Binary Iterative Hard Thresholding Research Articles

Photonic compressive sampling of wideband sparse radio frequency signals with 1-bit quantization.

Photonic compressive sampling (PCS) is an effective method to recover wideband sparse radio frequency (RF) signals. However, the noisy and high-loss photonic link leads to signal-to-noise ratio (SNR) degradation of the RF signal to be tested, which limits the recovery performance of the PCS system. In this paper, a random demodulator-based PCS system with 1-bit quantization is proposed. The system consists of a photonic mixer, a low-pass filter, a 1-bit analog-to-digital converter (ADC), and a digital signal processor (DSP). The 1-bit quantized result is used to recover the spectra of the wideband sparse RF signal with the binary iterative hard thresholding (BIHT) algorithm, which can alleviate the negative impact of the SNR degradation caused by the photonic link. A full theoretical framework of the PCS system with 1-bit quantization is given. Simulation results show that the PCS system with 1-bit quantization can provide better recovery performance than the traditional PCS system under low SNR and stringent bit budget.

1-Bit Radar Imaging Based on Adversarial Samples

Radar imaging with 1-bit data is attractive thanks to its low storage and transmission burden. Existing 1-bit radar imaging methods cannot satisfactorily suppress the artifacts in the imaging result induced by 1-bit quantization error and noise. In this article, we propose a new 1-bit compressive sensing (CS) based algorithm, i.e., the adversarial-sample-based binary iterative hard thresholding (AS-BIHT) algorithm, to improve the 1-bit radar imaging performance. First, we formulate a parametric model for 1-bit radar imaging with a new adjustable quantization level parameter. The parametric 1-bit radar imaging model updates the imaging scene and the quantization level parameter in an iterative fashion based on adversarial samples. Then, we design a mechanism to generate adversarial samples by attacking the 1-bit radar imaging model to resist the quantization consistency condition, such that forcing quantization consistent reconstruction on adversarial samples mitigates the quantization error and noise. The quantization level parameter is then tuned based on the adversarial samples. In this way, the ability of the model to adapt to echo data contaminated by noise and quantization error is enhanced, and the artifacts are well suppressed. Simulation and experimental results on real radar data demonstrate the effectiveness of the proposed AS-BIHT algorithm in 1-bit radar imaging.

Communication-Efficient Federated Learning Based on Compressed Sensing

In this article, we investigate the problem of federated learning (FL) in a communication-constrained environment of the Internet of Things (IoT), where multiple IoT clients train a global model collectively by communicating model updates with a central server instead of sending raw data sets. To ease the communication burden in IoT systems, several approaches have been proposed for the FL tasks, including sparsification methods and data quantization strategies. To overcome the shortcomings of the existing methods, we propose two new FL algorithms based on compressed sensing (CS) referred to as the CS-FL algorithm and the 1-bit CS-FL algorithm, both of which compress the upstream and downstream data while communicating between the clients and the central server. The proposed algorithms improve upon the existing algorithms by letting the clients send analog and 1-bit data, respectively, to the server after compression with a random measurement matrix. Based on that, in CS-FL and 1-bit CS-FL, the clients update the model locally utilizing the result of sparse reconstruction obtained by iterative hard thresholding (IHT) and binary IHT (BIHT), respectively. Experiments conducted on the MNIST and the Fashion-MNIST data sets reveal the superiority of the proposed algorithm over the baseline algorithms, SignSGD with a majority vote, FL based on sparse ternary compression, and FedAvg.

1-Bit direction of arrival estimation via improved complex-valued binary iterative hard thresholding

Aiming to estimate direction-of-arrival (DOA) using 1-bit quantized observation of sensor arrays, an improved complex-valued binary iterative hard thresholding (iCBIHT) algorithm is proposed in this research. In this work, an error function of signal reconstruction is defined. The signals are estimated by gradient descending. A refined hard threshold function and a novel stopping criterion are designed to judge the convergence. A bases-updating strategy is introduced to solve off-grid DOAs, which improves the accuracy of DOA estimation. A backtracking strategy is utilized to refine the estimated signals processed by the hard thresholding function as well as promote convergence. Simulations and analyses show that the proposed algorithm is superior to 1-bit multiple signal classification (MUSIC) and complex-valued binary iterative hard thresholding (CBIHT) with few snapshots and low signal-to-noise ratio (SNR).

One-Bit Radar Imaging Via Adaptive Binary Iterative Hard Thresholding

One-bit radar imaging has received much attention due to the low cost of the analog-to-digital converter (ADC) and the low storage and transmission burden. The one-bit radar imaging results using conventional one-bit compressive sensing (CS) algorithms, such as the binary iterative hard thresholding (BIHT) algorithm, are always contaminated by artifacts, especially under noisy conditions. In this paper, we present an adaptive-BIHT (A-BIHT) algorithm to mitigate artifacts and improve the one-bit radar imaging performance. In the proposed A-BIHT algorithm, we devise a quantization level parameter, and update the quantization level parameter and the imaging result in an iterative fashion by employing a relaxed quantization consistency condition. The relaxed quantization consistency condition is designed to allow some noisy one-bit measurements to be inconsistent. In this way, the proposed algorithm mitigates the effect of noise on consistent reconstruction, and thus, alleviates artifacts and improves the imaging quality. Simulations and experimental results demonstrate that the proposed A-BIHT method can provide superior imaging performance with suppressed artifacts compared with the conventional BIHT method.

Distributed Collaborative Spectrum Sensing Using 1-Bit Compressive Sensing in Cognitive Radio Networks

In cognitive radio (CR) networks, spectrum sensing is an essential task for enabling dynamic spectrum sharing. However, the problem becomes quite challenging in wideband spectrum sensing due to high sampling pressure, limited power and computing resources, and serious channel fading. To overcome these challenges, this paper proposes a distributed collaborative spectrum sensing scheme based on 1-bit compressive sensing (CS). Each secondary user (SU) performs local 1-bit CS and obtains support estimate information from the signal reconstruction. To utilize joint sparsity and achieve spatial diversity, the support estimate information among the network is fused via the average consensus technique based on distributed computation and one-hop communications. Then the fused result on support estimate is used as priori information to guide the next local signal reconstruction, which is implemented via our proposed weighted binary iterative hard thresholding (BIHT) algorithm. The local signal reconstruction and the distributed fusion of support information are alternately carried out until reliable spectrum detection is achieved. Simulations testify the effectiveness of our proposed scheme in distributed CR networks.

One-Bit Compressive Sensing With Projected Subgradient Method Under Sparsity Constraints

One-bit compressive sensing theory shows that the sparse signals can be almost exactly reconstructed from a small number of one-bit quantized linear measurements. This paper presents the convergence analysis of the binary iterative hard thresholding (BIHT) algorithm which is a state-of-the-art recovery algorithm in one-bit compressive sensing. The basic idea of the convergence analysis is to view BIHT as a kind of projected subgradient method under sparsity constrains. To the best of our knowledge, this is the first convergence analysis of BIHT. We first consider a general convex function subject to sparsity constraints and connect it with the non-convex model in one-bit compressive sensing literatures. A projected subgradient method is proposed to solve the general model and some convergence results are established. A stronger convergence theorem for $\alpha $ –strongly convex functions without assumption on differentiable condition is also established. Furthermore, the corresponding stochastic projected subgradient method is provided with convergence guarantee. In our settings, BIHT is a special case of the projected subgradient method. Therefore, the convergence analysis can be applied to BIHT naturally. Then, we apply the projected subgradient method to some related non-convex optimization models arising in compressive sensing with $\ell _{1}$ -constraint, sparse support vector machines, and rectifier linear units regression. Finally, some numerical examples are presented to show the validity of our convergence analysis. The numerical experiments also show that the proposed projected subgradient method is very simple to implement, robust to sparse noise, and effective for sparse recovery problems.

Multiband sparse signal reconstruction through direct one-bit sampling.

Compressive sensing (CS) aims at decreasing sampling rate to reduce the needed number of samples. On the other hand, the one-bit CS is proposed to reduce the quantization bit. In this paper, we proposed a one-bit CS system aiming at acquiring the multiband sparse signal which is a very popular signal model in wireless communication, especially in cognitive radio. This proposed system, called direct one-bit sampler (DOS), is simple in hardware implementation, and it consists of only a comparator working at Nyquist rate. In the stage of signal reconstruction, it can be equivalent to a special multicoset sampler which is a popular scheme in CS. Moreover, we propose an enhanced binary iterative hard thresholding (BIHT), a popular one-bit recovery algorithm, to deal with the multiple measurement vectors in the one-bit CS framework. Both the theoretical model and experimental results demonstrate that the proposed DOS, with the help of the enhanced BIHT, can not only accurately recover the positions of active subbands of the multiband sparse signal but also roughly estimate the power of each active subband.

Prior CSIT estimation for FDD massive MIMO system with 1‐bit feedback per dimension

AbstractIn massive multiple‐input–multiple‐output system, the accurate channel state information at the transmitter (CSIT) is required to achieve the high beamforming gain and spectral efficiency. To reduce the feedback overhead for CSIT acquisition in frequency division duplex system, a prior CSIT estimation with 1‐bit feedback per dimension is proposed to alleviate the overhead burden. Specifically, by exploiting the slow variation of channel support between the consecutive frames, the channel support in the previous frame is regarded as the prior information for CSIT estimation of current frame. Then, the received compressed channel measurements at the user side are quantized to 1 bit per measurement and only the sign information is fed back to the base station (BS). At the BS side, the CSIT recovery from the 1‐bit channel feedback information is formulated as a 1‐bit sparse complex‐value signal recovery problem with prior information. Finally, a prior support complex binary iterative hard thresholding algorithm is proposed to perform the CSIT estimation at the BS side. Simulation results demonstrate that the proposed scheme can reduce both the pilot and feedback overhead for CSIT estimation.

Joint Sparsity Pattern Recovery With 1-b Compressive Sensing in Distributed Sensor Networks

In this paper, we study the problem of joint sparse support recovery with 1-b quantized compressive measurements in a distributed sensor network. Multiple nodes in the network are assumed to observe sparse signals having the same but unknown sparse support. Each node quantizes its measurement vector element-wise to 1 b. First, we consider that all the quantized measurements are available at a central fusion center. We derive performance bounds for sparsity pattern recovery using 1-bit quantized measurements from multiple sensors when the maximum likelihood decoder is employed. We further develop two computationally tractable algorithms for joint sparse support recovery in the centralized setting. One algorithm minimizes a cost function defined as the sum of the likelihood function and the $l_{1,\infty }$ quasi-norm, while the other algorithm extends the binary iterative hard thresholding algorithm to the multiple measurement vector case. Second, we consider a decentralized setting where each node transmits 1-b measurements to its one-hop neighbors. The basic idea behind the algorithms developed in the decentralized setting is to embed collaboration among nodes and fusion strategies. We show that even with noisy 1-b compressed measurements, joint support recovery can be carried out accurately in both centralized and decentralized settings. We further show that the performance of the proposed 1-bit compressive sensing-based algorithms is very close to that of their real-valued counterparts except when the signal-to-noise ratio is very small.

Compressive sampling for spectrally sparse signal recovery via one-bit random demodulator

The one-bit compressive sampling (CS) framework aims at alleviating the quantization burden on analog-to-digital converters by quantizing each sample to one bit, i.e., capturing just the signs of samples. Motivated by one-bit CS theory, this paper addresses a new type of data acquisition system to recover spectrally sparse signals. This system is composed of a random demodulator and a one-bit quantizer. The former yields the signal compressed samples while the latter records the sign of each sample. With the observation sign data, the signal is eventually recovered by using the binary iterative hard thresholding algorithm. Through numerical experiments, we demonstrate that our scheme is high-efficient for spectrally sparse signal recovery in the situations of low signal-to-noise ratio, stringent bit budget and weak sparsity.

One-bit compressive sampling via ℓ 0 minimization

The problem of 1-bit compressive sampling is addressed in this paper. We introduce an optimization model for reconstruction of sparse signals from 1-bit measurements. The model targets a solution that has the least l 0-norm among all signals satisfying consistency constraints stemming from the 1-bit measurements. An algorithm for solving the model is developed. Convergence analysis of the algorithm is presented. Our approach is to obtain a sequence of optimization problems by successively approximating the l 0-norm and to solve resulting problems by exploiting the proximity operator. We examine the performance of our proposed algorithm and compare it with the renormalized fixed point iteration (RFPI) (Boufounos and Baraniuk, 1-bit compressive sensing, 2008; Movahed et al., A robust RFPI-based 1-bit compressive sensing reconstruction algorithm, 2012), the generalized approximate message passing (GAMP) (Kamilov et al., IEEE Signal Process. Lett. 19(10):607–610, 2012), the linear programming (LP) (Plan and Vershynin, Commun. Pure Appl. Math. 66:1275–1297, 2013), and the binary iterative hard thresholding (BIHT) (Jacques et al., IEEE Trans. Inf. Theory 59:2082–2102, 2013) state-of-the-art algorithms for 1-bit compressive sampling reconstruction.

Two-Part Reconstruction With Noisy-Sudocodes

We develop a two-part reconstruction framework for signal recovery in compressed sensing (CS), where a fast algorithm is applied to provide partial recovery in Part 1, and a CS algorithm is applied to complete the residual problem in Part 2. Partitioning the reconstruction process into two complementary parts provides a natural trade-off between runtime and reconstruction quality. To exploit the advantages of the two-part framework, we propose a Noisy-Sudocodes algorithm that performs two-part reconstruction of sparse signals in the presence of measurement noise. Specifically, we design a fast algorithm for Part 1 of Noisy-Sudocodes that identifies the zero coefficients of the input signal from its noisy measurements. Many existing CS algorithms could be applied to Part 2, and we investigate approximate message passing (AMP) and binary iterative hard thresholding (BIHT). For Noisy-Sudocodes with AMP in Part 2, we provide a theoretical analysis that characterizes the trade-off between runtime and reconstruction quality. In a 1-bit CS setting where a new 1-bit quantizer is constructed for Part 1 and BIHT is applied to Part 2, numerical results show that the Noisy-Sudocodes algorithm improves over BIHT in both runtime and reconstruction quality.

Compressed sensing with linear correlation between signal and measurement noise

Existing convex relaxation-based approaches to reconstruction in compressed sensing assume that noise in the measurements is independent of the signal of interest. We consider the case of noise being linearly correlated with the signal and introduce a simple technique for improving compressed sensing reconstruction from such measurements. The technique is based on a linear model of the correlation of additive noise with the signal. The modification of the reconstruction algorithm based on this model is very simple and has negligible additional computational cost compared to standard reconstruction algorithms, but is not known in existing literature. The proposed technique reduces reconstruction error considerably in the case of linearly correlated measurements and noise. Numerical experiments confirm the efficacy of the technique. The technique is demonstrated with application to low-rate quantization of compressed measurements, which is known to introduce correlated noise, and improvements in reconstruction error compared to ordinary Basis Pursuit De-Noising of up to approximately 7dB are observed for 1bit/sample quantization. Furthermore, the proposed method is compared to Binary Iterative Hard Thresholding which it is demonstrated to outperform in terms of reconstruction error for sparse signals with a number of non-zero coefficients greater than approximately 1/10th of the number of compressed measurements.

Robust 1-Bit Compressive Sensing via Binary Stable Embeddings of Sparse Vectors

The compressive sensing (CS) framework aims to ease the burden on analog-to-digital converters (ADCs) by reducing the sampling rate required to acquire and stably recover sparse signals. Practical ADCs not only sample but also quantize each measurement to a finite number of bits; moreover, there is an inverse relationship between the achievable sampling rate and the bit depth. In this paper, we investigate an alternative CS approach that shifts the emphasis from the sampling rate to the number of bits per measurement. In particular, we explore the extreme case of 1-bit CS measurements, which capture just their sign. Our results come in two flavors. First, we consider ideal reconstruction from noiseless 1-bit measurements and provide a lower bound on the best achievable reconstruction error. We also demonstrate that i.i.d. random Gaussian matrices provide measurement mappings that, with overwhelming probability, achieve nearly optimal error decay. Next, we consider reconstruction robustness to measurement errors and noise and introduce the binary e-stable embedding property, which characterizes the robustness of the measurement process to sign changes. We show that the same class of matrices that provide almost optimal noiseless performance also enable such a robust mapping. On the practical side, we introduce the binary iterative hard thresholding algorithm for signal reconstruction from 1-bit measurements that offers state-of-the-art performance.