Sparse Reconstruction Research Articles

Enhanced Second-Order Off-Grid DOA Estimation Method via Sparse Reconstruction Based on Extended Coprime Array Under Impulsive Noise

Enhanced Second-Order Off-Grid DOA Estimation Method via Sparse Reconstruction Based on Extended Coprime Array Under Impulsive Noise

Estimation of planar angles from non-orthogonal imaging.

Photogrammetry-based methods are traditionally used to estimate the geometrical parameters using optical images. These methods employ specific equipment, computationally sophisticated and expensive algorithms, and utilize projective geometry to reconstruct real-life scenes up to a scale. In this work, we used a computationally less-expensive method for sparse reconstruction to estimate the planar angles using two-view geometry and linear algorithms from non-orthogonal images acquired by a smartphone camera. First, intrinsic camera parameters were determined. Next, scale-invariant feature transform was used to identify the correspondence points from each pair of images. Epipolar constraint was applied on all these points to determine the essential matrix using the eight-point algorithm. Thereafter, extrinsic camera parameters were estimated from the essential matrix and combined with the intrinsic matrix to get the camera projection matrix. Finally, linear triangulation was used to get the sparse point cloud representing the scene. Planar angles were estimated by backprojecting the chosen image points and applying simple vector algebra on the obtained 3D points. The method was successful in estimating the planar angles in less than 10s on non-curved edges with an average error of 3% by using only ten images. Given the simplicity of methods used, this technique can be integrated into a smartphone for on-site measurements as well as large deformations.

An unrolled half-quadratic approach for sparse signal recovery in spectroscopy

This paper addresses the problem of sparse signal reconstruction frequently arising in analytical chemistry. Spectroscopic restoration is an important task that was tackled using two distinct approaches. First, model-based iterative methods were deployed. These methods rely on a strong theoretical background. However they face practical obstacles in terms of hyperparameter tuning. Conversely, approaches based on deep neural networks are fast and easy to implement. Nonetheless, they are often described as black-box tools, and their stability/robustness are ongoing research topics. In this paper, we propose a deep neural network based on unrolling a Majorization-Minimization (MM) Half-Quadratic (HQ) algorithm. This allows us to build interpretable layers mirroring iterations, making it possible to learn automatically data-driven hyperparameters such as regularization and stepsizes. Furthermore, we propose a dictionary of custom activation functions derived from potentials used in the original variational model. This interpretation of activations can be useful for analyzing the stability of neural networks. The efficiency of our method in comparison to iterative and learning-based methods is showcased through various experiments conducted on realistic mass spectrometry (MS) databases with various blur kernels and noise levels. All experiments show an improved reconstruction quality of chemical signals, while maintaining a low execution time at the test phase. All the results are reproducible, through the code shared on a repository available at https://github.com/GHARBIMouna/Unrolled-Half-Quadratic.

Sparse linear dictionary reconstruction for removing microphonic noise from nuclear spectrometry measurements

The deployment of precise and sensitive nuclear spectroscopy instrumentation, using high purity germanium (HPGe), requires sustained cryogenic temperatures that can be achieved with cryocooler heat pumps. However, these pumps introduce microphonic noise that broaden the peaks of the spectra. This work demonstrates the efficacy of L1-norm regularization for the purpose of removing microphonic noise generated by the cryocooler, while still recovering the correct detector pulse amplitudes. Data are first collected from an He3 neutron detector with an attached cryocooler which enables the controlled addition of microphonic noise. A dictionary is then created by combining two relatively incoherent matrices, the first is the Fourier basis and the second is a matrix created from normalized and shifted pulses. By applying this dictionary to background noise, the regularization parameter λ is obtained. Using an L1-regularization least squares solver, microphonic noise can be effectively separated, therefore reducing the variance of the detector pulses while preserving the correct amplitude.

Fast macroscopic forcing method

The macroscopic forcing method (MFM) of Mani and Park [1] and similar methods for obtaining turbulence closure operators, such as the Green's function-based approach of Hamba [2], recover reduced solution operators from repeated direct numerical simulations (DNS). MFM has already been used to successfully quantify Reynolds-averaged Navier–Stokes (RANS)-like operators for homogeneous isotropic turbulence and turbulent channel flows. Standard algorithms for MFM force each coarse-scale degree of freedom (i.e., degree of freedom in the RANS space) and conduct a corresponding fine-scale simulation (i.e., DNS), which is expensive. We combine this method with an approach recently proposed by Schäfer and Owhadi [3] to recover elliptic integral operators from a polylogarithmic number of matrix–vector products. The resulting Fast MFM introduced in this work applies sparse reconstruction to expose local features in the closure operator and reconstructs this coarse-grained differential operator in only a few matrix–vector products and correspondingly, a few MFM simulations. For flows with significant nonlocality, the algorithm first “peels” long-range effects with dense matrix–vector products to expose a more local operator. We demonstrate the algorithm's performance for the eddy diffusivity and eddy viscosity operators, which correspond to the unclosed parts of the ensemble-averaged transport equations, excluding the analytically known, closed parts of such equations. However, the algorithm can also be applied to the full operators. We focus on scalar transport in a laminar channel flow and momentum transport in a turbulent channel flow. For these problems, we recover eddy diffusivity- and eddy viscosity-like operators, respectively, at 1% of the cost of computing the exact operator via a brute-force approach for the laminar channel flow problem and 13% for the turbulent one. Applying these operators to compute the averaged fields of interest has visually indistinguishable behavior from the exact solution. Our results show that a similar number of simulations are required to reconstruct the operators to the same accuracy under grid refinement. Thus, the accuracy corresponds to the physics of the problem, not the numerics, so long as the grid is sufficiently refined. We glean that for problems in which the RANS space is reducible to one dimension, eddy diffusivity, and eddy viscosity operators can be reconstructed with reasonable accuracy using only a few simulations, regardless of simulation resolution or degrees of freedom.

The development of a generative approach for joint super-resolution image reconstruction from highly sparse raw data in the context of MR-PET imaging

The present study introduces a rapid and efficient approach for reconstructing high-resolution images in hybrid MRI-PET scanners. The application of sparsity, compressed sensing (CS), and super-resolution reconstruction (SRR) methodologies can significantly decrease the demands of data acquisition while concurrently attaining high-resolution output. G-guided generative multilevel networks for sparsely sampled MR-PET input are shown here. Compressed Sensing using conjugate symmetry and Partial Fourier methodology speeds up data collection over k-space sampling methods. GANs and k-space adjustments are used in this image domain technique. The employed methodology utilizes discrete preprocessing stages to effectively tackle the challenges associated with the deblurring, reducing motion artifacts, and denoising of layers. Initial trials offer contextual details and accelerate evaluations. Preliminary experiments provide contextual information and expedite assessments.

Inverse-free distributed neurodynamic optimization algorithms for sparse reconstruction

This article proposes three novel inverse-free distributed neurodynamic optimization algorithms to reconstruct sparse signal and image by addressing the L1-minimization problems. Based on multi-agent consensus theory, we successfully transform the original L1-minimization problem into a distributed optimization model. To tackle such model, a three-layer inverse-free distributed algorithm is proposed by using projection operator and derivative feedback, which enjoys global convergence. To simplify the structure of this three-layer distributed algorithm, a time-varying parameter-based two-layer inverse-free distributed algorithm is designed, which has global convergence. Moreover, to accelerate convergence and further simplify the structure of this two-layer distributed algorithm, we develop a Tikhonov-like regularization-based single-layer inverse-free distributed algorithm, which achieves consensus within finite time for any given initial point and possesses an O(1/ξ(t)) convergence rate of the linear-equality constraint function. Finally, experimental results on signal and image reconstruction are presented to illustrate the efficiency of our inverse-free distributed algorithms.

Reconstructing highly divergent wavefronts from sparse measurements

The paper presents a concept for the sparse measurement and reconstruction of highly divergent wavefronts enabling measurements at high throughputs and beyond the dynamic range of the wavefront sensor. In the proposed concept, a direct measurement of the wavefront is carried out, where a few segments of the wavefront are measured with Shack–Hartmann sensors (SHSs). In total about 1% of the wavefront is measured and used for the reconstruction of the entire wavefront, which makes the concept suitable for applications where low measurement times are needed. A simulation analysis and an experimental validation of the concept are carried out, and results show that a wavefront with a divergence of 62° can be reconstructed with a root-mean-square error of about 200 nm.

Sparse Reconstruction and Resolution Improvement of Synthetic Aperture Radar with Low Computational Complexity Using Deconvolution ISTA

Sparse Reconstruction and Resolution Improvement of Synthetic Aperture Radar with Low Computational Complexity Using Deconvolution ISTA

Lamb-Waves-Based Sparse Distributed Penetrating Communication via Phase-Position Modulation for Enclosed Metal Structures

Sensor nodes have been widely used for mechanical equipment condition monitoring, especially for enclosed metal structures. In these cases, it is important to achieve communication between the sensor nodes inside the enclosed metal structures and the outside receiver node. Conventional wired communication using cables will affect the structural integrity, and wireless communication using electromagnetic waves will be shielded by metal structures, so neither is desirable. Motivated by these issues, this study proposes a Lamb waves-based sparse distributed penetrating communication (SDPC) system using the propagation characteristics of Lamb waves considered harmful in previous studies to accomplish wireless simultaneous data communication. Combining phase shift keying and pulse position modulation mechanisms, a phase-position modulation (P-PM) technology is proposed to improve the communication rate. To overcome the intersymbol interference (ISI) problem caused by the propagation characteristics of Lamb waves, a phase-position sparse reconstruction (P-PSR) strategy is proposed for demodulation, which is more convenient and accurate compared with the conventional cross-correlation method. It should be noted that the maximum bit rate without bit error reaches 830.48 kbps via P-PM parameter optimization, which is 8.3 times higher than that of on-off keying modulation approach under the same experimental conditions. Finally, distributed communication experiments and simulations further verify the high accuracy, efficiency and strong robustness of the proposed SDPC system, which can meet the communication requirements of enclosed metal structures.

Volumetric MRI with sparse sampling for MR-guided 3D motion tracking via sparse prior-augmented implicit neural representation learning.

Volumetric reconstruction of magnetic resonance imaging (MRI) from sparse samples is desirable for 3D motion tracking and promises to improve magnetic resonance (MR)-guided radiation treatment precision. Data-driven sparse MRI reconstruction, however, requires large-scale training datasets for prior learning, which is time-consuming and challenging to acquire in clinical settings. To investigate volumetric reconstruction of MRI from sparse samples of two orthogonal slices aided by sparse priors of two static 3D MRI through implicit neural representation (NeRP) learning, in support of 3D motion tracking during MR-guided radiotherapy. A multi-layer perceptron network was trained to parameterize the NeRP model of a patient-specific MRI dataset, where the network takes 4D data coordinates of voxel locations and motion states as inputs and outputs corresponding voxel intensities. By first training the network to learn the NeRP of two static 3D MRI with different breathing motion states, prior information of patient breathing motion was embedded into network weights through optimization. The prior information was then augmented from two motion states to 31 motion states by querying the optimized network at interpolated and extrapolated motion state coordinates. Starting from the prior-augmented NeRP model as an initialization point, we further trained the network to fit sparse samples of two orthogonal MRI slices and the final volumetric reconstruction was obtained by querying the trained network at 3D spatial locations. We evaluated the proposed method using 5-min volumetric MRI time series with 340ms temporal resolution for seven abdominal patients with hepatocellular carcinoma, acquired using golden-angle radial MRI sequence and reconstructed through retrospective sorting. Two volumetric MRI with inhale and exhale states respectively were selected from the first 30s of the time series for prior embedding and augmentation. The remaining 4.5-min time series was used for volumetric reconstruction evaluation, where we retrospectively subsampled each MRI to two orthogonal slices and compared model-reconstructed images to ground truth images in terms of image quality and the capability of supporting 3D target motion tracking. Across the seven patients evaluated, the peak signal-to-noise-ratio between model-reconstructed and ground truth MR images was 38.02±2.60dB and the structure similarity index measure was 0.98±0.01. Throughout the 4.5-min time period, gross tumor volume (GTV) motion estimated by deforming a reference state MRI to model-reconstructed and ground truth MRI showed good consistency. The 95-percentile Hausdorff distance between GTV contours was 2.41±0.77mm, which is less than the voxel dimension. The mean GTV centroid position difference between ground truth and model estimation was less than 1mm in all three orthogonal directions. A prior-augmented NeRP model has been developed to reconstruct volumetric MRI from sparse samples of orthogonal cine slices. Only one exhale and one inhale 3D MRI were needed to train the model to learn prior information of patient breathing motion for sparse image reconstruction. The proposed model has the potential of supporting 3D motion tracking during MR-guided radiotherapy for improved treatment precision and promises a major simplification of the workflow by eliminating the need for large-scale training datasets.

Mobile edge assisted multi-view light field video system: Prototype design and empirical evaluation

Metaverse is recently envisioned as the main driver for immersive multimedia in future networks. Light field video (LFV), considered an intermediate transition scheme towards the metaverse, is conducive to sensing and reconstructing realistic scenes in the digital twins. However, the research on LFV systems still lacks comprehensive investigation, impeding their practical application. This paper addresses major technical challenges involved in LFV delivery through mobile networks, showing a trade-off between equipment cost, calibration effort, and workflow simplicity. It also considers the balance of communications and computations latency when maintaining reconstruction performance. Leveraging edge and cloud infrastructure, a novel Mobile Edge Assisted Multi-view Light-field-video System (MEAMLS) is proposed, integrating LFV collection, volumetric video construction, and an immersive viewing scheme. A custom-made LFV capture array is designed to capture real-world scenes, while employing a learning method-integrated edge server to facilitate adaptive LFV coding. Moreover, a fast sparse reconstruction algorithm is established, leveraging edge–cloud collaboration to minimize computation latency during volumetric video construction. Intelligent service for users is deployed on edge to enable viewport-driven virtual reality viewing. By providing an immersive visual experience, the proposed MEAMLS bridges the physical world and its digital twins. The system is prototyped on a realistic 5G network to empirically validate the performance under static and dynamic circumstances. Experimental results yield fundamental insights for designing mobile edge networks-assisted LFV system from the perspective of transmission resource, adaptability, and deployment.

Radial magnetic resonance image reconstruction with a deep unrolled projected fast iterative soft-thresholding network

Radially sampling of magnetic resonance imaging (MRI) is an effective way to accelerate the imaging. How to preserve the image details in reconstruction is always challenging. In this work, a deep unrolled neural network is designed to emulate the iterative sparse image reconstruction process of a projected fast soft-threshold algorithm (pFISTA). The proposed method, an unrolled pFISTA network for Deep Radial MRI (pFISTA-DR), include the preprocessing module to refine coil sensitivity maps and initial reconstructed image, the learnable convolution filters to extract image feature maps, and adaptive threshold to robustly remove image artifacts. Experimental results show that, among the compared methods, pFISTA-DR provides the best reconstruction and achieved the highest PSNR, the highest SSIM and the lowest reconstruction errors.

Joint learning of sparse and limited-view guided waves signals for feature reconstruction and imaging

Sparse and limited-view ultrasonic guided wave imaging has become a research hotspot in the field. Studies have shown that traditional under-sampling ultrasonic imaging methods either require a significant amount of time to recover the full data or produce poor quality imaging results. To address these issues, this paper proposes an end-to-end ultrasonic guided wave joint learning imaging method for sparse and limited-view transducer arrays, which integrates sparse feature reconstruction and deep learning imaging methods. Numerical and experimental studies demonstrate that this approach significantly improves the quality of imaging results. The quality of imaging results for sparse and limited-view transducer arrays is evaluated and quantified using average correlation coefficients on the testing set. The feasibility and effectiveness of the proposed method have been verified.

Sparse Microwave Imaging Algorithm Based on L1/2 Threshold Iteration and an Approximate Observation Operator

Aiming at the problems of synthetic-aperture radar (SAR), such as high sampling rate and vulnerability to noise interference in imaging, a sparse reconstruction algorithm based on approximate observation and L1/2 threshold iteration is proposed in this paper. To solve the problem of the large dimension and high computational complexity of the measurement matrix, a sparse reconstruction model based on approximate observation is constructed, and a threshold iterative algorithm to rapidly solve the L1/2 regularization problem is introduced, which can realize sparse signal reconstruction with fewer sampling data and quickly solve the problem. The simulation results of point targets and the measured data of spaceborne SAR show that compared with the traditional matched filtering algorithm and L1 threshold algorithm based on a two-step iteration, the proposed sparse reconstruction algorithm has a faster iteration speed and improves the image quality.

High-speed mapping of surface charge dynamics using sparse scanning Kelvin probe force microscopy

Unraveling local dynamic charge processes is vital for progress in diverse fields, from microelectronics to energy storage. This relies on the ability to map charge carrier motion across multiple length- and timescales and understanding how these processes interact with the inherent material heterogeneities. Towards addressing this challenge, we introduce high-speed sparse scanning Kelvin probe force microscopy, which combines sparse scanning and image reconstruction. This approach is shown to enable sub-second imaging (>3 frames per second) of nanoscale charge dynamics, representing several orders of magnitude improvement over traditional Kelvin probe force microscopy imaging rates. Bridging this improved spatiotemporal resolution with macroscale device measurements, we successfully visualize electrochemically mediated diffusion of mobile surface ions on a LaAlO3/SrTiO3 planar device. Such processes are known to impact band-alignment and charge-transfer dynamics at these heterointerfaces. Furthermore, we monitor the diffusion of oxygen vacancies at the single grain level in polycrystalline TiO2. Through temperature-dependent measurements, we identify a charge diffusion activation energy of 0.18 eV, in good agreement with previously reported values and confirmed by DFT calculations. Together, these findings highlight the effectiveness and versatility of our method in understanding ionic charge carrier motion in microelectronics or nanoscale material systems.

Hybrid technique for crop image compression using discrete wavelet transform and sparse singular vector reconstruction

In this paper, a hybrid compression technique, based on discrete wavelet transform (DWT) and singular vector sparse reconstruction (SVSR), is proposed. In the initial phase, an original image has been divided into four sub-band by using the DWT technique. After that, SVSR is utilized for boosting the compression ratio and to improve reconstruction using piecewise cubic Hermite interpolation (PCHIP). Inverse discrete wavelet transform (IDWT) process has been applied to obtain a compressed crop image. The first time, this developed technique has been applied for compression. The performance of proposed hybrid techniques has been assessed in terms of several evaluation parameters, which are compression ratio (CR), peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM), and mean square error (MSE) on ten crop image data sets. It is observed from the results that the proposed technique is quite effective in compression of different types of crop images. Further, the experimental results show that the proposed hybrid method achieved significantly higher compression over the existing techniques. The proposed technique with Haar wavelet provides 412.5% and 94.97% higher CR as compared to Singular Value Decomposition (SVD), and SVSR respectively with desirable image quality. Further, other wavelets Db4 provide 396.48% and 88.88% and Bior3.5 also provides 306.74% and 54.74% higher CR as compared to SVD, and SVSR respectively with similar image quality.

Nectarine Disease Identification Based on Color Features and Label Sparse Dictionary Learning with Hyperspectral Images

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.

Projection neural networks with finite-time and fixed-time convergence for sparse signal reconstruction

Projection neural networks with finite-time and fixed-time convergence for sparse signal reconstruction

The application of visual communication art in brand pattern design under the modern aesthetic perspective

Abstract This paper combines the personalized and diversified features of modern aesthetic vision, highlighting the static and dynamic performance of pattern visuals. The visual communication of brand pattern is based on computer graphic image design to interpret the information in a visual medium, and the image processing method is used to sample the visual image of brand modeling, extract the edge contour feature amount of the visual image of brand modeling, construct the 3D visual reconstruction model, and carry out 3D feature analysis and sparse surface feature reconstruction. The visual communication art cognition of the brand pattern is analyzed from the analysis of the visual perceptual, psychological evaluation of the pattern and the analysis of the effect of the pattern diameter and spacing. If the pattern's brightness and background brightness are higher, the livelier the space feels. However, the relationship between the lively and solemn sense of space and the patterns' graph diameter and spacing was not obvious, with correlation coefficients of -0.618 and -0.345, respectively, p<0.01.