Redundant Dictionary Research Articles

Technique for Kernel Matching Pursuit Based on Intuitionistic Fuzzy c-Means Clustering

Kernel matching pursuit (KMP) requires every step of the searching process to be global optimal searching in the redundant dictionary of functions in order to select the best matching signal structure. Namely, the dictionary learning time of KMP is too long. To solve the above drawbacks, a rough dataset was divided into some small-sized dictionaries to substitute local searching for global searching by using the property superiority of dynamic clustering performance, which is also superior in the intuitionistic fuzzy c-means (IFCM) algorithm. Then, we proposed a novel technique for KMP based on IFCM (IFCM-KMP). Subsequently, three tests including classification, effectiveness, and time complexity were carried out on four practical sample datasets, the conclusions of which fully demonstrate that the IFCM-KMP algorithm is superior to FCM and KMP.

Adaptive convolutional sparsity with sub-band correlation in the NSCT domain for MRI image fusion

Objective. Multimodal medical image fusion (MMIF) technologies merges diverse medical images with rich information, boosting diagnostic efficiency and accuracy. Due to global optimization and single-valued nature, convolutional sparse representation (CSR) outshines the standard sparse representation (SR) in significance. By addressing the challenges of sensitivity to highly redundant dictionaries and robustness to misregistration, an adaptive convolutional sparsity scheme with measurement of the sub-band correlation in the non-subsampled contourlet transform (NSCT) domain is proposed for MMIF. Approach. The fusion scheme incorporates four main components: image decomposition into two scales, fusion of detail layers, fusion of base layers, and reconstruction of the two scales. We solved a Tikhonov regularization optimization problem with source images to obtain the base and detail layers. Then, after CSR processing, detail layers were sparsely decomposed using pre-trained dictionary filters for initial coefficient maps. NSCT domain’s sub-band correlation was used to refine fusion coefficient maps, and sparse reconstruction produced the fused detail layer. Meanwhile, base layers were fused using averaging. The final fused image was obtained via two-scale reconstruction. Main results. Experimental validation of clinical image sets revealed that the proposed fusion scheme can not only effectively eliminate the interference of partial misregistration, but also outperform the representative state-of-the-art fusion schemes in the preservation of structural and textural details according to subjective visual evaluations and objective quality evaluations. Significance. The proposed fusion scheme is competitive due to its low-redundancy dictionary, robustness to misregistration, and better fusion performance. This is achieved by training the dictionary with minimal samples through CSR to adaptively preserve overcompleteness for detail layers, and constructing fusion activity level with sub-band correlation in the NSCT domain to maintain CSR attributes. Additionally, ordering the NSCT for reverse sparse representation further enhances sub-band correlation to promote the preservation of structural and textural details.

Adaptive weighted dictionary representation using anchor graph for subspace clustering

Samples are commonly represented as sparse vectors in many dictionary representation algorithms. However, this method may result in loss of discriminatory information. Moreover, a redundant dictionary can increase the computational complexity of the algorithm. To tackle these challenges, we propose a novel method named Adaptive Weighted Dictionary Representation using Anchor Graph for Subspace Clustering (AWDR). First, AWDR constructs an anchor graph that encodes the classification information and establishes accurate connectivity components between anchors and clusters, thereby fully utilizing the discriminative information of the original samples. In addition, AWDR learns a complete-dictionary in the subspace to eliminate the noise and out-of-sample effects of the original sample space, while also improving computational efficiency. Finally, AWDR computes the coefficients for the samples in an adaptively weighted manner to find discriminative representation of the samples from the dictionary. Extensive experiments on real-world datasets demonstrate that our method is effective and efficient compared to the state-of-the-art methods.

An Improved GOMP Sparse Channel Estimation for Vehicle-to-Vehicle Communications

Reliable channel estimation is critical for wireless communication performance, especially in vehicle-to-vehicle (V2V) communication scenarios. Aiming at the major challenges of channel tracking and estimating as the highly dynamic nature of vehicle environments, an improved generalized orthogonal matching pursuit (iGOMP) is proposed for V2V channel estimation. The iGOMP algorithm transforms the channel estimation problem into a sparse signal recovery problem and replaces the classical inner product criterion with the Dice atom matching criterion. Additionally, the atomic weak progressive selection method is integrated to avoid the suboptimal selection of atoms from the redundant dictionary using the inner product criterion. The proposed iGOMP method can achieve optimal channel estimation by iterating feedback results. Simulation results demonstrate that the iGOMP method has superior estimation accuracy, mean square error (MSE), and bit error rate (BER) performance compared with traditional channel estimation methods in V2V communications.

Identification of Moving Vehicle Loads Using Instantaneous Vision-Based Vehicle Spatiotemporal Information and Improved Time Domain Method

Accurate identification of moving vehicle loads on bridges is one of the challenging tasks in bridge structural health monitoring, but lacks of intensive investigations to merge the heterogeneous data of vision-based vehicle spatiotemporal information (VVSI) and vehicle-induced bridge responses for moving force identification (MFI) in the existing time domain methods (TDM). In this study, a novel MFI method is proposed by integrating instantaneous VVSI and an improved TDM (iTDM). At first, a novel VVSI method combining background subtraction with template matching is presented to accurately track moving vehicles on bridges. With the calibration technique and camera perspective transformation model, the distribution of vehicles (DOV) on bridges is obtained and used as a priori information in the subsequent MFI. Then, the iTDM is developed based on the MFI equation re-formed in the form of instantaneous VVSI instead of the constant speed vehicle crossing bridges assumed in the traditional TDM. Finally, based on the redundant dictionary matrix composed of Haar functions for a moving load, the MFI problem is converted to explore a solution to the atom vectors and then solved by the Tikhonov regularization method. Experimental verifications in laboratory and a comparative study with the existing three methods are conducted to assess the feasibility of the proposed method. The results show that the proposed MFI method outperforms the existing methods and can effectively identify the moving vehicle loads with a higher and acceptable accuracy. It is successful for the proposed method to replace the assumption of constant speed vehicle crossing bridge in the traditional TDM with the instantaneous VVSI in the MFI problem.

Transient fault extraction for wind turbine generator bearing based on Bayesian biorthogonal sparse representation using adaptive redundant lifting wavelet dictionary

Aiming at the problem that it is difficult to detect effective transient impact characteristics of wind turbine generator bearing fault signals due to non-stationary and strong noise, a fault diagnosis method based on adaptive redundant lifting wavelet dictionary and Bayesian biorthogonal sparse representation (SR) algorithm is proposed. First, a Bayesian model is integrated into the biorthogonal matching pursuit (MP) algorithm to improve the use of dictionary atoms in the effective support set. Then, an adaptive redundant lifting wavelet is used to construct a dictionary matching the transient characteristics of the signal. Finally, the SR algorithm is established by integrating the Bayesian biorthogonal MP model and adaptive redundant lifting wavelet dictionary. Simulation and experimental results show that the proposed method can improve the accuracy of signal reconstruction of transient components and effectively extract bearing fault features, thus verifying the effectiveness and robustness of the method.

Sensing User's Channel and Location With Terahertz Extra-Large Reconfigurable Intelligent Surface Under Hybrid-Field Beam Squint Effect

This paper investigates the sensing of user's uplink channel and location in terahertz extra-large reconfigurable intelligent surface (XL-RIS) systems, where the unique hybrid far-near field effect and the beam squint effect caused by the XL array aperture as well as the XL bandwidth are overcome. Specifically, we first propose a joint channel and location sensing scheme, which consists of a location-assisted generalized multiple measurement vector orthogonal matching pursuit (LA-GMMV-OMP) algorithm for channel estimation (CE) and a complete dictionary based localization (CDL) scheme, where a frequency selective polar-domain redundant dictionary is proposed to overcome the hybrid field beam squint effect. The CE module outputs coarse on-grid angle estimation (respectively observed from the BS and RIS) to the localization module, which returns the fine off-grid angle estimation to improve CE. Particularly, with RIS, CDL can obtain user's location via line intersection, and a polar-domain gradient descent (PGD) algorithm at the base station is proposed to achieve the off-grid angle estimation with super-resolution accuracy. Additionally, to further reduce the sensing overhead, we propose a partial dictionary-based localization scheme, which is decoupled from CE, where RIS is served as an anchor to lock the user on the hyperbola according to time difference of arrival and the user's off-grid location can be obtained by using the proposed PGD algorithm. Simulation results demonstrate the superiority of the two proposed localization schemes and the proposed CE scheme over state-of-the-art baseline approaches.

ISAR Imaging of Non-Stationary Moving Target Based on Parameter Estimation and Sparse Decomposition

This paper studies the inverse synthetic aperture radar imaging problem for a non-stationary moving target and proposes a non-search imaging method based on parameter estimation and sparse decomposition. The echoes received by radar can be thought of as consisting of chirp signals with varying chirp rates and center frequencies. Lv’s distribution (LVD) is introduced to accurately estimate these parameters. Considering their inherent sparsity, the signals are reconstructed via sparse representation using a redundant chirp dictionary. An efficient algorithm is developed to tackle the optimization problem for sparse decompositions. Then, by using the reconstructed data, adaptive joint time–frequency imaging techniques are employed to create high-quality images of the non-stationary moving target. Finally, the simulated experiments and measured data processing results confirm the proposed method’s validity.

Infrared and visible image fusion based on domain transform filtering and sparse representation

Infrared and visible image fusion is an important branch in the field of information fusion. Fused images can provide more comprehensive and objective interpretations of complex scenes with confusing or hidden information. This paper proposes a novel infrared and visible image fusion method based on domain transform filtering (DTF) and sparse representation (SR). First, infrared and visible images are decomposed using a low-pass filter into base and detail layers, respectively. An SR-based rule is designed to fuse the detail layers. To improve the feature expression ability of a redundant dictionary, we introduce a multiscale detail enhancement technique to preprocess the training data. Additionally, a fast but effective rule is proposed based on salient structure extraction and DTF base layer fusion. The structure and border information of source images can be successfully transformed into the fused image. The proposed method can effectively retain the salient structure and edge information of the source images in the fused image. Experimental results demonstrate that the proposed method can outperform state-of-the-art methods in terms of both subjective visual and objective quantitative evaluations. The source code of the proposed method is released at https://github.com/ixilai/DTF-SR.

Enhancing sparse representation of color images by cross channel transformation.

Transformations for enhancing sparsity in the approximation of color images by 2D atomic decomposition are discussed. The sparsity is firstly considered with respect to the most significant coefficients in the wavelet decomposition of the color image. The discrete cosine transform is singled out as an effective 3 point transformation for this purpose. The enhanced feature is further exploited by approximating the transformed arrays using an effective greedy strategy with a separable highly redundant dictionary. The relevance of the achieved sparsity is illustrated by a simple encoding procedure. On typical test images the compression at high quality recovery is shown to significantly improve upon JPEG and WebP formats.

High-Dimensional Generalized Orthogonal Matching Pursuit With Singular Value Decomposition

Matching pursuit (MP) is an algorithm which can reconstruct signal accurately, and is widely used in signal processing. However, MP algorithm has efficiency problem in processing large amount of data like five-dimensional (5D) seismic data. Generalized orthogonal matching pursuit with singular value decomposition (SVD_GOMP) is an algorithm which can improve the calculation efficiency a lot, and keeps the advantage of high accuracy. In this study, a redundant atom dictionary includes incident angles and azimuth is built. Then the five-dimensional seismic data is reconstructed efficiently and accurately by the generalize orthogonal matching pursuit with singular value decomposition algorithm. Compared with traditional matching pursuit method, the proposed method decomposes the five-dimensional seismic data at the same time and recovers the angle information efficiently. The reconstructed results of synthetic and field data examples are utilized to demonstrate the feasibility, computational efficiency and precision of the proposed method.

Identification of Time-Varying External Force Using Group Sparse Regularization and Redundant Dictionary.

How to accurately identify unknown time-varying external force from measured structural responses is an important engineering problem, which is critical for assessing the safety condition of the structure. In the context of a few available accelerometers, this paper proposes a novel time-varying external force identification method using group sparse regularization based on the prior knowledge in the redundant dictionary. Firstly, the relationship between time-varying external force and acceleration responses is established, and a redundant dictionary is designed to create a sparse expression of external force. Then, the relevance of atoms in the redundant dictionary is revealed, and this prior knowledge is used to determine the group structures of atoms. As a result, a force identification governing equation is formulated, and the group sparse regularization is reasonably introduced to ensure the accuracy of the identified results. The contribution of this paper is that the group structures of atoms are reasonably determined based on prior knowledge, and the complexity in the process for identifying external force from measured acceleration responses is reduced. Finally, the effectiveness of the proposed method is demonstrated by numerical simulations and an experimental structure. The illustrated results show that, compared with the force identification method based on the standard l1-norm regularization, the proposed method can further improve the identified accuracy of unknown external force and greatly enhance the computational efficiency for the force identification problem.

Enhanced Bayesian sparse representation of mechanical fault signals by structural feature-oriented matching composite dictionary construction

The traditional orthogonal matching pursuit algorithm exploits only the overall sparsity of signals without considering the effects caused by structural characteristics. To this end, this paper proposes an enhanced Bayesian sparse representation (EBSR) of mechanical fault signals by structural feature-oriented matching redundant dictionary construction. First, an EBSR model which can improve sparse reconstruction results is proposed. The proposed model improves the recovery accuracy and robustness of the sparse representation by using the structural information as a priori information. Subsequently, a composite dictionary is designed combining a Sin-Chirplet dictionary with an Impulse dictionary, and a multi-group and multi-strategy grey wolf optimizer algorithm is employed to enable the composite dictionary match the structural features of the fault signal and reduce its redundancy degree. Finally, the optimized matching composite dictionary is introduced into the EBSR algorithm, endowing it with an efficient atom selection strategy and reducing the complexity of the sparse representation. The simulation and experimental results demonstrated that the proposed method can effectively reduce the interference from background noise and impurity frequencies, verifying the effectiveness and applicability of the proposed method for the sparse representation of mechanical faults.

Utilizing the structure of a redundant dictionary comprised of wavelets and curvelets with compressed sensing

The discrete curvelet transform decomposes an image into a set of fundamental components that are distinguished by direction and size as well as a low-frequency representation. The curvelet representation is approximately sparse; thus, it is a useful sparsifying transformation to be used with compressed sensing. However, the low-frequency portion is seldom sparse. This manuscript presents a method to modify the redundant sparsifying transformation comprised of the wavelet and curvelet transforms to take advantage of this fact with compressed sensing image reconstruction. Instead of relying on sparsity for this low-frequency estimate, the Nyquist-Shannon theorem specifies a square region centered on the $0$ frequency to be collected, which is used to generate a blurry estimate. A Basis Pursuit Denoising problem is solved to determine the missing details after modifying the sparsifying transformation to take advantage of the known fully sampled region. Improvements in quality are shown on magnetic resonance and optical images.

Super-Resolution TOA and AOA Estimation for OFDM Radar Systems Based on Compressed Sensing

This article presents a compressed sensing-based time of arrival (TOA) and angle-of-arrival (AOA) estimation algorithm for orthogonal frequency division multiplexing (OFDM) radar systems. The algorithm is designed for noncooperative targets based on a uniform linear array using a cyclic prefix (CP) added OFDM signal. The algorithm makes three key technical contributions. First, the algorithm adopts the CP-based OFDM signal for the radar TOA/AOA estimation to suppress the multitarget interference and the impact of time delay on the subcarrier orthogonality. Second, this article exploits the structure of the CP-OFDM radar signal model to construct the optimization problem of the joint TOA/AOA recovery. The super-resolution AOA estimation is obtained by using a redundant dictionary containing much more basis than the number of antennas. Third, the algorithm proposes an efficient way to solve the optimization by utilizing the properties of the circulant matrix, fast Fourier transform, and Hadamard multiplication. The simulation results indicate the effectiveness of the proposed algorithm.

Sparse Bayesian Learning of Explicit Algebraic Reynolds-Stress models for turbulent separated flows

A novel Sparse Bayesian Learning (SBL) framework is introduced for generating stochastic Explicit Algebraic Reynolds Stress (EARSM) closures for the Reynolds-Averaged Navier–Stokes (RANS) equations from high-fidelity data. Building on the recently proposed SpaRTA (Sparse Regression of Turbulent Stress Anisotropy) algorithm of Schmelzer et al. (2020), corrections to an underlying Linear-Eddy-Viscosity Models (LEVM) (namely, the k−ω SST model) are formulated as physically-interpretable, frame-invariant tensor polynomials and built from a redundant dictionary of candidate functions. The SBL-SpaRTA algorithm yields a sparse model structure (which favors interpretability and reduces overfitting), while endowing model coefficients with a measure of uncertainty, namely, posterior probability distributions. The framework is used to learn customized stochastic closure models for three separated flow configurations, characterized by different geometries but similar Reynolds number. The resulting stochastic models are then propagated through a CFD solver for all three configurations by means of probabilistic chaos collocation (Loeven et al., 2007). SBL-SpaRTA predictions of velocity profiles and friction coefficient distributions outperform those of the baseline LEVM, for training as well as for test cases. Furthermore, the prediction uncertainty intervals encompass reasonably well the reference data and tend to become large in regions of large discrepancy between RANS and high-fidelity predictions, thus warning the user about model reliability. Finally, a global sensitivity analysis of the stochastic models is carried out, illustrating the role of the dominant corrective terms and providing insights for future improvement of data-driven turbulence models.

A fast algorithm for spatiotemporal signals recovery using arbitrary dictionaries with application to electrocardiographic imaging

This paper presents a method to solve a linear regression problem subject to group lasso and ridge penalisation when the model has a Kronecker structure. This model was developed to solve the inverse problem of electrocardiography using sparse signal representation over a redundant dictionary or frame. The optimisation algorithm was performed using the block coordinate descent and proximal gradient descent methods. The explicit computation of the underlying Kronecker structure in the regression was avoided, reducing space and temporal complexity. We developed an algorithm that supports the use of arbitrary dictionaries to obtain solutions and allows a flexible group distribution.

Sampling Rates for $$\ell ^1$$-Synthesis

This work investigates the problem of signal recovery from undersampled noisy sub-Gaussian measurements under the assumption of a synthesis-based sparsity model. Solving the \(\ell ^1\)-synthesis basis pursuit allows for a simultaneous estimation of a coefficient representation as well as the sought-for signal. However, due to linear dependencies within redundant dictionary atoms, it might be impossible to identify a specific representation vector, although the actual signal is still successfully recovered. The present manuscript studies both estimation problems from a non-uniform, signal-dependent perspective. By utilizing recent results on the convex geometry of linear inverse problems, the sampling rates describing the phase transitions of each formulation are identified. In both cases, they are given by the conic Gaussian mean width of an \(\ell ^1\)-descent cone that is linearly transformed by the dictionary. In general, this expression does not allow for a simple calculation by following the polarity-based approach commonly found in the literature. Hence, two upper bounds involving the sparsity structure of coefficient representations are provided: The first one is based on a local condition number and the second one on a geometric analysis that makes use of the thinness of high-dimensional polyhedral cones with not too many generators. It is furthermore revealed that both recovery problems can differ dramatically with respect to robustness to measurement noise—a fact that seems to have gone unnoticed in most of the related literature. All insights are carefully validated through numerical simulations.

A sparse representation strategy to eliminate pseudo-HFO events from intracranial EEG for seizure onset zone localization

Objective. High-frequency oscillations (HFOs) are considered a biomarker of the epileptogenic zone in intracranial EEG recordings. However, automated HFO detectors confound true oscillations with spurious events caused by the presence of artifacts. Approach. We hypothesized that, unlike pseudo-HFOs with sharp transients or arbitrary shapes, real HFOs have a signal characteristic that can be represented using a small number of oscillatory bases. Based on this hypothesis using a sparse representation framework, this study introduces a new classification approach to distinguish true HFOs from the pseudo-events that mislead seizure onset zone (SOZ) localization. Moreover, we further classified the HFOs into ripples and fast ripples by introducing an adaptive reconstruction scheme using sparse representation. By visualizing the raw waveforms and time-frequency representation of events recorded from 16 patients, three experts labeled 6400 candidate events that passed an initial amplitude-threshold-based HFO detector. We formed a redundant analytical multiscale dictionary built from smooth oscillatory Gabor atoms and represented each event with orthogonal matching pursuit by using a small number of dictionary elements. We used the approximation error and residual signal at each iteration to extract features that can distinguish the HFOs from any type of artifact regardless of their corresponding source. We validated our model on sixteen subjects with thirty minutes of continuous interictal intracranial EEG recording from each. Main results. We showed that the accuracy of SOZ detection after applying our method was significantly improved. In particular, we achieved a 96.65% classification accuracy in labeled events and a 17.57% improvement in SOZ detection on continuous data. Our sparse representation framework can also distinguish between ripples and fast ripples. Significance. We show that by using a sparse representation approach we can remove the pseudo-HFOs from the pool of events and improve the reliability of detected HFOs in large data sets and minimize manual artifact elimination.

Elimination of pseudo-HFOs in iEEG using sparse representation and Random Forest classifier.

High-Frequency Oscillation (HFO) is a promising biomarker of the epileptogenic zone. However, sharp artifacts might easily pass the conventional HFO detectors as real HFOs and reduce the seizure onset zone (SOZ) localization. We hypothesize that, unlike pseudo-HFOs, which originates from artifacts with sharp changes or arbitrary waveform characteristic, real HFOs could be represented by a limited number of oscillatory waveforms. Accordingly, to distinguish true ones from pseudo-HFOs, we established a new classification method based on sparse representation of candidate events that passed an initial detector with high sensitivity but low specificity. Specifically, using the Orthogonal Matching Pursuit (OMP) and a redundant Gabor dictionary, each event was represented sparsely in an iterative fashion. The approximation error was estimated over 30 iterations which were concatenated to form a 30-dimensional feature vector and fed to a random forest classifier. Based on the selected dictionary elements, our method can further classify HFOs into Ripples (R) and Fast Ripples (FR). In this scheme, two experts visually inspected 2075 events captured in iEEG recordings from 5 different subjects and labeled them as true-HFO or Pseudo-HFO. We reached 90.22% classification accuracy in labeled events and a 21.16% SOZ localization improvement compared to the conventional amplitude-threshold-based detector. Our sparse representation framework also classified the detected HFOs into R and FR subcategories. We reached 91.24% SOZ accuracy with the detected [Formula: see text] events. Clinical Relevance---This sparse representation framework establishes a new approach to distinguish real from pseudo-HFOs in prolonged iEEG recordings. It also provides reliable SOZ identification without the selection of artifact-free segments.