimization algorithm (WOA) and simulated annealing (SA) along with curvelet transform. The resulting combined algorithm is abbreviated as hybrid whale optimization algorithm with simulated annealing. Initially, hWOA-SA has been applied to enhancing the quality of image using de-noising scheme. Afterwards, the curvelet transform has been employed to carry out the fusion of images. In terms of PSNR, the curvelet transform exhibits the better performance. The effectiveness and validation of the proposed scheme has been carried-out using quality matrices. The performance analysis is carried out after checking the effectiveness of proposed approach by evaluating the various parameters such as: RSME, PFE, MAE, CORR, SNR, PSNR, MI, UQI and SSIM and compared with numerous techniques. Simulation results obtained from proposed hWOA-SA based image fusion are very competitive and better than other image fusion technique available in the literature.

Group K-SVD for the classification of gene expression data

In this paper, we propose a new sparse learning model for the classification of gene expression data, named Group K-Singular Value Decomposition (Group K-SVD). It learns the optimal dictionary and sparse representation from the training data, and then assigns the out-of-sample data to the class with the nearest centroid. Group K-SVD reduces the redundancy of over-complete dictionary by using a group update strategy during the dictionary update stage. To solve the optimization problem, we also develop a Multivariate Orthogonal Matching Pursuit (MOMP) algorithm for the sparse coefficient update stage. In the evaluation of the performance of Group K-SVD model, we implement three Group K-SVD algorithms by incorporating MOMP as well as another two popular optimization algorithms into the sparse coefficient update stage. Sufficient experimental results demonstrate that our Group K-SVD algorithms are both effective and efficient in comparison with the state-of-the-methods on real-world gene expression datasets.

Reconstruction of missing seismic traces based on sparse dictionary learning and the optimization of measurement matrices

Due to limitations arising under complicated geological conditions and field collection environments, we often cannot collect complete and regular field seismic data. To solve that problem, the reconstruction of seismic data has been widely studied. In this paper, we propose a reconstruction algorithm for seismic data with missing traces based on sparse dictionary learning and measurement matrix optimization. The algorithm views the seismic data as a matrix. It first uses the neighboring channel to fill in the missing trace and then uses the transposed matrix and applies the K-singular value decomposition (K-SVD) algorithm by columns to train the sample, obtaining an over-complete dictionary that can be used to develop an optimal sparse representation of seismic data. In the process of seismic data reconstruction, we first transpose the seismic data with missing traces, adopt the regularized orthogonal matching pursuit (ROMP) algorithm to obtain optimum estimations of the data in each column and then transpose the matrix to obtain the reconstructed seismic data. To further increase the quality of seismic data reconstructions, the algorithm presented in this paper also introduces the Equiangular Tight Frame (ETF) method to optimize the measurement matrix. The experiments indicate that this paper's algorithm can achieve high-quality reconstructions of seismic data.

Group Sparse Representation Based Dictionary Learning for SAR Image Despeckling

Since the sparse representation coefficients of synthetic aperture radar (SAR) images often appear in clusters with intrinsic structure, traditional sparse representation theory cannot capture this property. In this paper, the concept of group sparse representation (GSR) is utilized to exploit the intrinsic structure of SAR images. Different from traditional patch-based sparse representation theory, GSR is able to sparsely represent images in the domain of group which contains the image patches with similar structure. Based on the multiplicative speckle noise model, a novel dictionary learning algorithm based on GSR (GSR-DL) for SAR image despeckling is proposed. The proposed algorithm mainly consists of three steps. First, in order to realize the recovery of despeckled SAR image by the GSR model, a mean filter is included in the modeling process. Second, the proposed GSR-DL algorithm is used to calculate the optimal dictionary and group sparse representation coefficients. Third, the despeckled SAR image is reconstructed by the learned dictionary and coefficients. The experimental results on SAR images manifest that the proposed GSR-DL algorithm achieves a better performance than other state-of-the-art despeckling algorithms.

Effective Urban Structure Inference from Traffic Flow Dynamics

Mobility in a city is represented as traffic flows in and out of defined urban travel or administrative zones. While the zones and the road networks connecting them are fixed in space, traffic flows between pairs of zones are dynamic through the day. Understanding these dynamics in real time is crucial for real time traffic planning in the city. In this paper, we use real time traffic flow data to generate dense functional correlation matrices between zones during different times of the day. Then, we derive optimal sparse representations of these dense functional matrices, that accurately recover not only the existing road network connectivity between zones, but also reveal new latent links between zones that do not yet exist but are suggested by traffic flow dynamics. We call this sparse representation the time-varying effective traffic connectivity of the city. A convex optimization problem is formulated and used to infer the sparse effective traffic network from time series data of traffic flow for arbitrary levels of temporal granularity. We demonstrate the results for the city of Doha, Qatar on data collected from several hundred bluetooth sensors deployed across the city to record vehicular activity through the city's traffic zones. While the static road network connectivity between zones is accurately inferred, other long range connections are also predicted that could be useful in planning future road linkages in the city. Further, the proposed model can be applied to socio-economic activity other than traffic, such as new housing, construction, or economic activity captured as functional correlations between zones, and can also be similarly used to predict new traffic linkages that are latently needed but as yet do not exist. Preliminary experiments suggest that our framework can be used by urban transportation experts and policy specialists to take a real time data-driven approach towards urban planning and real time traffic planning in the city, especially at the level of administrative zones of a city.