Signal Recovery Algorithm Research Articles

Enhancing single-pixel imaging reconstruction using hybrid transformer network with adaptive feature refinement

Single-pixel imaging (SPI) is a novel imaging technique that applies to acquiring spatial information under low light, high absorption, and backscattering conditions. The existing reconstruction techniques, such as pattern analysis and signal-recovery algorithms, are inefficient due to their iterative behaviors and substantial computational requirements. In this paper, we address these issues by proposing a hybrid convolutional-transformer network for efficient and accurate SPI reconstruction. The proposed model has a universal pre-reconstruction layer that can reconstruct the single-pixel measurements collected using any SPI method. Moreover, we utilize the hierarchical encoder-decoder network in U-Net architectures and employ the proposed CONText AggregatIon NEtwoRk (Container) as the adaptive feature refinement module to adaptively leverage the significance of globally and locally enhanced features in SPI reconstruction. As such, we can improve the conventional SPI methods in terms of reconstruction speed and accuracy. Extensive experiments show that the proposed model achieve a significant performance improvement as compared to traditional SPI methods digitally and experimentally while increasing the reconstruction frame rates by threefold. Moreover, the proposed model also outperforms state-of-the-art deep learning models in performing single-pixel imaging reconstruction.

Iterative gradient denoising algorithm for signal recovery using analysis-based implicit prior

To recover a signal from its linear measurements, the present paper considers the relaxed analysis LASSO (RALASSO) optimization model. An algorithm involving a gradient descent operator and a soft shrinkage operator in each iteration is proposed to solve RALASSO, termed iterative gradient descent shrinkage (IGDS). Further, being not restricted to the sparsity regime, we replace the ℓ1-norm regularizer in RALASSO by a general regularization function, and derive an algorithm framework for solving this more general problem. The framework employs a denoiser as a black-box to replace the soft shrinkage operator, thus we call it iterative gradient descent denoising (IGDD). IGDS can be viewed as a special instance of IGDD. The recovery performance of IGDD armed with a good denoiser will be better than that of IGDS. Extensive experimental results based on several numerical examples and image restoration tasks show that our algorithms have advantages over some analysis-model-based algorithms and denoiser-based ones, in terms of recovery capability or run-time.

A Robust Proportionate Graph Recursive Least Squares Algorithm for Adaptive Graph Signal Recovery

A Robust Proportionate Graph Recursive Least Squares Algorithm for Adaptive Graph Signal Recovery

Binary Least Squares: An Algorithm for Binary Sparse Signal Recovery

Binary Least Squares: An Algorithm for Binary Sparse Signal Recovery

Sufficient condition based on nearly optimal order RIC for IHT algorithm

Iterative hard thresholding (IHT) is one class of sparse signal recovery algorithms widely used in compressed sensing. The well-known restricted isometry constant (RIC) is one of the most popular frameworks used to ensure the convergence of recovery algorithms. In previous literature, sufficient conditions to guarantee the recovery performance of the IHT algorithm have usually been established based on RICs with orders 3 s and 2 s , while no such condition in terms of RIC with order less than 2 s has been reported yet. In this study, based on the theoretical optimal step-length, we develop the RIC condition γ < ( 5 − 1 ) / 8 ≈ 0.1545 for successful recovery via the IHT algorithm. Here, γ = δ s if s is an even number, otherwise γ = δ s + 1 . To the best of our knowledge, this is the first result based on RIC with nearly optimal order for the IHT algorithm.

Hard threshold acceleration algorithms for sparse signal recovery

Hard threshold acceleration algorithms for sparse signal recovery

The ADMM algorithm for audio signal recovery and performance modification with the dual Douglas-Rachford dynamical system

&lt;abstract&gt;&lt;p&gt;Practitioners employ operator splitting methods—such as alternating direction method of multipliers (ADMM) and its "dual" Douglas-Rachford method (DR)—to solve many kinds of optimization problems. We provide a gentle introduction to these algorithms, and illustrations of their duality-like relationship in the context of solving basis pursuit problems for audio signal recovery. Recently, researchers have used the dynamical systems associated with the iterates of splitting methods to motivate the development of schemes to improve performance. These developments include a class of methods that act by iteratively minimizing surrogates for a Lyapunov function for the dynamical system. An exemplar of this class is currently state-of-the-art for the feasibility problem of finding wavelets with special structure. Early experimental evidence has also suggested that, when implemented in a primal-dual (ADMM and DR) framework, this exemplar may provide improved performance for basis pursuit problems. We provide a reasonable way to compute the updates for this exemplar, and we study the application of this method to the aforementioned basis pursuit audio problems. We provide experimental results and visualizations of the dynamical system for the dual DR sequence. We observe that for highly structured problems with real data, the algorithmic behavior is noticeably different than for randomly generated problems.&lt;/p&gt;&lt;/abstract&gt;

Federated Consensus-Based Algorithm for Stable Recovery of Sparse Signals

Federated Consensus-Based Algorithm for Stable Recovery of Sparse Signals

Low-Complexity Blind Parameter Estimation in Wireless Systems with Noisy Sparse Signals

Baseband processing algorithms often require knowledge of the noise power, signal power, or signal-to-noise ratio (SNR). In practice, these parameters are typically unknown and must be estimated. Furthermore, the mean-square error (MSE) is a desirable metric to be minimized in a variety of estimation and signal recovery algorithms. However, the MSE cannot directly be used as it depends on the true signal that is generally unknown to the estimator. In this paper, we propose novel blind estimators for the average noise power, average receive signal power, SNR, and MSE. The proposed estimators can be computed at low complexity and solely rely on the large-dimensional and sparse nature of the processed data. Our estimators can be used (i) to quickly track some of the key system parameters while avoiding additional pilot overhead, (ii) to design low-complexity nonparametric algorithms that require such quantities, and (iii) to accelerate more sophisticated estimation or recovery algorithms. We conduct a theoretical analysis of the proposed estimators for a Bernoulli complex Gaussian (BCG) prior, and we demonstrate their efficacy via synthetic experiments. We also provide three application examples that deviate from the BCG prior in millimeter-wave multi-antenna and cell-free wireless systems for which we develop nonparametric denoising algorithms that improve channel-estimation accuracy with a performance comparable to denoisers that assume perfect knowledge of the system parameters.

A ReLU-based hard-thresholding algorithm for non-negative sparse signal recovery

In numerous applications, such as DNA microarrays, face recognition, and spectral unmixing, we need to acquire a non-negative K-sparse signal x from an underdetermined linear model y=Ax+v, where A is a sensing matrix and v is a noise vector. In this paper, we first propose a ReLU-based hard-thresholding algorithm (RHT) to recover x by taking advantage of its non-negative sparsity. Two sufficient conditions for stable recovery with RHT are then developed, which are respectively based on the restricted isometry property (RIP) and mutual coherence of the sensing matrix A. As far as we know, these two sufficient conditions are the best for hard-thresholding-type algorithms. Numerical experiments show that RHT has better overall recovery performance in the recovery non-negative sparse signals than the non-negative least squares (NNLS) algorithm, some hard-thresholding-type algorithms including the iterative hard-thresholding (IHT) algorithm, hard-thresholding pursuit (HTP), Newton-step-based iterative hard-thresholding algorithm (NSIHT), and Newton-step-based hard-thresholding pursuit (NSHTP), several non-negative sparse recovery approaches including non-negative orthogonal matching pursuit (NNOMP), fast NNOMP (FNNOMP), non-negative orthogonal least squares (NNOLS), and non-negative regularization (NNREG) method. In terms of efficiency, RHT has a similar performance to IHT, and is much more efficient than other tested algorithms.

A truncated approximate difference algorithm for sparse signal recovery

In this paper, we study the regularization lp-norm minimization problem to recover the sparse signals. We first prove that every global optimal solution to the regularization lp-norm minimization problem also solves the l0-norm minimization problem if the certain conditions are satisfied, and then generate a truncated approximated difference algorithm to recover the sparse signals. At last, we provide some numerical simulations to test the performance of the truncated approximated difference algorithm, and the numerical results show that the proposed algorithm performs effectively in recovering the sparse signals compared with some state-of-art methods.

CORDIC KSVD based Online Dictionary Learning for Speech Enhancement on ASIC/FPGA Platforms

Background: The enhancement of real-world speech signals is still a challenging task to eliminate noises, namely reverberation, background, street, and babble noises. Recently learned methods like dictionary learning have become increasingly popular and showed promising results in speech enhancement. The K-means Singular Value Decomposition (KSVD) algorithm is best suited for dictionary learning among many sparse representation algorithms. Moreover, the orthogonal matching pursuit (OMP) based algorithm used for signal recovery is given. The orthogonal matching pursuit (OMP) based algorithm for signal recovery gives the best enhancement results. On the other hand, FPGAs and ASICs are widely used to accelerate speech enhancement applications. FPGAs are commonly used in healthcare and consumer applications, where speech enhancement plays a crucial role. Methods: This paper proposes a modified KSVD algorithm that can easily be implemented onto hardware platforms like FPGAs and ASICS. Instead of using the double-precision arithmetic for the singular value decomposition part of the KSVD algorithm, we proposed to use CORDIC (Coordinate Rotation Digital Computer) based QR decomposition and QR-based singular value decomposition in dictionary learning. Results: The proposed KSVD algorithm is optimal with the CORDIC algorithm that can reduce by 7-8 times the processing time. Conclusion: The finding indicates that the proposed work is best suited to FPGA or ASIC platforms.

Graph Sparsification by Universal Greedy Algorithms

Graph sparsification is to approximate an arbitrary graph by a sparse graph and is useful in many applications, such as simplification of social networks, least squares problems, numerical solution of symmetric positive definite linear systems and etc. In this paper, inspired by the well-known sparse signal recovery algorithm called orthogonal matching pursuit (OMP), we introduce a deterministic, greedy edge selection algorithm called universal greedy approach (UGA) for graph sparsification. For a general spectral sparsification problem, e.g., positive subset selection problem from a set of $m$ vectors from $\mathbb{R}^n$, we propose a nonnegative UGA algorithm which needs $O(mn^2+ n^3/\epsilon^2)$ time to find a $\frac{1+\epsilon/\beta}{1-\epsilon/\beta}$-spectral sparsifier with positive coefficients with sparsity $\le\lceil\frac{n}{\epsilon^2}\rceil$, where $\beta$ is the ratio between the smallest length and largest length of the vectors. The convergence of the nonnegative UGA algorithm will be established. For the graph sparsification problem, another UGA algorithm will be proposed which can output a $\frac{1+O(\epsilon)}{1-O(\epsilon)}$-spectral sparsifier with $\lceil\frac{n}{\epsilon^2}\rceil$ edges in $O(m+n^2/\epsilon^2)$ time from a graph with $m$ edges and $n$ vertices under some mild assumptions. This is a linear time algorithm in terms of the number of edges that the community of graph sparsification is looking for. The best result in the literature to the knowledge of the authors is the existence of a deterministic algorithm which is almost linear, i.e. $O(m^{1+o(1)})$ for some $o(1)=O(\frac{(\log\log(m))^{2/3}}{\log^{1/3}(m)})$. Finally, extensive experimental results, including applications to graph clustering and least squares regression, show the effectiveness of proposed approaches.

An Efficient Compressive Sensing Event-Detection Scheme for Internet of Things System Based on Sparse-Graph Codes

This work studied the event-detection problem in an Internet of Things (IoT) system, where a group of sensor nodes are placed in the region of interest to capture sparse active event sources. Using compressive sensing (CS), the event-detection problem is modeled as recovering the high-dimensional integer-valued sparse signal from incomplete linear measurements. We show that the sensing process in IoT system produces an equivalent integer CS using sparse graph codes at the sink node, for which one can devise a simple deterministic construction of a sparse measurement matrix and an efficient integer-valued signal recovery algorithm. We validated the determined measurement matrix, uniquely determined the signal coefficients, and performed an asymptotic analysis to examine the performance of the proposed approach, namely event detection with integer sum peeling (ISP), with the density evolution method. Simulation results show that the proposed ISP approach achieves a significantly higher performance compared to existing literature at various simulation scenario and match that of the theoretical results.

Heavy-ball-based hard thresholding algorithms for sparse signal recovery

The hard thresholding technique plays a vital role in the development of algorithms for sparse signal recovery. By merging this technique and heavy-ball acceleration method which is a multi-step extension of the traditional gradient descent method, we propose the so-called heavy-ball-based hard thresholding (HBHT) and heavy-ball-based hard thresholding pursuit (HBHTP) algorithms for signal recovery. It turns out that the HBHT and HBHTP can successfully recover a k-sparse signal if the restricted isometry constant of the measurement matrix satisfies δ3k<0.618 and δ3k<0.577, respectively. The guaranteed success of HBHT and HBHTP is also shown under the conditions δ2k<0.356 and δ2k<0.377, respectively. Moreover, the finite convergence of HBHTP and stability of the two algorithms are also established in this paper. Simulations on random problem instances are performed to compare the performance of the proposed algorithms and several existing ones. Empirical results indicate that the HBHTP performs very comparably to a few existing algorithms and it takes less average time to achieve the signal recovery than these existing methods.

Performance analysis of compressive sensing and reconstruction by LASSO and OMP for audio signal processing applications

Audio signal processing is used in acoustic IoT sensor nodes which have limitations in data storage, computation speed, hardware size and power. In most audio signal processing systems, the recovered data constitutes far less fraction of the sampled data providing scope for compressive sensing (CS) as an efficient way for sampling and signal recovery. Compressive sensing is a signal processing technique in which a sparse approximated signal is reconstructed at the receiving node by a signal recovery algorithm, using fewer samples compared to traditional sampling methods. It has two main stages: sparse approximation to convert the signal into a sparse domain and reconstruction through sparse signal recovery algorithms. Recovery algorithms involve complex matrix multiplication and linear equations in sampling and reconstruction, increasing the computational complexity and leading to highly resourceful hardware implementations. This work reconstructs the sparse audio signal using LASSO and orthogonal matching pursuit (OMP) algorithm. OMP is an iterative greedy algorithm involving least square method that takes a compressed signal as input and recovers it from the sparse approximation, while LASSO is L1 norm based with a controlled L2 penalty. The paper reviews the reconstruction and study of sparsity and error obtained for reconstructing an audio signal by OMP and LASSO.

Target parameter estimation for OTFS radar using sparse signal processing

In this paper, we consider a monostatic radar receiver for a joint communication and radar (JCR) system that transmits orthogonal time frequency space (OTFS) frames for target detection and parameter estimation. The circular prolate pulse shape (CPPS) is employed over the OTFS signal as it has lower out-of-band (OoB) power radiation in comparison with the rectangular pulse shaped (RPS) OTFS. The PAPR of CPPS OTFS signal shows lowest value for larger frame duration and hence the signal can be considered to be a good candidate for JCR system. In the Delay-Doppler (DD) domain, the radar channel is sparse and therefore, we model the target detection problem as a sparse recovery problem to generate target profiles with higher peak-to-sidelobe ratio (PSLR). The target detection is carried out in the DD domain, the time–frequency (TF) domain, and in the time domain (TD). Sparse signal recovery algorithms like the orthogonal matching pursuit (OMP) algorithm, the subspace pursuit (SP) algorithm, and the sparse Bayesian learning (SBL) based algorithm are used in target parameter estimation. The performance of these algorithms are compared in terms of their computational complexity, the root mean squared error (RMSE) in the estimates of range and velocity and PSLR value in the target profiles. Simulation results validate that the proposed CPPS OTFS based radar system could detect the targets accurately in all the three domains and produce target profiles with almost zero side lobes.

Proportionate Adaptive Graph Signal Recovery

This paper generalizes the proportionate-type adaptive algorithm to the graph signal processing and proposes two proportionate-type adaptive graph signal recovery algorithms. The gain matrix of the proportionate algorithm leads to faster convergence than least mean squares (LMS) algorithm. In this paper, the gain matrix is obtained in a closed-form by minimizing the gradient of the mean-square deviation (GMSD). The first algorithm is the proportionate-type graph LMS (Pt-GLMS) algorithm which simply uses a gain matrix in the recursion process of the LMS algorithm and accelerates the convergence of the Pt-GLMS algorithm compared to the LMS algorithm. The second algorithm is the proportionate-type graph extended LMS (Pt-GELMS) algorithm, which uses the previous signal vectors alongside the signal of the current iteration. The Pt-GELMS algorithm utilizes two gain matrices to control the effect of the signal of the previous iterations. The stability analyses of the algorithms are also provided. Simulation results demonstrate the efficacy of the two proposed proportionate-type LMS algorithms.

Improved Sufficient Conditions Based on RIC of Order 2s for IHT and HTP Algorithms

Reconstructing an s-sparse signal x from an un- derdetermined noisy linear model arises in many applications. The iterative hard thresholding (IHT) and hard thresholding pursuit (HTP) algorithms are two popular sparse signal recovery algorithms. Since their recovery performances can be theoreti- cally characterized by their sufficient conditions of stable sparse signal recovery, it is essential to establish less restrictive sufficient conditions. This work develops δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2s</sub> -based sufficient conditions for stable recovery with IHT and HTP. The two new sufficient conditions are significantly less restrictive than the state-of-the- art ones for IHT and HTP.

Improved RIP-based bounds for guaranteed performance of two compressed sensing algorithms

Iterative hard thresholding (IHT) and compressive sampling matching pursuit (CoSaMP) are two mainstream compressed sensing algorithms using the hard thresholding operator. The guaranteed performance of the two algorithms for signal recovery was mainly analyzed in terms of the restricted isometry property (RIP) of sensing matrices. At present, the best known bound using the RIP of order 3k for guaranteed performance of IHT (with the unit stepsize) is \({\delta _{3k}} < 1/\sqrt 3 \approx 0.5774\), and the bound for CoSaMP using the RIP of order 4k is δ4k < 0.4782. A fundamental question in this area is whether such theoretical results can be further improved. The purpose of this paper is to affirmatively answer this question and to rigorously show that the above-mentioned RIP bound for guaranteed performance of IHT can be significantly improved to \({\delta _{3k}} < \left( {\sqrt 5 - 1} \right)/2 \approx 0.618\), and the bound for CoSaMP can be improved to δ4k < 0.5102.