A Sparse Recovery Algorithm for Suppressing Multiple Linear Frequency Modulation Interference in the Synthetic Aperture Radar Image Domain.

In synthetic aperture radar (SAR) signal processing, compared with the raw data of level-0, level-1 SAR images are more readily accessible and available in larger quantities. However, an amount of level-1 images are affected by radio frequency interference (RFI), which typically originates from Linear Frequency Modulation (LFM) signals emitted by ground-based radars. Existing research on interference suppression in level-1 data has primarily focused on two methods: transforming SAR images into simulated echo data for interference suppression, or focusing interference in the frequency domain and applying notching filters to reduce interference energy. However, these methods overlook the effective utilization of the interference parameters or are confined to suppressing only one type of LFM interference at a time. In certain SAR images, multiple types of LFM interference manifest bright radiation artifacts that exhibit varying lengths along the range direction while remaining constant in the azimuth direction. It is necessary to suppress multiple LFM interference on SAR images when original echo data are unavailable. This article proposes a joint sparse recovery algorithm for interference suppression in the SAR image domain. In the SAR image domain, two-dimensional LFM interference typically exhibits differences in parameters such as frequency modulation rate and pulse width in the range direction, while maintaining consistency in the azimuth direction. Based on this observation, this article constructs a series of focusing operators for LFM interference in SAR images. These operators enable the sparse representation of dispersed LFM interference. Subsequently, an optimization model is developed that can effectively suppress multi-LFM interference and reduce image loss with the assistance of a regularization term in the image domain. Simulation experiments conducted in various scenarios validate the superior performance of the proposed method.

Distributed continuous-time accelerated neurodynamic approaches for sparse recovery via smooth approximation to L1-minimization.

This paper develops two continuous-time distributed accelerated neurodynamic approaches for solving sparse recovery via smooth approximation to L1-norm minimization problem. First, the L1-norm minimization problem is converted into a distributed smooth optimization problem by utilizing multiagent consensus theory and smooth approximation. Then, a distributed primal-dual accelerated neurodynamic approach is designed by using Karush-Kuhn-Tucker (KKT) condition and Nesterov's accelerated method. Furthermore, in order to reduce the structure complexity of the presented neurodynamic approach, based on the projection matrix, we eliminate a dual variable in the KKT condition and propose a distributed accelerated neurodynamic approach with a simpler structure. It is proved that the two proposed distributed neurodynamic approaches both achieve O(1t2) convergence rate. Finally, the simulation results of sparse recovery are given to demonstrate the effectiveness of the proposed approaches.

Reweighted Off-Grid Sparse Spectrum Fitting for DOA Estimation in Sensor Array with Unknown Mutual Coupling.

In the environment of unknown mutual coupling, many works on direction-of-arrival (DOA) estimation with sensor array are prone to performance degradation or even failure. Moreover, there are few literatures on off-grid direction finding using regularized sparse recovery technology. Therefore, the scenario of off-grid DOA estimation in sensor array with unknown mutual coupling is investigated, and then a reweighted off-grid Sparse Spectrum Fitting (Re-OGSpSF) approach is developed in this article. Inspired by the selection matrix, an undisturbed array output is formed to remove the unknown mutual coupling effect. Subsequently, a refined off-grid SpSF (OGSpSF) recovery model is structured by integrating the off-grid error term obtained from the first-order Taylor approximation of the higher-order term into the underlying on-grid sparse representation model. After that, a novel Re-OGSpSF framework is formulated to recover the sparse vectors, where a weighted matrix is developed by the MUSIC-like spectrum function to enhance the solution's sparsity. Ultimately, off-grid DOA estimation can be realized with the help of the recovered sparse vectors. Thanks to the off-grid representation and reweighted strategy, the proposed method can effectively and efficiently achieve high-precision continuous DOA estimation, making it favorable for real-time direction finding. The simulation results validate the superiority of the proposed method.

Framework for Segmented threshold ℓ0 gradient approximation based network for sparse signal recovery.

Signal reconstruction from compressed sensed data need iterative methods since the sparse measurement matrix is analytically non invertible. The iterative thresholding and ℓ0 function minimization are of special interest as these two operations provide sparse solution. However these methods need an inverse operation corresponding to the measurement matrix for estimating the reconstruction error. The pseudo-inverse of the measurement matrix is used in general for this purpose. Here a sparse signal recovery framework using an approximate inverse matrix Q and iterative segment thresholding of ℓ0 and ℓ1 norm with residue addition is presented. Two recovery algorithms are developed using this framework. The ℓ0 based method is later developed to a basis function dictionary based network for sparse signal recovery. The proposed framework enables the users experiment with different inverse matrix to achieve better efficiency in sparse signal recovery and implement the algorithm in computationally efficient way.

Sparse Multichannel Decomposition of Electrodermal Activity With Physiological Priors.

Goal: Inferring autonomous nervous system (ANS) activity is a challenging issue and has critical applications in stress regulation. Sweat secretions caused by ANS activity influence the electrical conductance of the skin. Therefore, the variations in skin conductance (SC) measurements reflect the sudomotor nerve activity (SMNA) and can be used to infer the underlying ANS activity. These variations are strongly correlated with emotional arousal as well as thermoregulation. However, accurately recovering ANS activity and the corresponding state-space system from a single channel signal is difficult due to artifacts introduced by measurement noise. To minimize the impact of noise on inferring ANS activity, we utilize multiple channels of SC data. Methods: We model skin conductance using a second-order differential equation incorporating a time-shifted sparse impulse train input in combination with independent cubic basis spline functions. Finally, we develop a block coordinate descent method for SC signal decomposition by employing a generalized cross-validation sparse recovery approach while including physiological priors. Results: We analyze the experimental data to validate the performance of the proposed algorithm. We demonstrate its capacity to recover the ANS activations, the underlying physiological system parameters, and both tonic and phasic components. Finally, we present an overview of the algorithm's comparative performance under varying conditions and configurations to substantiate its ability to accurately model ANS activity. Our results show that our algorithm performs better in terms of multiple metrics like noise performance, AUC score, the goodness of fit of reconstructed signal, and lower missing impulses compared with the single channel decomposition approach. Conclusion: In this study, we highlight the challenges and benefits of concurrent decomposition and deconvolution of multichannel SC signals.

Robust RFID Tag Identification.

Fast and reliable identification of Radio Frequency Indentification (RFID) tags by means of anticollision (MAC) protocols has been a problem of substantial interest for more than a decade. However, improvements in identification rate have been slow, as most solutions rely on sequential approaches that try to avoid collisions, which have limited margin for performance improvement. Recently, there has been growing interest in concurrent techniques that exploit the structure of collisions to recover tag IDs. While these techniques promise substantial improvements in speed, a key question that remains unaddressed is how to deal with noise or interference that might introduce errors in the recovery process at the reader. Our goal in this paper is to consider a noisy wireless channel and add robustness to concurrent RFID identification techniques. We propose a new protocol, called CIRF (Concurrent Identification of RFids), which uses multiple antennas to add robustness to noise and leverages block sparsity-based optimization to recover EPC IDs of transmitting tags. We include fail-safe methods to handle errors that persist after the optimization stage. Extensive simulations show that CIRF achieves substantial resilience improvement in a range of very low to medium Signal-to-Noise (SNR) situations, being able to always correctly recover 99% of tags.

Group Testing with Blocks of Positives and Inhibitors.

The main goal of group testing is to identify a small number of specific items among a large population of items. In this paper, we consider specific items as positives and inhibitors and non-specific items as negatives. In particular, we consider a novel model called group testing with blocks of positives and inhibitors. A test on a subset of items is positive if the subset contains at least one positive and does not contain any inhibitors, and it is negative otherwise. In this model, the input items are linearly ordered, and the positives and inhibitors are subsets of small blocks (at unknown locations) of consecutive items over that order. We also consider two specific instantiations of this model. The first instantiation is that model that contains a single block of consecutive items consisting of exactly known numbers of positives and inhibitors. The second instantiation is the model that contains a single block of consecutive items containing known numbers of positives and inhibitors. Our contribution is to propose efficient encoding and decoding schemes such that the numbers of tests used to identify only positives or both positives and inhibitors are less than the ones in the state-of-the-art schemes. Moreover, the decoding times mostly scale to the numbers of tests that are significantly smaller than the state-of-the-art ones, which scale to both the number of tests and the number of items.

Extreme Compressed Sensing of Poisson Rates from Multiple Measurements.

Compressed sensing (CS) is a signal processing technique that enables the efficient recovery of a sparse high-dimensional signal from low-dimensional measurements. In the multiple measurement vector (MMV) framework, a set of signals with the same support must be recovered from their corresponding measurements. Here, we present the first exploration of the MMV problem where signals are independently drawn from a sparse, multivariate Poisson distribution. We are primarily motivated by a suite of biosensing applications of microfluidics where analytes (such as whole cells or biomarkers) are captured in small volume partitions according to a Poisson distribution. We recover the sparse parameter vector of Poisson rates through maximum likelihood estimation with our novel Sparse Poisson Recovery (SPoRe) algorithm. SPoRe uses batch stochastic gradient ascent enabled by Monte Carlo approximations of otherwise intractable gradients. By uniquely leveraging the Poisson structure, SPoRe substantially outperforms a comprehensive set of existing and custom baseline CS algorithms. Notably, SPoRe can exhibit high performance even with one-dimensional measurements and high noise levels. This resource efficiency is not only unprecedented in the field of CS but is also particularly potent for applications in microfluidics in which the number of resolvable measurements per partition is often severely limited. We prove the identifiability property of the Poisson model under such lax conditions, analytically develop insights into system performance, and confirm these insights in simulated experiments. Our findings encourage a new approach to biosensing and are generalizable to other applications featuring spatial and temporal Poisson signals.

Sparse System Identification of Leptin Dynamics in Women With Obesity.

The prevalence of obesity is increasing around the world at an alarming rate. The interplay of the hormone leptin with the hypothalamus-pituitary-adrenal axis plays an important role in regulating energy balance, thereby contributing to obesity. This study presents a mathematical model, which describes hormonal behavior leading to an energy abnormal equilibrium that contributes to obesity. To this end, we analyze the behavior of two neuroendocrine hormones, leptin and cortisol, in a cohort of women with obesity, with simplified minimal state-space modeling. Using a system theoretic approach, coordinate descent method, and sparse recovery, we deconvolved the serum leptin-cortisol levels. Accordingly, we estimate the secretion patterns, timings, amplitudes, number of underlying pulses, infusion, and clearance rates of hormones in eighteen premenopausal women with obesity. Our results show that minimal state-space model was able to successfully capture the leptin and cortisol sparse dynamics with the multiple correlation coefficients greater than 0.83 and 0.87, respectively. Furthermore, the Granger causality test demonstrated a negative prospective predictive relationship between leptin and cortisol, 14 of 18 women. These results indicate that increases in cortisol are prospectively associated with reductions in leptin and vice versa, suggesting a bidirectional negative inhibitory relationship. As dysregulation of leptin may result in an abnormality in satiety and thereby associated to obesity, the investigation of leptin-cortisol sparse dynamics may offer a better diagnostic methodology to improve better treatments plans for individuals with obesity.

A Fast Space-Time Adaptive Processing Algorithm Based on Sparse Bayesian Learning for Airborne Radar.

Space-time adaptive processing (STAP) plays an essential role in clutter suppression and moving target detection in airborne radar systems. The main difficulty is that independent and identically distributed (i.i.d) training samples may not be sufficient to guarantee the performance in the heterogeneous clutter environment. Currently, most sparse recovery/representation (SR) techniques to reduce the requirement of training samples still suffer from high computational complexities. To remedy this problem, a fast group sparse Bayesian learning approach is proposed. Instead of employing all the dictionary atoms, the proposed algorithm identifies the support space of the data and then employs the support space in the sparse Bayesian learning (SBL) algorithm. Moreover, to extend the modified hierarchical model, which can only apply to real-valued signals, the real and imaginary components of the complex-valued signals are treated as two independent real-valued variables. The efficiency of the proposed algorithm is demonstrated both with the simulated and measured data.

Maximal Dependence Capturing as a Principle of Sensory Processing.

Sensory inputs conveying information about the environment are often noisy and incomplete, yet the brain can achieve remarkable consistency in recognizing objects. Presumably, transforming the varying input patterns into invariant object representations is pivotal for this cognitive robustness. In the classic hierarchical representation framework, early stages of sensory processing utilize independent components of environmental stimuli to ensure efficient information transmission. Representations in subsequent stages are based on increasingly complex receptive fields along a hierarchical network. This framework accurately captures the input structures; however, it is challenging to achieve invariance in representing different appearances of objects. Here we assess theoretical and experimental inconsistencies of the current framework. In its place, we propose that individual neurons encode objects by following the principle of maximal dependence capturing (MDC), which compels each neuron to capture the structural components that contain maximal information about specific objects. We implement the proposition in a computational framework incorporating dimension expansion and sparse coding, which achieves consistent representations of object identities under occlusion, corruption, or high noise conditions. The framework neither requires learning the corrupted forms nor comprises deep network layers. Moreover, it explains various receptive field properties of neurons. Thus, MDC provides a unifying principle for sensory processing.

Corrigendum: Sparse system identification of leptin dynamics in women with obesity.

[This corrects the article DOI: 10.3389/fendo.2022.769951.].

WEAK SINDY FOR PARTIAL DIFFERENTIAL EQUATIONS.

Sparse Identification of Nonlinear Dynamics (SINDy) is a method of system discovery that has been shown to successfully recover governing dynamical systems from data [6, 39]. Recently, several groups have independently discovered that the weak formulation provides orders of magnitude better robustness to noise. Here we extend our Weak SINDy (WSINDy) framework introduced in [28] to the setting of partial differential equations (PDEs). The elimination of pointwise derivative approximations via the weak form enables effective machine-precision recovery of model coefficients from noise-free data (i.e. below the tolerance of the simulation scheme) as well as robust identification of PDEs in the large noise regime (with signal-to-noise ratio approaching one in many well-known cases). This is accomplished by discretizing a convolutional weak form of the PDE and exploiting separability of test functions for efficient model identification using the Fast Fourier Transform. The resulting WSINDy algorithm for PDEs has a worst-case computational complexity of O ( N D + 1 log ( N ) ) for datasets with N points in each of D + 1 dimensions. Furthermore, our Fourier-based implementation reveals a connection between robustness to noise and the spectra of test functions, which we utilize in an a priori selection algorithm for test functions. Finally, we introduce a learning algorithm for the threshold in sequential-thresholding least-squares (STLS) that enables model identification from large libraries, and we utilize scale invariance at the continuum level to identify PDEs from poorly-scaled datasets. We demonstrate WSINDy's robustness, speed and accuracy on several challenging PDEs. Code is publicly available on GitHub at https://github.com/MathBioCU/WSINDy_PDE.

Compressed Sensing of Extracellular Neurophysiology Signals: A Review.

This article presents a comprehensive survey of literature on the compressed sensing (CS) of neurophysiology signals. CS is a promising technique to achieve high-fidelity, low-rate, and hardware-efficient neural signal compression tasks for wireless streaming of massively parallel neural recording channels in next-generation neural interface technologies. The main objective is to provide a timely retrospective on applying the CS theory to the extracellular brain signals in the past decade. We will present a comprehensive review on the CS-based neural recording system architecture, the CS encoder hardware exploration and implementation, the sparse representation of neural signals, and the signal reconstruction algorithms. Deep learning-based CS methods are also discussed and compared with the traditional CS-based approaches. We will also extend our discussion to cover the technical challenges and prospects in this emerging field.

WEAK SINDy: GALERKIN-BASED DATA-DRIVEN MODEL SELECTION.

We present a novel weak formulation and discretization for discovering governing equations from noisy measurement data. This method of learning differential equations from data fits into a new class of algorithms that replace pointwise derivative approximations with linear transformations and variance reduction techniques. Compared to the standard SINDy algorithm presented in [S. L. Brunton, J. L. Proctor, and J. N. Kutz, Proc. Natl. Acad. Sci. USA, 113 (2016), pp. 3932-3937], our so-called weak SINDy (WSINDy) algorithm allows for reliable model identification from data with large noise (often with ratios greater than 0.1) and reduces the error in the recovered coefficients to enable accurate prediction. Moreover, the coefficient error scales linearly with the noise level, leading to high-accuracy recovery in the low-noise regime. Altogether, WSINDy combines the simplicity and efficiency of the SINDy algorithm with the natural noise reduction of integration, as demonstrated in [H. Schaeffer and S. G. McCalla, Phys. Rev. E, 96 (2017), 023302], to arrive at a robust and accurate method of sparse recovery.

Sparse Recovery Beyond Compressed Sensing: Separable Nonlinear Inverse Problems.

Extracting information from nonlinear measurements is a fundamental challenge in data analysis. In this work, we consider separable inverse problems, where the data are modeled as a linear combination of functions that depend nonlinearly on certain parameters of interest. These parameters may represent neuronal activity in a human brain, frequencies of electromagnetic waves, fluorescent probes in a cell, or magnetic relaxation times of biological tissues. Separable nonlinear inverse problems can be reformulated as underdetermined sparse-recovery problems, and solved using convex programming. This approach has had empirical success in a variety of domains, from geophysics to medical imaging, but lacks a theoretical justification. In particular, compressed-sensing theory does not apply, because the measurement operators are deterministic and violate incoherence conditions such as the restricted-isometry property. Our main contribution is a theory for sparse recovery adapted to deterministic settings. We show that convex programming succeeds in recovering the parameters of interest, as long as their values are sufficiently distinct with respect to the correlation structure of the measurement operator. The theoretical results are illustrated through numerical experiments for two applications: heat-source localization and estimation of brain activity from electroencephalography data.

Axial super-resolution in ultrasound imaging with application to non-destructive evaluation.

A fundamental challenge in non-destructive evaluation using ultrasound is to accurately estimate the thicknesses of different layers or cracks present in the object under examination, which implicitly corresponds to accurately localizing the point-sources of the reflections from the measured signal. Conventional signal processing techniques cannot overcome the axial-resolution limit of the ultrasound imaging system determined by the wavelength of the transmitted pulse. In this paper, starting from the solution to the 1-D wave equation, we show that the ultrasound reflections could be effectively modeled as finite-rate-of-innovation (FRI) signals. The FRI modeling approach is a new paradigm in signal processing. Apart from allowing for the signals to be sampled below the Nyquist rate, the FRI framework also transforms the reconstruction problem into one of parametric estimation. We employ high-resolution parametric estimation techniques to solve the problem. We demonstrate axial super-resolution capability (resolution below the theoretical limit) of the proposed technique both on simulated as well as experimental data. A comparison of the FRI technique with time-domain and Fourier-domain sparse recovery techniques shows that the FRI technique is more robust. We also assess the resolvability of the proposed technique under different noise conditions on data simulated using the Field-II software and show that the reconstruction technique is robust to noise. For experimental validation, we consider Teflon sheets and Agarose phantoms of varying thicknesses. The experimental results show that the FRI technique is capable of super-resolving by a factor of three below the theoretical limit.

Group testing performance evaluation for SARS-CoV-2 massive scale screening and testing.

BACKGROUND: The capacity of the current molecular testing convention does not allow high-throughput and community level scans of COVID-19 infections. The diameter in the current paradigm of shallow tracing is unlikely to reach the silent clusters that might be as important as the symptomatic cases in the spread of the disease. Group testing is a feasible and promising approach when the resources are scarce and when a relatively low prevalence regime is observed on the population. METHODS: We employed group testing with a sparse random pooling scheme and conventional group test decoding algorithms both for exact and inexact recovery. RESULTS: Our simulations showed that significant reduction in per case test numbers (or expansion in total test numbers preserving the number of actual tests conducted) for very sparse prevalence regimes is available. Currently proposed COVID-19 group testing schemes offer a gain up to 15X-20X scale-up. There is a good probability that the required scale up to achieve massive scale testing might be greater in certain scenarios. We investigated if further improvement is available, especially in sparse prevalence occurrence where outbreaks are needed to be avoided by population scans. CONCLUSION: Our simulations show that sparse random pooling can provide improved efficiency gains compared to conventional group testing or Reed-Solomon error correcting codes. Therefore, we propose that special designs for different scenarios could be available and it is possible to scale up testing capabilities significantly.

Compressive Sensing Spectroscopy Using a Residual Convolutional Neural Network.

Compressive sensing (CS) spectroscopy is well known for developing a compact spectrometer which consists of two parts: compressively measuring an input spectrum and recovering the spectrum using reconstruction techniques. Our goal here is to propose a novel residual convolutional neural network (ResCNN) for reconstructing the spectrum from the compressed measurements. The proposed ResCNN comprises learnable layers and a residual connection between the input and the output of these learnable layers. The ResCNN is trained using both synthetic and measured spectral datasets. The results demonstrate that ResCNN shows better spectral recovery performance in terms of average root mean squared errors (RMSEs) and peak signal to noise ratios (PSNRs) than existing approaches such as the sparse recovery methods and the spectral recovery using CNN. Unlike sparse recovery methods, ResCNN does not require a priori knowledge of a sparsifying basis nor prior information on the spectral features of the dataset. Moreover, ResCNN produces stable reconstructions under noisy conditions. Finally, ResCNN is converged faster than CNN.

Sparsity-Aware Noise Subspace Fitting for DOA Estimation.

We propose a sparsity-aware noise subspace fitting (SANSF) algorithm for direction-of-arrival (DOA) estimation using an array of sensors. The proposed SANSF algorithm is developed from the optimally weighted noise subspace fitting criterion. Our formulation leads to a convex linearly constrained quadratic programming (LCQP) problem that enjoys global convergence without the need of accurate initialization and can be easily solved by existing LCQP solvers. Combining the weighted quadratic objective function, the ℓ 1 norm, and the non-negative constraints, the proposed SANSF algorithm can enhance the sparsity of the solution. Numerical results based on simulations, using real measured ultrasonic, and radar data, show that, compared to existing sparsity-aware methods, the proposed SANSF can provide enhanced resolution with a lower computational burden.