Wavelet-based spatiotemporal sparse quaternion dictionary learning for reconstruction of multi-channel vibration data

The method of orthogonal matching pursuit is used to solve the sparse deterministic deconvolution problem for poststack seismic data. A description of the theory is given and algorithmic implementation is discussed. This method is then applied to synthetic and real data. The orthogonal matching pursuit method, like other sparse spike techniques, produces high apparent resolution (spiky appearance) in the output. What value this and other such sparse spike estimators might bring to stratigraphic interpretation, if any, is still under assessment.

Damage identification methods based on structural modal parameters are influenced by the structure form, number of measuring sensors and noise, resulting in insufficient modal data and low damage identification accuracy. The additional virtual mass method introduced in this study is based on the virtual deformation method for deriving the frequency-domain response equation of the virtual structure and identify its mode to expand the modal information of the original structure. Based on the initial condition assumption that the structural damage was sparse, the damage identification method based on sparsity with l1 and l2 norm of the damage-factor variation and the orthogonal matching pursuit (OMP) method based on the l0 norm were introduced. According to the characteristics of the additional virtual mass method, an improved OMP method (IOMP) was developed to improve the localization of optimal solution determined using the OMP method and the damage substructure selection process, analyze the damage in the entire structure globally, and improve damage identification accuracy. The accuracy and robustness of each damage identification method for multi-damage scenario were analyzed and verified through simulation and experiment.

An improved orthogonal matching pursuit method for denoising high-frequency ultrasonic detection signals of flip chips

In this paper, we present improved performance compressed sensing (CS) based pulse Doppler radar. CS is an emerging sampling technique which uses very few number of samples to reconstruct original signal. Improvement in performance is achieved using Orthogonal Matching Pursuit (OMP) method with Fourier dictionary at low signal to noise ratio (SNR). OMP is an iterative and fast reconstruction method while Fourier dictionary is used to transform the original signal from time domain to Fourier domain. A significant reduction of sampling frequency by a factor of 360 is achieved at SNR as low as 10 dB, while preserving essential signal information. Low signal reconstruction error leads to good detection performance using Generalized Likelihood Ratio Test (GLRT), a detector based on ratio of probabilities of detection and false alarm. Simulation results demonstrate usefulness of the ideas presented.

In this paper, a novel sparse convex representation learning algorithm is proposed for estimating the intrinsic dimension of a dataset. Caratheodory's theorem states that if a point x of Rd lies in the convex hull of a set P, there is a subset of P consisting of d + 1 or fewer points such that x lies in the convex hull of P'. We believe that the maximum value, among the numbers of the nonzero elements of the sparsest convex representation of all points, implies the intrinsic dimension of a data set. The sparsest convex representation of a point lying in a convex hull means that it is a convex combination of the minimum number of the extreme points. Based on this basic idea, we constructed an objective function. Moreover, an improved orthogonal matching pursuit (OMP) method is proposed for solving it to derive a sparse convex representation. The obtained solutions can be used for estimating the dimension of the data set. The experiment results show the effectiveness and efficiency of our proposed method.

We present Probabilistic Orthogonal Matching Pursuit (PrOMP), a novel probabilistic approach that builds upon orthogonal matching pursuit (OMP) for sparse representations of data. Like OMP, PrOMP is a greedy algorithm for regression that iteratively selects columns of a matrix according to a score. This score is based on a rarely employed feature of the EM algorithm and thus optimizes a marginal probability distribution. While OMP uses correlation as the score, in our probabilistic approach we define the scores to be the value of the resulting marginal likelihood—if adding a new signal does not improve this term, the algorithm automatically terminates. Our theoretical analysis also builds on the previous theory for OMP. We demonstrate the algorithm with a focus on a sparse dictionary learning and signal representation task using Bayesian nonparametrics. We first consider the nonparametric Beta Process Factor Analysis (BPFA) model. In addition, we present a new model based on BPFA that we call Beta Process Subspace Analysis (BPSA) which learns a set of subspaces and their respective dimensionalities from data.

In this paper, joint compressed sensing (CS)-based estimation of transmit power, geographical location and frequency bands of active primary users (PUs) using three reconstruction algorithms, orthogonal matching pursuit (OMP), compressive sampling matching pursuit (CoSaMP) and iterative hard thresholding (IHT) methods is investigated. In the first simulations, the performances of OMP, CoSaMP and IHT methods are evaluated in different signal to noise ratios (SNRs) and different values of sparsity. The first experiment demonstrates that OMP is the high performance reconstruction algorithm but it needs a bit higher complexity. Moreover, two scenarios for decision-making is considered in fusion center (FC) and respected simulation results for two cases, ideal and non-ideal lossy channels between secondary users (SUs) and fusion center, are represented. Second experiments show that decision-making based on integrated reconstruction is more efficient than averaging on three separate reconstructions in both ideal and lossy channels.

Fruit cracking and rust spots are common diseases of nectarines that seriously affect their yield and quality. Therefore, it is essential to construct fast and accurate disease-identification models for agricultural products. In this paper, a sparse dictionary learning method was proposed to realize the rapid and nondestructive identification of nectarine disease based on multiple color features combined with improved LK-SVD (Label K-Singular Value Decomposition). According to the color characteristics of the nectarine itself and the significant color differences existing in the three categories of nectarine (diseased, normal, and background parts), multiple color spaces of RGB, HSV, Lab, and YCbCr were studied. It was concluded that the G channel in RGB space, Y channel in YCbCr space, and L channel in Lab space can better distinguish the diseased part from the other parts. At the model-training stage, pixels of the diseased, normal, and background parts in the nectarine image were randomly selected as the initial training sets, and then, the neighboring image blocks of the pixels were selected to construct the feature vectors based on the above color space channels. An improved LK-SVD dictionary learning algorithm was proposed that integrated the category label into the process of dictionary learning, and thus, an over-complete feature dictionary with significant discrimination was obtained. At the model-testing stage, the orthogonal matching pursuit (OMP) algorithm was used for sparse reconstruction of the original data, which can obtain the classification categories based on the optimized feature dictionary. The experimental results show that the sparse dictionary learning method based on multi-color features combined with improved LK-SVD can identify fruit cracking and rust spot diseases of nectarines quickly and accurately, and the average overall classification accuracies were 92.06% and 88.98%, respectively, which were better than those of k-nearest neighbor (KNN), support vector machine (SVM), DeepLabV3+, and Unet++; the identification results of DeepLabV3+ and Unet++ were also relatively high, but their average time costs were much higher, requiring 126.46~265.65 s. It is demonstrated that this study can provide technical support for disease identification in agricultural products.

International audience

[1] Sparse geologic dictionaries provide a novel approach for subsurface flow model representation and calibration. Learning sparse dictionaries from prior training data sets is an effective approach to describe complex geologic connectivity patterns in subsurface imaging applications. However, the computational cost of sparse learning algorithms becomes prohibitive for large models. Performing the sparse dictionary learning process on smaller image patches (segments) provides a simple approach to address this problem in image processing applications. However, in underdetermined subsurface flow model calibration inverse problems, reconstruction of a segmented image can introduce significant structural distortion and discontinuity at the boundaries of the segments. This paper proposes an alternative sparse learning approach where the sparse dictionaries are learned from low-rank representations of the large-scale training data set in spectral domains (e.g., frequency domain). The objective is to develop a computationally efficient dictionary learning approach that emphasizes large-scale spatial connectivity patterns. This is achieved by removing the strong spatial correlations in the training data, thereby eliminating a large number of insignificant components from the sparse learning computation. In addition to improving the computational complexity, sparse learning from low-rank training data sets suppresses the small-scale details from entering the reconstruction of large-scale connectivity patterns, thereby providing a regularization effect in solving the resulting ill-posed inverse problems. We apply the proposed approach to travel-time tomography inversion and nonlinear subsurface flow model calibration inverse problems to demonstrate its effectiveness and practicality.

ABSTRACTThe biggest challenge of the traditional 3D orthogonal matching pursuit (OMP) method for direction-of-departure (DOD), direction-of-arrival (DOA) and Doppler frequency estimation in bistatic multiple-input multiple-output (MIMO) radar is the heavy computational burden due to a large number of atoms in the overcomplete dictionary. In this paper, low complexity 3D-OMP algorithms are investigated. First, the traditional 3D-OMP algorithm is given. Then, two-dimensionality reduced OMP-based algorithms are proposed exploiting the property of Khatri-Rao product and proper sparse representation. Also, the multiple measurement vectors (MMV) model is introduced to our OMP algorithms to guarantee the estimation performance. The simulation results show that the DOD, DOA and Doppler frequency can be effectively estimated with a small number of pulses and low computation cost. With similar accuracy compared with the traditional 3D-OMP method, much lower computational burden can be achieved by using the proposed methods.

Compressed Sensing (CS) has been considered a very effective means of reducing energy consumption at the energy-constrained wireless body sensor networks for monitoring the multi-lead Electrocardiogram (MECG) signals. This paper develops the compressed sensing theory for sparse modeling and effective multi-channel ECG compression. A basis matrix with Gaussian kernels is proposed to obtain the sparse representation of each channel, which showed the closest similarity to the ECG signals. Thereafter, the greedy orthogonal matching pursuit (OMP) method is used to obtain the sparse representation of the signals. After obtaining the sparse representation of each ECG signal, the compressed sensing theory could be used to compress the signals as much as possible. Following the compression, the compressed signal is reconstructed utilizing the greedy orthogonal matching pursuit (OMP) optimization technique to demonstrate the accuracy and reliability of the algorithm. Moreover, as the wavelet basis matrix is another sparsifying basis to sparse representations of ECG signals, the compressed sensing is applied to the ECG signals using the wavelet basis matrix. The simulation results indicated that the proposed algorithm with Gaussian basis matrix reduces the reconstruction error and increases the compression ratio.

In order to solve the blurred structural details and over-smoothing effects in sparse representation dictionary learning reconstruction algorithm, this study aims to test sparse angle CT reconstruction with weighted dictionary learning algorithm based on adaptive Group-Sparsity Regularization (AGSR-SART). First, a new similarity measure is defined in which Covariance is introduced into Euclidean distance, Non-local image patches are adaptively divided into groups of different sizes as the basic unit of sparse representation. Second, the weight factor of the regular constraint terms is designed through the residuals represented by the dictionary, so that the algorithm takes different smoothing effects on different regions of the image during the iterative process. The sparse reconstructed image is modified according to the difference between the estimated value and the intermediate image. Last, The SBI (Split Bregman Iteration) iterative algorithm is used to solve the objective function. An abdominal image, a pelvic image and a thoracic image are employed to evaluate performance of the proposed method. In terms of quantitative evaluations, experimental results show that new algorithm yields PSNR of 48.20, the maximum SSIM of 99.06% and the minimum MAE of 0.0028. This study demonstrates that new algorithm can better preserve structural details in reconstructed CT images. It eliminates the effect of excessive smoothing in sparse angle reconstruction, enhances the sparseness and non-local self-similarity of the image, and thus it is superior to several existing reconstruction algorithms.

Feature learning that extracts concise and general- izable representations for data is one of the central problems in machine learning and signal processing. Sparse dictionary learning, also known as sparse coding, distinguishes from other feature learning techniques in sparsity exploitation, allowing the formulation of nonconvex optimizations that simultaneously uncover a structured dictionary and sparse representations. Despite the popularity of dictionary learning in applications, the landscapes of these optimizations that enable effective learning largely remain a mystery. This work characterizes the local optimization geometry for a simplified version of sparse coding where the L1 norm of the sparse coefficient matrix is minimized subject to orthogonal dictionary constraints. In particular, we show that the ground-truth dictionary and coefficient matrix are locally identifiable under the assumption that the coefficient matrix is sufficiently sparse and the number of training data columns is sufficiently large.

In this paper, we consider the theoretical bound of the probability of error in compressed sensing (CS) with the Bayesian approach. In the detection problem, the signal is sparse and is reconstructed from a compressed measurement vector. Utilizing the oracle estimator in CS, we provide a theoretical bound of the probability of error when the noise in CS is white Gaussian noise (WGN). We show that without any additional information in CS, the probability of error obtained using the signal reconstructed by four recovery algorithms: the basis pursuit denoising (BPDN) algorithm, the Dantzig selector, the orthogonal matching pursuit (OMP) method and the compressive sampling matching pursuit (CoSaMP) algorithm is always larger than the derived theoretical bound. Simulation results demonstrate the effectiveness of our result.