Sparse Reconstruction Problem Research Articles

Positive Competitive Networks for Sparse Reconstruction.

We propose and analyze a continuous-time firing-rate neural network, the positive firing-rate competitive network (PFCN), to tackle sparse reconstruction problems with nonnegativity constraints. These problems, which involve approximating a given input stimulus from a dictionary using a set of sparse (active) neurons, play a key role in a wide range of domains, including, for example, neuroscience, signal processing, and machine learning. First, by leveraging the theory of proximal operators, we relate the equilibria of a family of continuous-time firing-rate neural networks to the optimal solutions of sparse reconstruction problems. Then we prove that the PFCN is a positive system and give rigorous conditions for the convergence to the equilibrium. Specifically, we show that the convergence depends only on a property of the dictionary and is linear-exponential in the sense that initially, the convergence rate is at worst linear and then, after a transient, becomes exponential. We also prove a number of technical results to assess the contractivity properties of the neural dynamics of interest. Our analysis leverages contraction theory to characterize the behavior of a family of firing-rate competitive networks for sparse reconstruction with and without nonnegativity constraints. Finally, we validate the effectiveness of our approach using a numerical example.

Improved Analytic Learned Iterative Shrinkage Thresholding Algorithm and Its Application to Tomographic Synthetic Aperture Radar Building Object Height Inversion

Tomographic Synthetic Aperture Radar (TomoSAR) building object height inversion is a sparse reconstruction problem that utilizes the data obtained from several spacecraft passes to invert the scatterer position in the height direction. In practical applications, the number of passes is often small, and the observation data are also small due to the objective conditions, so this study focuses on the inversion under the restricted observation data conditions. The Analytic Learned Iterative Shrinkage Thresholding Algorithm (ALISTA) is a kind of deep unfolding network algorithm, which is a combination of the Iterative Shrinkage Thresholding Algorithm (ISTA) and deep learning technology, and it has the advantages of both. The ALISTA is one of the representative algorithms for TomoSAR building object height inversion. However, the structure of the ALISTA algorithm is simple, which has neither the excellent connection structure of a deep learning network nor the acceleration format combined with the ISTA algorithm. Therefore, this study proposes two directions of improvement for the ALISTA algorithm: firstly, an improvement in the inter-layer connection of the network by introducing a connection similar to residual networks obtains the Extragradient Analytic Learned Iterative Shrinkage Thresholding Algorithm (EALISTA) and further proves that the EALISTA achieves linear convergence; secondly, there is an improvement in the iterative format of the intra-layer iteration of the network by introducing the Nesterov momentum acceleration, which obtains the Fast Analytic Learned Iterative Shrinkage Thresholding Algorithm (FALISTA). We first performed inversion experiments on simulated data, which verified the effectiveness of the two proposed algorithms. Then, we conducted TomoSAR building object height inversion experiments on limited measured data and used the deviation metric P to measure the robustness of the algorithms to invert under restricted observation data. The results show that both proposed algorithms have better robustness, which verifies the superior performance of the two algorithms. In addition, we further analyze how to choose the most suitable algorithms for inversion in engineering practice applications based on the results of the experiments on measured data.

An efficient projection algorithm for solving convex constrained monotone operator equations and sparse signal reconstruction problems

An efficient projection algorithm for solving convex constrained monotone operator equations and sparse signal reconstruction problems

A co-evolutionary algorithm based on sparsity clustering for sparse large-scale multi-objective optimization

Sparse large-scale multi-objective optimization problems (LSMOPs), which are characterized by high dimensional search space and sparse Pareto optimal solutions, have a widespread existence in academic research and practical applications. While the high dimensional decision space poses challenges to multi-objective evolutionary algorithms (MOEAs), the difficulty of solving sparse LSMOPs can be alleviated by utilizing the prior knowledge that the optimal solutions are sparse. In this paper, a co-evolutionary algorithm based on sparsity clustering, namely SCEA, is proposed, where the prior knowledge of sparse optimal solutions is utilized explicitly. At each generation, SCEA first calculates the current optimal sparsity by sparsity clustering. Then, SCEA divides the population into a winner subpopulation and two loser subpopulations. While the winner subpopulation reproduces offspring solutions by conventional genetic operators, the loser subpopulations generate offspring solutions along two competitive directions under the guidance of current optimal sparsity and variable importance. In the experiments, four state-of-the-art MOEAs are selected as the comparative algorithms. Experimental results show that the proposed algorithm is superior to the four competitors on both benchmark problems and practical applications, which include the sparse signal reconstruction problem, the community detection problem, and the instance selection problem.

Noisy One-bit Compressed Sensing with Side-Information

We consider the problem of sparse signal reconstruction from noisy one-bit compressed measurements when the receiver has access to side-information (SI). We assume that compressed measurements are corrupted by additive white Gaussian noise before quantization and sign-flip error after quantization. A generalized approximate message passing-based method for signal reconstruction from noisy one-bit compressed measurements is proposed which is then extended for the case where the receiver has access to a signal that aids signal reconstruction, i.e., side-information. Two different scenarios of SI are considered-a) SI consisting of support information only, and b) SI consisting of support and amplitude information. SI is either a noisy version of the signal or a noisy estimate of the support of the signal. We develop reconstruction algorithms from one-bit measurements using noisy SI available at the receiver. Laplacian distribution and Bernoulli distribution are used to model the two types of noises which when applied to the signal and the support, yield the SI for the above two cases, respectively. The Expectation-Maximization algorithm is used to estimate the noise parameter using noisy one-bit compressed measurements and the SI. We show that one-bit compressed measurement-based signal reconstruction is quite sensitive to noise, and the reconstruction performance can be significantly improved by exploiting available side-information at the receiver.

Two Novel Noise-Suppression Projection Neural Networks With Fixed-Time Convergence for Variational Inequalities and Applications.

This article proposes two novel projection neural networks (PNNs) with fixed-time ( FIXt ) convergence to deal with variational inequality problems (VIPs). The remarkable features of the proposed PNNs are FIXt convergence and more accurate upper bounds for arbitrary initial conditions. The robustness of the proposed PNNs under bounded noises is further studied. In addition, the proposed PNNs are applied to deal with absolute value equations (AVEs), noncooperative games, and sparse signal reconstruction problems (SSRPs). The upper bounds of the settling time for the proposed PNNs are tighter than the bounds in the existing neural networks. The effectiveness and advantages of the proposed PNNs are confirmed by numerical examples.

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.

Damage imaging using multipath-scattered Lamb waves under a sparse reconstruction framework

This paper presents a damage sparse imaging method using multipath-scattered Lamb waves. It leverages a large number of echoes and reverberations in the recorded signal that may be usually ignored in conventional methods. First, reflections of Lamb waves at free edges are viewed as waves transmitted from a virtual transducer which is located at the mirror point of the actual one. On this basis, an optimized transducers-layout strategy is proposed based on the multipath propagation model of the Lamb wave. Benefiting from that, the direct damage-scattered wave and several waves scattered by both the damage and edges could be separately identified in the time domain, and further, each wave could be matched with a sensing path (either actual or virtual) in the expanded sensor network. Subsequently, a dictionary is constructed from the Lamb wave propagation and scattering model. By solving the sparse reconstruction problem, the pixel value of each point in the region of interest is obtained, and the whole area can be finally visualized. The proposed method is validated using experiments conducted on an aluminum plate with simulated damages. Results show that the damages can be correctly detected and accurately localized with only a single transmitter–receiver pair.

Second Order Rectified Parallel Factor Model Based Cascaded Channel Estimation in IRS-Assisted SWIPT System

This paper investigates cascaded channel estimation in intelligent reflecting surface (IRS)-assisted simultaneous wireless information and power transfer (SWIPT) system. Multiple-input multiple-output (MIMO) transceiver structures combined with transmitter active beamforming and IRS passive beamforming are studied. Cascaded channel estimation is transformed into sparse signal reconstruction problem, and compressed sensing (CS) is applied to solve this problem. Only a small amount of training overhead provides reliable channel estimation gains as well as better beamforming gains. Second order rectified parallel factor (PARAFA) model is implemented in IRS-assisted SWIPT system, which is described by tensor decomposition method. The received signal can be represented by PARAFA model with algebraic structure and IRS phase shift. Two cascaded channel estimation approaches, namely, bilinear alternating least squares (BALS) and least squares Khatri-Rao factorization (LSKRF), are proposed respectively. Simulation results show that, compared with orthogonal matching pursuit (OMP) approach, the proposed BALS cascaded channel estimation approach obtains better normalized mean square error (NMSE) and convergence performance with the least parameter constraints.

Compressive frequency-difference direction-of-arrival estimation

Direction-of-arrival estimation is difficult for signals spatially undersampled by more than half the wavelength. Frequency-difference beamforming [Abadi, Song, and Dowling (2012). J. Acoust. Soc. Am. 132, 3018–3029] offers an alternative approach to avoid such spatial aliasing by using multifrequency signals and processing them at a lower frequency, the difference-frequency. As with the conventional beamforming method, lowering the processing frequency sacrifices spatial resolution due to a beam broadening. Thus, unconventional beamforming is detrimental to the ability to distinguish between closely spaced targets. To overcome spatial resolution deterioration, we propose a simple yet effective method by formulating the frequency-difference beamforming as a sparse signal reconstruction problem. Similar to compressive beamforming, the improvement (compressive frequency-difference beamforming) promotes sparse nonzero elements to obtain a sharp estimate of the spatial direction-of-arrival spectrum. Analysis of the resolution limit demonstrates that the proposed method outperforms the conventional frequency-difference beamforming in terms of separation if the signal-to-noise ratio exceeds 4 dB. Ocean data from the FAF06 experiment support the validity.

A microstructure estimation Transformer inspired by sparse representation for diffusion MRI

Diffusion magnetic resonance imaging (dMRI) is an important tool in characterizing tissue microstructure based on biophysical models, which are typically multi-compartmental models with mathematically complex and highly non-linear forms. Resolving microstructures from these models with conventional optimization techniques is prone to estimation errors and requires dense sampling in the q-space with a long scan time. Deep learning based approaches have been proposed to overcome these limitations. Motivated by the superior performance of the Transformer in feature extraction than the convolutional structure, in this work, we present a learning-based framework based on Transformer, namely, a Microstructure Estimation Transformer with Sparse Coding (METSC) for dMRI-based microstructural parameter estimation. To take advantage of the Transformer while addressing its limitation in large training data requirement, we explicitly introduce an inductive bias-model bias into the Transformer using a sparse coding technique to facilitate the training process. Thus, the METSC is composed with three stages, an embedding stage, a sparse representation stage, and a mapping stage. The embedding stage is a Transformer-based structure that encodes the signal in a high-level space to ensure the core voxel of a patch is represented effectively. In the sparse representation stage, a dictionary is constructed by solving a sparse reconstruction problem that unfolds the Iterative Hard Thresholding (IHT) process. The mapping stage is essentially a decoder that computes the microstructural parameters from the output of the second stage, based on the weighted sum of normalized dictionary coefficients where the weights are also learned. We tested our framework on two dMRI models with downsampled q-space data, including the intravoxel incoherent motion (IVIM) model and the neurite orientation dispersion and density imaging (NODDI) model. The proposed method achieved up to 11.25 folds of acceleration while retaining high fitting accuracy for NODDI fitting, reducing the mean squared error (MSE) up to 70% compared with the previous q-space learning approach. METSC outperformed the other state-of-the-art learning-based methods, including the model-free and model-based methods. The network also showed robustness against noise and generalizability across different datasets. The superior performance of METSC indicates its potential to improve dMRI acquisition and model fitting in clinical applications.

Second order self-adaptive dynamical system for sparse signal reconstruction and applications to image recovery

In this article, we consider sparse signal reconstruction problems by an alternative second order self-adaptive dynamical system. By split feasibility problem of sparse signal reconstruction, we introduce a new second order self-adaptive dynamical system. Then, we prove that the proposed system has a unique solution under reasonable conditions. Furthermore, it is shown that the corresponding orbit of the system always converges. Finally, all kinds of numerical results on synthetic data and data from practical problems verify the efficiency of the proposed approach.

Target location and velocity estimation with the multistatic MU‐MIMO‐OFDM modulation signal

AbstractIn passive radar and joint communication and radar sensing (JCRS), target sensing with the multiuser multiple input multiple output orthogonal frequency division multiplexing (MU‐MIMO‐OFDM) modulation signal is gaining increasing interest. Multiple transmit nodes emitting the MU‐MIMO‐OFDM modulation signals at the same carrier frequency and one receiver collecting the target‐reflected signals for target location and velocity estimation are considered. This is a typical scenario when using the fifth‐generation (5G) communication network signal for target sensing. In this scenario, the echo signals corresponding to different transmit nodes are not resolved in the receiver, and the modulated data symbols cannot be removed from the received signals. Most traditional parameter estimation methods in passive radar and JCRS may not be suitable here. A location and velocity estimation method with the received echo signals is proposed. Specifically, the location parameters are extracted directly from the received echo signals. The location estimation is cast into a block sparse vector reconstruction problem. The variational Bayesian sparsity learning (VBSL) method is exploited for the reconstruction of the block sparse vector. Accelerated VBSL methods are developed for improving the computational efficiency. Simulations verify the effectiveness of the proposed methods.

Improved Reconstruction Algorithm of Wireless Sensor Network Based on BFGS Quasi-Newton Method

Aiming at the problems of low reconstruction rate and poor reconstruction precision when reconstructing sparse signals in wireless sensor networks, a sparse signal reconstruction algorithm based on the Limit-Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) quasi-Newton method is proposed. The L-BFGS quasi-Newton method uses a two-loop recursion algorithm to find the descent direction dk directly by calculating the step difference between m adjacent iteration points, and a matrix Hk approximating the inverse of the Hessian matrix is constructed. It solves the disadvantages of BFGS requiring the calculation and storage of Hk, reduces the algorithm complexity, and improves the reconstruction rate. Finally, the experimental results show that the L-BFGS quasi-Newton method has good experimental results for solving the problem of sparse signal reconstruction in wireless sensor networks.

Multi-regularization sparse reconstruction based on multifactorial multiobjective optimization

In recent sparse reconstruction, the sparsity and reconstruction error can be considered as two objectives and tackled by multiobjective optimization methods. Since the sparse reconstruction problem can be modeled in multiple regularization forms, it can be addressed in a multifactorial multiobjective optimization paradigm by the evolutionary multitasking approach to transfer useful information across multiple regularization forms to help solve the problem. In this paper, a multi-regularization based on multifactorial multiobjective optimization is proposed to solve the sparse reconstruction problem. First, the sparse reconstruction problem is constructed as a multi-regularization model. Then, this model is optimized by a multifactorial multiobjective optimization method. In the evolutionary process, considering the priority of different regularization in the multi-regularization model, a preference-based selection method is designed. In addition, to accommodate the sparsity characteristic of the sparse reconstruction problem, a sparsity-oriented crossover operator is performed. Finally, an iterative-thresholding-based local search is incorporated into the algorithm to improve the convergence performance. Experiments on multiple datasets and image reconstruction tasks demonstrate the effectiveness and practicality of the proposed algorithm.

IMRecoNet: Learn to Detect in Index Modulation Aided MIMO Systems With Complex Valued Neural Networks

Index modulation (IM) reduces the power consumption and hardware cost of the multiple-input multiple-output (MIMO) system by activating part of the antennas for data transmission. However, IM significantly increases the complexity of the receiver and needs accurate channel estimation to guarantee its performance. To tackle these challenges, in this paper, we design a deep learning (DL) based detector for the IM aided MIMO (IM-MIMO) systems. We first formulate the detection process as a sparse reconstruction problem by utilizing the inherent attributes of IM. Then, based on greedy strategy, we design a DL based detector, called IMRecoNet, to realize this sparse reconstruction process. Different from the general neural networks, we introduce complex value operations to adapt the complex signals in communication systems. To the best of our knowledge, this is the first attempt that introduce complex valued neural network to the design of detector for the IM-MIMO systems. Finally, to verify the adaptability and robustness of the proposed detector, simulations are carried out with consideration of inaccurate channel state information (CSI) and correlated MIMO channels. The simulation results demonstrate that the proposed detector outperforms existing algorithms in terms of antenna recognition accuracy and bit error rate under various scenarios.

Sparse-view CT reconstruction method for in-situ non-destructive testing of reinforced concrete

ABSTRACT X-ray CT is an important in-situ non-destructive testing method that plays an important role in both production and materials research. In-situ CT of concrete can acquire images of concrete slices in the state of holding force loading, which is meaningful for the study of concrete crack development characteristics. However, existing X-ray CT equipment either cannot penetrate large reinforced concrete due to energy limitations or does not address the extremely sparse angular reconstruction problem associated with in-situ testing. In this paper, a sinogram Transformer method based on a priori projection data is proposed to solve this extremely sparse data complementation problem on a large-scale electron accelerator X-ray in-situ CT system. The simulated concrete sparse-view projection data and the full projection data are used as the input and label of the proposed method in order to experiment the method. The results demonstrate the feasibility of using a priori projected sine diagrams with ultra-sparse sine diagram residuals to track sine diagram variation, and verify that structures such as cracks and reinforcement, which dominate the deformation residuals of sinograms in concrete sections, can also be successfully recovered using Transformer in the ultra-sparse view projection of views 4–8.

Identifying hidden target nodes for spreading in complex networks

Using measurable data to realize targeted spreading of vital nodes in complex networks is an important issue connecting to various real applications such as commercial advertising, medication selection, and even military attack. However, a significant challenge is that the target nodes are not always known, which hinders the best allocation of initial spreaders to maximize the affected target nodes. To address this issue, this study develops a general framework to map the target node identification problem to the solution of underdetermined equations. Similar to the sparse signal reconstruction problem, it can be solved by the standard compressed sensing algorithm. Our research is completely driven by the limited data fed back after each spread realization. The experimental results show that this decoding method can efficiently achieve a high calculation accuracy both in the artificial networks and the actual networks. Finally, the effects of network structure, infection probability and initial spreader on the accuracy are discussed, aiming to provide theoretical guidance and new enlightenment for practical applications.

A linearly convergent self-adaptive gradient projection algorithm for sparse signal reconstruction in compressive sensing

<abstract><p>For sparse signal reconstruction (SSR) problem in compressive sensing (CS), by the splitting technique, we first transform it into a continuously differentiable convex optimization problem, and then a new self-adaptive gradient projection algorithm is proposed to solve the SSR problem, which has fast solving speed and pinpoint accuracy when the dimension increases. Global convergence of the proposed algorithm is established in detail. Without any assumptions, we establish global $ R- $linear convergence rate of the proposed algorithm, which is a new result for constrained convex (rather than strictly convex) quadratic programming problem. Furthermore, we can also obtain an approximate optimal solution in a finite number of iterations. Some numerical experiments are made on the sparse signal recovery and image restoration to exhibit the efficiency of the proposed algorithm. Compared with the state-of-the-art algorithms in SSR problem, the proposed algorithm is more accurate and efficient.</p></abstract>

A modified spectral gradient projection-based algorithm for large-scale constrained nonlinear equations with applications in compressive sensing

To solve large-scale nonlinear equations with convex constraints efficiently and overcome the shortcomings of other algorithms, such as large storage and high complexity, we develop a descent and derivative-free algorithm based on a classical spectral gradient method, the projection technique and a new monotone line search method. The new algorithm has the following features: (1) There is lower storage and derivative-free information; (2) It is suitable to solve large-scale nonlinear equations; (3) Its direction possesses sufficient descent and trust region properties; (4) The spectral parameter is bounded. The global convergence of the new algorithm is proven under some appropriate assumptions. If the local error bound condition is satisfied, the proposed algorithm is linearly convergent. Preliminary numerical results demonstrate that the new algorithm is effective and robust. Furthermore, we also extend this algorithm to solve the sparse signal reconstruction problem and the blurred image recovery problem in compressed sensing.