Real-time sparse signal reconstruction via KKT-conditions-driven analog circuit solver.

The viability and market value of pumpkin seeds are critically dependent on their internal plumpness, which is a comprehensive indicator of seed quality and can be compromised by factors such as hollow kernels resulting from improper storage or processing. Traditional methods for assessing internal quality are often destructive, time-consuming, and inefficient. In this study, the internal quality of pumpkin seeds is evaluated for the first time using the nondestructive terahertz (THz) time-domain imaging system combining compressed sensing (CS) with the Real-World Enhanced Super-Resolution Generative Adversarial Network (Real-ESRGAN) method. Using the Alternating Direction Method of Multipliers-Total Variation (ADMM_TV) as the reconstruction algorithm, five measurement matrices, including the Gauss Matrix (GaussMtx) and the Part-Fourier Matrix (PartFourierMtx), were compared. After selecting GaussMtx, the performance of five reconstruction algorithms, including Basis Pursuit (BP) and Stagewise Weak Orthogonal Matching Pursuit (SWOMP), was further compared. The super-resolution reconstruction of THz images reconstructed by CS was performed through Real-ESRGAN. The image quality was evaluated by objective indicators, and the detection accuracy was verified by the plumpness error. The results indicate that the combination of GaussMtx and ADMM_TV performs best in terms of PSNR, NMSE, and SSIM. After processing with Real-ESRGAN, the edge sharpness and details of THz images were significantly improved. The fullness error was only 2.23%, and the average detection error on the verification set was 3.37%. In summary, the combination of GaussMtx and ADMM_TV reconstruction algorithm, followed by super-resolution processing with Real-ESRGAN, can effectively improve the efficiency and accuracy of pumpkin seed quality detection. PRACTICAL APPLICATIONS: This research enables seed companies and food processors to quickly and accurately identify plump, high-quality pumpkin seeds without damaging them. By using an advanced imaging technique, the method can help automate quality control on production lines, ensuring better seed selection for planting and more consistent product quality for consumers. This contributes to reducing waste and improving the overall value of the agricultural products.

Mid-wave infrared (MWIR) hyperspectral detection enables a significant enhancement in target camouflage recognition capability. Methods based on computational spectroscopy demonstrate absolute predominance in real-time performance, detection range, and spatial resolution. This work presents an MWIR GaSb-substrate metallic metasurface compatible with a single-step lift-off fabrication process for hyperspectral computational spectral imaging. All simulations and experiments in this paper were conducted under the condition of 0° linearly polarized incident light. The finite-difference time-domain (FDTD) method is utilized to simulate the transmission spectra of 36 metasurface unit cells, construct the observation matrices, and analyze their correlation coefficients and energy utilization efficiency. Through a greedy algorithm, 11 low-correlation structures are screened, reducing the average correlation coefficient from 0.539 to 0.376 while boosting the energy utilization efficiency to 63.6%, thereby remarkably enhancing the system's compressive sensing performance. The basis pursuit algorithm is employed for reconstructing Gaussian and complex sparse spectral signals, revealing that the co-design of metasurface structural optimization and compressed sensing algorithms plays a pivotal role in improving the performance of miniature spectrometers. This paper provides a viable pathway for the development of portable spectral imaging systems for complex environments, with extensive application prospects in fields including environmental monitoring, food safety, and biomedical engineering.

Monte Carlo simulations of neutronic systems are computationally intensive and demand significant memory resources for high-fidelity modeling. Compressed sensing enables accurate reconstruction of signals from significantly fewer samples than traditional methods. The specific implementation of compressed sensing investigated here involves the use of overlapping cells to collect tallies. Increasing the number of samples improves the reconstruction accuracy, although the marginal gains diminish with more samples. Reconstruction quality is strongly influenced by the sparsity parameter used in basis pursuit denoising. Across the three test cases considered, memory reductions of up to 81.25% (96.25%) are demonstrated for 2D (3D) reconstructions, with select scenarios achieving reconstruction errors within 1 standard deviation of the corresponding high-fidelity reference results.

In this paper, we propose a new primal-dual algorithmic framework for a class of convex-concave saddle point problems frequently arising from image processing and machine learning. Our algorithmic framework updates the primal variable between the twice calculations of the dual variable, thereby appearing a symmetric iterative scheme, which is accordingly called the symmetric primal-dual algorithm (SPIDA). It is noteworthy that the subproblems of our SPIDA are equipped with Bregman proximal regularization terms, which make SPIDA versatile in the sense that it enjoys an algorithmic framework to understand the iterative schemes of some existing algorithms, such as the classical augmented Lagrangian method (ALM), linearized ALM, and Jacobian splitting algorithms for linearly constrained optimization problems. Besides, our algorithmic framework allows us to derive some customized versions so that SPIDA works as efficiently as possible for structured optimization problems. Theoretically, under some mild conditions, we prove the global convergence of SPIDA and estimate the linear convergence rate under a generalized error bound condition defined by Bregman distance. Finally, a series of numerical experiments on the basis pursuit, robust principal component analysis, and image restoration demonstrate that our SPIDA works well on synthetic and real-world datasets.

Aiming at the situation where the measurement matrix B has a flexible block decomposition, this article designs two novel distributed continuous- and discrete-time projection neurodynamic approaches to solve the basis pursuit (BP) problem for sparse recovery. These approaches only require information from each flexible block of the measurement matrix B, rather than from each row, column, or the entire matrix. First, with the aid of the primal-dual dynamical approach, projection operator, and second-order multiagent consensus condition, a novel distributed projection neurodynamic approach in continuous time (DPNA-CT-B) is proposed, and its optimality and global asymptotic stability are rigorously proved. Moreover, based on the forward and backward Euler methods and variable substitution methods, a corresponding distributed projection neurodynamic approach in discrete time (DPNA-DT-B) is designed. Finally, through sparse signal and image reconstruction experiments, the effectiveness and superiority of the proposed neurodynamic approaches are verified.

This paper explores the application of transform-domain sparsification and compressed sensing (CS) techniques to improve the efficiency and quality of magnetic resonance imaging (MRI). We implement and evaluate three sparsifying methods—discrete wavelet transform (DWT), fast Fourier transform (FFT), and discrete cosine transform (DCT)—which are used to simulate subsampled reconstruction via inverse transforms. Additionally, one accurate CS reconstruction algorithm, basis pursuit (BP), using the L1-MAGIC toolbox, is implemented as a benchmark based on convex optimization with L1-norm minimization. Emphasis is placed on basis pursuit (BP), which satisfies the formal requirements of CS theory, including incoherent sampling and sparse recovery via nonlinear reconstruction. Each method is assessed in MATLAB R2024b using standardized DICOM images and varying sampling rates. The evaluation metrics include peak signal-to-noise ratio (PSNR), root mean square error (RMSE), structural similarity index measure (SSIM), execution time, memory usage, and compression efficiency. The results show that although discrete cosine transform (DCT) outperforms the others under simulation in terms of PSNR and SSIM, it is inconsistent with the physics of MRI acquisition. Conversely, basis pursuit (BP) offers a theoretically grounded reconstruction approach with acceptable accuracy and clinical relevance. Despite the limitations of a controlled experimental setup, this study establishes a reproducible benchmarking framework and highlights the trade-offs between the quality of transform-based reconstruction and computational complexity. Future work will extend this study by incorporating clinically validated CS algorithms with L0 and nonconvex Lp (0 < p < 1) regularization to align with state-of-the-art MRI reconstruction practices.

An improved proximal primal–dual ALM-based algorithm with convex combination proximal centers for equality-constrained convex programming in basis pursuit practical problems

Abstract We optimize the running time of the primal-dual algorithms by optimizing their stopping criteria for solving convex optimization problems under affine equality constraints, which means terminating the algorithm earlier with fewer iterations. We study the relations between four stopping criteria and show under which conditions they are accurate to detect optimal solutions. The uncomputable one: "Optimality gap and Feasibility error", and the computable ones: the "Karush–Kuhn–Tucker error", the "Projected Duality Gap", and the "Smoothed Duality Gap". Assuming metric sub-regularity or quadratic error bound, we establish that all of the computable criteria provide practical upper bounds for the optimality gap, and approximate it effectively. Furthermore, we establish comparability between some of the computable criteria under certain conditions. Numerical experiments on basis pursuit, and quadratic programs with(out) non-negative weights corroborate these findings and show that the smoothed duality gap is more widely applicable than the rest.

Abstract Reconstructing the network interaction structure from multivariate time series is an important problem in multiple fields of science. When the network dynamics is represented as a linear combination of multivariate polynomials, the reconstruction can be formulated as an optimisation problem. For large networks, this optimisation problem does not always have a unique solution, leading to wrong reconstruction. We propose the Ergodic Basis Pursuit (EBP) method, which leverages the statistical properties of the network dynamics to accurately reconstruct sparse networks. The key idea is that the restricted isometry property of the associated library matrix—a crucial condition for ensuring unique reconstruction—can be derived from the ergodic properties of the network dynamics. We show that when the data length scales quadratically with node degree and logarithmically with network size the reconstruction is unique. Compared to traditional methods, the EBP reconstructs sparse networks using significantly less data and is robust to noise. We validate its effectiveness using experimental time series from optoelectronic networks.

Bearing fault diagnosis is crucial for mechanical system reliability. Numerous techniques have been developed to identify faults in bearings. However, the signals under time-varying speed condition are nonstationary, and most diagnosis methods suffer from the nonstationary property caused by time-varying speed problem. The change of speed changes the fault pulse frequency, but the structure of pulse remains the same. Shift-invariant dictionary learning (SIDL) can learn the repetitive structure in the signal without the limitation of the structure's size. Thus, the fault pulses in the fault signal under time-varying speed condition. Union of circulants dictionary learning (UCDL) is a kind of SIDL, where the algorithm takes the advantage of explicit circulant structures and has the powerful ability to learn the fault pulses into the atoms. In this work, we use UCDL to extract features under time-varying speed condition, and hidden Markov model (HMM) is used to diagnose faults. We further found that UCDL with the global sparse coding named basis pursuit, which can maintain the stability of the coefficient solution, has a better performance in the time-varying diagnosis. To validate the performance of the proposed method named improved SIDL, both simulation and experimental signals are processed, and the diagnosis results prove the high efficiency of the proposed method in the time-varying diagnosis. The improved SIDL method achieved an average diagnostic accuracy of 100% in simulations and 98.32% in experiments, both of which are superior to traditional methods.

ABSTRACTWe study signals that are sparse either on the vertices of a graph or in the graph spectral domain. Recent results on the algebraic properties of random integer matrices as well as on the boundedness of eigenvectors of random matrices imply two types of support size uncertainty principles for graph signals. Indeed, the algebraic properties imply uniqueness results if a sparse signal is sampled at any set of minimal size in the other domain. The boundedness properties of eigenvectors imply stable reconstruction by basis pursuit if a sparse signal is sampled at a slightly larger randomly selected set in the other domain.

Abstract Spicules have often been proposed as substantial contributors toward the mass and energy balance of the solar corona. While their transition region (TR) counterpart has unequivocally been established over the past decade, the observations concerning the coronal contribution of spicules have often been contested. This is mainly attributed to the lack of adequate coordinated observations, their small spatial scales, highly dynamic nature, and complex multithermal evolution, which are often observed at the limit of our current observational facilities. Therefore, it remains unclear how much heating occurs in association with spicules to coronal temperatures. In this study, we use coordinated high-resolution observations of the solar chromosphere, TR, and corona of a quiet-Sun region and a coronal hole with the Interface Region Imaging Spectrograph (IRIS) and the Atmospheric Imaging Assembly (AIA) to investigate the (lower) coronal (∼1 MK) emission associated with spicules. We perform differential emission measure analysis on the AIA passbands using basis pursuit and a newly developed technique based on Tikhonov regularization to probe the thermal structure of the spicular environment at coronal temperatures. We find that the emission measure (EM) maps at 1 MK reveal the presence of ubiquitous, small-scale jets with a clear spatiotemporal coherence with the spicules observed in the IRIS/TR passband. Detailed spacetime analysis of the chromospheric, TR, and EM maps show unambiguous evidence of rapidly outward-propagating spicules with strong emission (2–3 times higher than the background) at 1 MK. Our findings are consistent with previously reported MHD simulations that show heating to coronal temperatures associated with spicules.

We address the inverse problem of identifying nonlocal interaction potentials in nonlinear aggregation–diffusion equations from noisy discrete trajectory data. Our approach involves formulating and solving a regularized variational problem, which requires minimizing a quadratic error functional across a set of hypothesis functions, further augmented by a sparsity-enhancing regularizer. We employ a partial inversion algorithm, akin to the CoSaMP and subspace pursuit algorithms, to solve the basis pursuit problem. A key theoretical contribution is our novel stability estimate for the PDEs, validating the error functional ability in controlling the 2-Wasserstein distance between solutions generated using the true and estimated interaction potentials. Our work also includes an error analysis of estimators caused by discretization and observational errors in practical implementations. We demonstrate the effectiveness of the methods through various 1D and 2D examples showcasing collective behaviors.

Abstract Super-resolution of pointwise sources is of utmost importance in various areas of imaging sciences. Specific instances of this problem arise in single molecule fluorescence, spike sorting in neuroscience, astrophysical imaging, radar imaging and nuclear resonance imaging. In all these applications, the Lasso method (also known as Basis Pursuit or $ \ell ^{1} $-regularization) is the de facto baseline method for recovering sparse vectors from low-resolution measurements. This approach requires discretization of the domain, which leads to quantization artefacts and consequently, an overestimation of the number of sources. While grid-less methods, such as Prony-type methods or non-convex optimization over the source position, can mitigate this, the Lasso remains a strong baseline due to its versatility and simplicity. In this work, we introduce a simple extension of the Lasso, termed ‘super-resolved Lasso’ (SR-Lasso). Inspired by the Continuous Basis Pursuit (C-BP) method, our approach introduces an extra parameter to account for the shift of the sources between grid locations. Our method is more comprehensive than C-BP, accommodating both arbitrary real-valued or complex-valued sources. Furthermore, it can be solved similarly to the Lasso as it boils down to solving a group-Lasso problem. A notable advantage of SR-Lasso is its theoretical properties, akin to grid-less methods. Given a separation condition on the sources and a restriction on the shift magnitude outside the grid, SR-Lasso precisely estimates the correct number of sources.

Effective noise management and control of periodic fluctuations in spaceborne atomic clocks are essential for the accuracy and reliability of Global Navigation Satellite Systems. Time-varying periodic terms can impact both the performance evaluation and prediction accuracy of satellite clocks, making it crucial to mitigate these influences in the clock bias. We propose methods based on the Fourier dictionary and basis pursuit, namely the Fourier basis pursuit (FBP) spectrum and the Fourier basis pursuit bandpass filter (FBPBPF), to analyze and extract periodic terms in the satellite clock bias. The FBP method minimizes the L1-norm to improve spectral quality, while the FBPBPF reduces boundary effects and noise. Our experimental results show that the FBP spectrum has a more obvious main lobe and reduces spectral leakage compared to traditional windowed Fourier transforms. In simulation experiments, the FBPBPF achieves periodic term extraction with errors reduced by 6.81% to 26.55% compared to traditional signal processing methods, and boundary extraction errors reduced by up to 63.67%. Using the BeiDou Navigation Satellite System’s precise clock bias for verification, the FBP-based prediction method has significantly improved the prediction accuracy compared to the spectral analysis model. For 6, 12, 18, and 24 h predictions, the average root mean square error of the FBP prediction method is reduced by 15.85%, 11.04%, 6.45%, and 4.01%, respectively.

Difficulty in extracting nonlinear sparse impulse features due to variable speed conditions and redundant noise interference leads to challenges in diagnosing variable speed faults. Therefore, an improved spectral amplitude modulation based on sparse feature adaptive convolution (ISAM-SFAC) is proposed to enhance the fault features under variable speed condition. First, an optimal bi-damped wavelet construction method is proposed to learn signal impulse features, which selects the optimal bi-damped wavelet parameters with correlation criterion and particle swarm optimization (PSO). Second, a convolutional basis pursuit denoising model based on optimal bi-damped wavelet is proposed for resolving sparse impulses. A model regularization parameter selection method based on weighted fault characteristic amplitude ratio (WFCAR) assistance is proposed. Then, an improved spectral amplitude modulation method based on kurtosis threshold is proposed to further enhance the fault information of sparse signal. Finally, the type of variable speed faults is determined by order spectrum analysis. Various experimental results, such as spectral amplitude modulation and Morlet wavelet matching, verify the effectiveness and advantages of the ISAM-SFAC method. Conflict of Interest Statement The authors declare no conflicts of interest.

An ocean target electric field signal is an effective approach for analyzing the ocean environment and is widely used for detecting ocean targets, extracting their features, and tracking them. Low-frequency analysis and recording (LOFAR) is a commonly used time–frequency analysis tool that provides the time–frequency spectrum of a signal; however, its reliance on the Fourier transform (FT) results in a low frequency resolution and signal-to-noise ratio (SNR), which limits its target detection capabilities. To address this problem, we propose a method called low-frequency analysis and recording based on basis pursuit (LOFAR-BP) for analyzing and detecting ocean target electric field signals. LOFAR-BP uses basis pursuit (BP) with the L1 norm for frequency analysis, whereas LOFAR utilizes the FT. We demonstrate that the FT is the L2 norm mathematically. LOFAR-BP generates the time–frequency spectrum in the same way that LOFAR does. By extracting characteristic values from the time–frequency spectrum, targets can be detected using an appropriate threshold. Both simulation and ocean experiments showed that LOFAR-BP effectively enhances target signals and suppresses noise. Compared with LOFAR, LOFAR-BP improved the frequency resolution by 60% in both experiments and increased the SNR by 54.82 dB in the simulation experiment and by 39.59 dB in the ocean experiment. When applied to target detection, LOFAR-BP can detect targets 6 s earlier than LOFAR can.

Unwrapping error and fading signal correction on multi-looked InSAR data

Photoacoustic tomography (PAT) has emerged as a promising imaging modality for breast cancer detection, offering unique advantages in visualizing tissue composition without ionizing radiation. However, limited-view scenarios in clinical settings present significant challenges for image reconstruction quality and computational efficiency. This paper introduces novel unrolled deep learning networks based on split Bregman total variation (SBTV) and relaxed basis pursuit alternating direction method of multipliers (rBP-ADMM) algorithms to address these challenges. Our approach combines transfer learning from full-view to limited-view scenarios with U-Net denoiser integration, achieving state-of-the-art reconstruction quality (MS-SSIM> 0.95) while reducing reconstruction time by 92% compared to traditional methods. The effectiveness of different sensor configurations is analyzed through restricted isometry property (RIP) analysis and coherence values, demonstrating that semicircular arrays achieve a RIP constant of 0.76 and coherence of 0.77, closely approximating full-view performance (RIP: 0.75, coherence: 0.78). These metrics validate the theoretical foundation for accurate sparse signal recovery in limited-view scenarios. Comprehensive evaluations across semicircular, concave, and convex sensor arrangements show that the proposed U-SBTV network consistently outperforms existing methods, particularly when combined with the U-Net denoiser. This advancement in limited-view PAT reconstruction brings the technology closer to practical clinical application, potentially improving early breast cancer detection capabilities.