Compressive Sensing Theory Research Articles

Online quantum state tomography of N-qubit via continuous weak measurement and compressed sensing

In this paper, we propose an online state tomography method for [Formula: see text]-qubit quantum system based on the continuous weak measurement and compressed sensing (CS). The quantum system is described by stochastic master equation. The continuous weak measurement operators for the [Formula: see text]-qubit quantum system, which are indirectly acted on the quantum system, are derived according to the measurement operator results of two-level quantum system. The online time-varying measurement operators are obtained by means of the dynamic evolution equation of the system. The quantum state is online estimated by solving the optimization problem of minimizing the two-norm with the positive definite constraints of density matrix, and we use the nonnegative least squares algorithm to solve the optimization problem. CS theory is used to reduce the number of the measurements in the process of online state estimation. In the numerical experiments, we study the effects of external control field, measurement rate and the different numbers of qubits on the performance in the proposed method. The minimum required numbers of measurements for 2, 3, 4 and 5 qubits are found. The normalized distance and fidelity of our proposed method can achieve satisfying accuracy with small number of measurements.

Soft computing based compressive sensing techniques in signal processing: A comprehensive review

AbstractIn this modern world, a massive amount of data is processed and broadcasted daily. This includes the use of high energy, massive use of memory space, and increased power use. In a few applications, for example, image processing, signal processing, and possession of data signals, etc., the signals included can be viewed as light in a few spaces. The compressive sensing theory could be an appropriate contender to manage these limitations. “Compressive Sensing theory” preserves extremely helpful while signals are sparse or compressible. It very well may be utilized to recoup light or compressive signals with less estimation than customary strategies. Two issues must be addressed by CS: plan of the estimation framework and advancement of a proficient sparse recovery calculation. The essential intention of this work expects to audit a few ideas and utilizations of compressive sensing and to give an overview of the most significant sparse recovery calculations from every class. The exhibition of acquisition and reconstruction strategies is examined regarding the Compression Ratio, Reconstruction Accuracy, Mean Square Error, and so on.

An MCM-Enhanced Compressive Sensing for Weak Fault Feature Extraction of Rolling Element Bearings under Variable Speeds

The compressive sensing (CS) theory provides a new slight to the big-data problem led by the Shannon sampling theorem in rolling element bearings condition monitoring, where the measurement matrix of CS tends to be designed by the random matrix (RM) to preserve the integrity of signal roughly. However, when the signal to be analyzed is infected with strong noise, not only does the signal become insufficiently sparse, but the randomness of the measurement matrix will bring down the sensing efficiency, resulting in the loss of fault feature. Thus, a sensing-enhanced CS scheme based on a series of modes after VMD decomposition is proposed under this paper. The core of this scheme is as follows: (1) the principal mode of VMD with better sparsity replaces the raw signal for compressive sensing; (2) all these modes contain the time-frequency characteristics of the raw signal; (3) a new measurement matrix called mode-circulant matrix (MCM) is defined by circulating the mode matrix, and when the amount of samples is shrunk, the sensing efficiency can be enhanced greatly. Besides, considering the fault signal of rolling bearings under variable speed, there is a need to use order tracking to overcome the nonstationarity of the signal before applying CS theory. The analysis results of simulation and experiment prove that the VMD- and MCM-based CS can successfully extract the weak fault feature of rolling bearings with operating speed changing.

Application of CS in weak signal quantum measurement and protein structure calculation

It has been more than 15 years since the compressed sensing (CS) theory was put forward in 2006. The CS theory has been successfully applied and developed in many classical fields such as the single-pixel camera, CT imaging and radar imaging system, but there is still much space for its applications in quantum and biological system. In this paper, the basic knowledge of CS theory and its application/development history are briefly introduced. Then a review is given on a series of achievements in the CS theory applied in quantum precision measurement and biological system, mainly obtained by the Center for Quantum Technology Research in Beijing Institute of Technology (BIT). The review covers several different topics including the measurement and imaging in extremely weak signals, the density matrix calculation for multi-body quantum state tomography and the protein structure reconstruction from matrix completion theory, which is developed based on the CS theory. With the above reviews, we show that the CS theory has great potential for further application, not only in weak signal detection, but also in quantum calculation and even the research on bio-macromolecules. In the end, the summary and outlook are given on the future developments and applications of the CS theory.

2-D Joint Sparse Reconstruction and Micro-Motion Parameter Estimation for Ballistic Target Based on Compressive Sensing.

The sparse frequency band (SFB) signal presents a serious challenge to traditional wideband micro-motion curve extraction algorithms. This paper proposes a novel two-dimension (2-D) joint sparse reconstruction and micro-motion parameter estimation (2D-JSR-MPE) algorithm based on compressive sensing (CS) theory. In this technique, the 2D-JSR signal model and the micro-motion parameter dictionary are established based on the segmented SFB echo signal, in which the idea of piecewise effectively reduces the model complexity of ballistic target. With the accommodation of the CS theory, the 2D-JSR-MPE of the echo signal is transformed into solving a sparsity-driven optimization problem. Via an improved orthogonal matching pursuit (OMP) algorithm, the high-resolution range profiles (HRRP) can be reconstructed accurately, and the precise micro-motion curves can be simultaneously extracted on phase accuracy. The employment of 2-D joint processing can effectively avoid the interference of the sparse reconstruction error caused by cascaded operation in the subsequent micro-motion parameter estimation. The proposed algorithm benefits from the anti-jamming characteristic of the SFB signal and 2-D joint processing, thus remarkably enhancing its accuracy, robustness and practicality. Extensive experimental results are provided to verify the effectiveness and robustness of the proposed algorithm.

Design and implementation of proposed pipelined adaptive recovery CAMP algorithm for LFMCW radar

Recently, Compressive Sensing (CS) theory based on the traditional CAMP reconstruction algorithm has applied in radar systems to achieve the benefits of CS such as low sampling rate, small memory size, less complexity in hardware and consequently reduces the required processing time as using a low speed Analog-to-Digital Converter. A modified reconstruction Complex Approximate Massage Passing (CAMP) algorithm designed as an adaptive recovery algorithm is introduced. The adaptive recovery algorithm depends on selecting the comparison threshold in an adaptive manner resembling the Constant False Alarm Rate processing. In this paper, design and implementation of the adaptive algorithm for Linear Frequency Modulated Continuous Wave radar signals are achieved using Field Programmable Gate Array (FPGA). A proposed pipelined process-based scheme is used in the implementation that leads to a more redundant in complexity and processing time. A generic methodology based on segmenting the acquired radar signal and applying the adaptive recovery algorithm on each segment is proposed. This method enables the investigation of the adaptive recovery algorithm on any signal length with fixed hardware resources. A suggested processing method is implemented called pipelined adaptive recovery CAMP algorithm, which enhances the performance of reconstructing the radar signal better than the traditional CAMP algorithm. Hardware implementation using FPGA and experiments are met, and their results agree very well with the simulation outcomes.

WDAT‐OMS: A two‐level scheme for efficient data gathering in mobile‐sink wireless sensor networks using compressive sensing theory

This study addresses the problems of energy and delay in wireless sensor networks equipped with mobile sinks. The authors jointly consider the compressive sensing (CS) theory, cluster-based routing, and sink mobility to propose a data collection method named ‘weighted data aggregation trees with optimal mobile sink(s) (WDAT-OMS)’. The proposed scheme relies on a two-level architecture in which sensors are clustered at the first level. WDAT-OMS uses the CS theory along with load-balanced data aggregation trees to route packets from sensors to the corresponding cluster heads (CHs). In this regard, they present an efficient metric named ‘energy-and distance-aware CH selection’ to fairly distribute the energy consumption among different sensors. At the second level, one or more sinks traverse the network to collect the aggregated data of CHs. As an advantage, WDAT-OMS not only balances the energy consumption among different sensors but also increases the network scalability. Numerical results demonstrate that the proposed algorithm reduces energy consumption in comparison with ‘centralised clustering algorithm’, ‘energy-aware CS-based data aggregation’, and ‘energy-balanced high-level data aggregation tree ‘by 66%, 62%, and 63% for an average number of clusters, respectively. It also decreases the sink delay in comparison with the ‘single-hop data-gathering problem’ by 10%.

Recovering compressed images for automatic crack segmentation using generative models

In a structural health monitoring (SHM) system that uses digital cameras to monitor cracks of structural surfaces, techniques for reliable and effective data compression are essential to ensure a stable and energy-efficient crack images transmission in wireless devices, e.g., drones and robots with high definition cameras installed. Compressive sensing (CS) is a signal processing technique that allows accurate recovery of a signal from a sampling rate much smaller than the limitation of the Nyquist sampling theorem. Different from the popular approach of simultaneously training encoder and decoder using neural network models, the CS theory ensures a high probability of accurate signal reconstruction based on random measurements that is shorter than the length of the original signal under a sparsity constraint. Such method is particularly useful when measurements are expensive, such as wireless sensing of civil structures, because its hardware implementation allows down sampling of signals during the sensing process. Hence, CS methods can achieve significant energy saving for the sensing devices. However, the strong assumption of the signals being highly sparse in an invertible space is relatively hard to guarantee for many real images, such as image of cracks. In this paper, we present a new approach of CS that replaces the sparsity regularization with a generative model that is able to effectively capture a low dimension representation of targeted images. We develop a recovery framework for automatic crack segmentation of compressed crack images based on this new CS method. We demonstrate the remarkable performance of our method that takes advantage of the strong capability of generative models to capture the necessary features required in the crack segmentation task even the backgrounds of the generated images are not well reconstructed. The superior performance of our recovery framework is illustrated by comparisons to three existing CS algorithms. Furthermore, we show that our framework is potentially extensible to other common problems in automatic crack segmentation, such as defect recovery from motion blurring and occlusion.

A signal reconstruction method of wireless sensor network based on compressed sensing

Compressed sensing (CS) is a new theory for sampling and recovering signal-based sparse transformation. This theory could help us to acquire complete signal at low cost. Therefore, it also satisfies the requirement of low-cost sampling since bandwidth and capability of sampling is not sufficient. However, wireless sensor network is an open scene, and signal is easily affected by noise in the open environment. Specially, CS theory indicates a method of sub-Nyquist sampling which is effective to reduce cost in the process of data acquirement. However, the sampling is “imperfect”, and the corresponding data is more sensitive to noise. Consequently, it is urgently requisited for robust and antinoise reconstruction algorithms which can ensure the accuracy of signal reconstruction. In the article, we present a proximal gradient algorithm (PRG) to reconstruct sub-Nyquist sampling signal in the noise environment. This algorithm iteratively uses a straightforward shrinkage step to find the optimum solution of constrained formula, and then restores the original signal. Finally, in the experiment, PRG shows excellent performance comparing to OMP, BP, and SP while signal is corrupted by noise.

Compressive Sensing Approach to Harmonics Detection in the Ship Electrical Network.

The contribution of this paper is to show the opportunities for using the compressive sensing (CS) technique for detecting harmonics in a frequency sparse signal. The signal in a ship’s electrical network, polluted by harmonic distortions, can be modeled as a superposition of a small number of sinusoids and the discrete Fourier transform (DFT) basis forms its sparse domain. According to the theory of CS, a signal may be reconstructed from under-sampled incoherent linear measurements. This paper highlights the use of the discrete Radon transform (DRT) techniques in the CS scheme. In the reconstruction algorithm section, a fast algorithm based on the inverse DRT is presented, in which a few randomly sampled projections of the input signal are used to correctly reconstruct the original signal. However, DRT requires a very large set of measurements that can defeat the purpose of compressive data acquisition. To acquire the wideband data below the Nyquist frequency, the K-rank-order filter is applied in the sparse transform domain to extract the most significant components and accelerate the convergence of the solution. While most CS research efforts focus on random Gaussian measurements, the Bernoulli matrix with different values of the probability of ones is applied in the presented algorithm. Preliminary results of numerical simulation confirm the effectiveness of the algorithm used, but also indicate its limitations. A significant advantage of the proposed approach is the speed of analysis, which uses fast Fourier transform (FFT) and inverse FFT (IFFT) algorithms widely available in programming environments. Moreover, the data processing algorithm is quite simple, and therefore memory usage and burden of the data processing load are relatively low.

Compressive seismic data acquisition in a desert area of western China: A case study

The seismic exploration industry continuously demands better imaging quality and consequently requires denser spatial sampling, which increases acquisition cost and time. To alleviate this burden, compressive sensing (CS) theory has been introduced in the design of acquisition geometry, as it requires fewer shot and receiver locations than traditional methods. In 2017, we conducted a field experiment in a desert area in western China. This was the first such test in China to utilize CS theory in a field test. The survey had 1760 shot records with irregular shot and receiver locations designed with guidance from CS theory. By way of data reconstruction, a seismic data set with higher sampling density (7.5 × 7.5 m bin size) was acquired, and the imaging quality was improved significantly compared to existing legacy data (15 × 15 m bin size). These results indicate that a CS-designed acquisition may reduce cost while enhancing imaging quality.

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.

Algorithms of signal parameter estimation based on the theory of Compressive Sensing and their computer simulation

The problem of estimating unknown signal parameters in the presence of noise is a classical problem in statistical radio engineering. There are many algorithms for solving this problem. Many of these algorithms are based on the use of well-known statistical optimality criteria in order to improve the estimation efficiency. Therefore, they acquire a high computational complexity. In this article, in order to reduce computational complexity, it is proposed to modernize the classical correlation algorithm based on the new Compressive Sensing theory, which has been actively developed in recent decades. The article presents a new simplified algorithm of signal parameters estimation, outlines operational speed benefits, and compares the efficiency of the proposed algorithm to the efficiency of the classical algorithm as well as some other algorithms. The proposed algorithm has also been compared to the classical one according to computational complexity. Practical implementation of the proposed algorithm requires much smaller number of arithmetical operations with some deterioration in unknown parameter estimation accuracy.

Ground Moving Target Imaging Based on Compressive Sensing Framework With Single-Channel SAR

Ground moving target imaging (GMTIm) is considered one of the most important applications of synthetic aperture radar (SAR). Phase modulation from a moving target's higher-order movements severely degrades the focusing quality of SAR images, because the conventional SAR-GMTIm algorithm assumes a constant target velocity in high-resolution GMTIm with single channel SAR. To solve this problem, a novel SAR-GMTIm algorithm in the compressive sensing (CS) framework is proposed to obtain high-resolution SAR images with highly focused responses and accurate relocation. After taking direct action on data in the defocused region of interest (ROI) from the entire image scene, CS theory is used to decompose an SAR-GMTIm signal into a set of the polynomial basis functions to remove the various phase errors related to higherorder movements. A modified orthogonal matching pursuit (MOMP)-type basis function-searching scheme is adopted to determine the motion parameter and reconstruct the sensing dictionary matrix. We can generate a refocused image of SAR-GMTIm from the complete SAR-GMTIm signal recovered using the proposed method. Finally, simulated and real measured SAR data are used to validate the effectiveness and superiority of the proposed method for SAR-GMTIm.

Research on Image Optimization Technology Based on Compressed Sensing

Compressed Sensing (CS) theory is one of the most active research fields in electronic information engineering. CS theory overcomes the limits dictated by Nyquist sampling theorem. Compared to the required minimum sampling quantity, CS proves that the original signal can be restored with high probability by fewer measurements, which saves the time cost of data acquisition and processing without losing information features. CS theory can essentially be regarded as a tool for dealing with linear signal recovery problems, so it has obvious advantages in solving inverse problems of signals and images. Image degradation is one of them, and the process of restoring high-quality images is image optimization. In order to promote the academic research and practical application of CS theory, the basic principle of CS is introduced. Based on the previous research, this paper studies on CS-based image optimization technology in three main aspects: denoising, deblurring and super resolution. Finally, the problems and challenges are discussed, and the current trends are analyzed to provide reference and help for future work.

Compressive Sensing Based Channel Estimation for Millimeter-Wave Full-Dimensional MIMO With Lens-Array

Channel estimation (CE) for millimeter-wave (mmWave) lens-array suffers from prohibitive training overhead, whereas the state-of-the-art solutions require an extra complicated radio frequency phase shift network. By contrast, lens-array using antenna switching network (ASN) simplifies the hardware, but the associated CE is a challenging task due to the constraint imposed by ASN. This paper proposes a compressive sensing (CS)-based CE solution for full-dimensional (FD) lens-array, where the mmWave channel sparsity is exploited. Specifically, we first propose an approach of pilot training under the more severe haraware constraint imposed by ASN, and formulate the associated CE of lens-array as a CS problem. Then, a redundant dictionary is tailored for FD lens-array to combat the power leakage caused by the continuous angles of multipath components. Further, we design the baseband pilot signals to minimize the total mutual coherence of the measurement matrix based on CS theory for more reliable CE performance. Our solution provides a framework for applying CS techniques to lens-array using simple and practical ASN. Simulation results demonstrate the effectiveness of the proposed scheme.

Estimador de canal basado en sensado compresivo y LDPC para OFDM usando SDR

Este trabajo propone la aplicación de un estimador de canal basado en sensado compresivo (CS, del inglés Compressive Sensing) sobre un sistema que usa multiplexación por división de frecuencias ortogonales (OFDM, del inglés Orthogonal Frequency Division Multiplexing) usando dispositivos de radio definido por \emph{software} (SDR, del inglés Software Defined Radio). La aplicación de la teoría de CS se da a través del uso de algoritmos de reconstrucción dispersa como Orthogonal Matching Pursuit (OMP) y Compressive Sampling Matching Pursuit (CoSaMP) con el fin de aprovechar la naturaleza dispersa de las subportadoras piloto usadas en OFDM optimizando el ancho de banda del sistema. Además, para mejorar el rendimiento de estos algoritmos, se utiliza el concepto de la matriz de comprobación de paridad dispersa que se implementa en el despliegue de códigos de comprobación de paridad de baja densidad (LDPC, del inglés Low Density Parity Check) para obtener una matriz de sensado que mejore la propiedad de restricción isométrica (RIP, del inglés Isometric Restriction Property) perteneciente al paradigma de CS. El documento muestra el modelo implementado en los equipos SDR analizando la tasa de error de bit y la cantidad de símbolos piloto usados.

Snapshot Compressed Sensing: Performance Bounds and Algorithms

Snapshot compressed sensing (CS) refers to compressive imaging systems in which multiple frames are mapped into a single measurement frame. Each pixel in the acquired frame is a noisy linear mapping of the corresponding pixels in the frames that are combined together. While the problem can be cast as a CS problem, due to the very special structure of the sensing matrix, standard CS theory cannot be employed to study such systems. In this paper, a compression-based framework is employed for theoretical analysis of snapshot CS systems. It is shown that this framework leads to two novel, computationally-efficient and theoretically-analyzable compression-based recovery algorithms. The proposed methods are iterative and employ compression codes to define and impose the structure of the desired signal. Theoretical convergence guarantees are derived for both algorithms. In the simulations, it is shown that, in the cases of both noise-free and noisy measurements, combining the proposed algorithms with a customized video compression code, designed to exploit nonlocal structures of video frames, significantly improves the state-of-the-art performance.

Comparison of sparse Bayesian learning and atomic norm minimization in detecting passive tonal signals

The frequency estimation of tonal signals in passive sonar systems is crucial to the identification of the marine object. In this study, we introduce the frequency estimation of tonal signals using the multiple measurement vector atomic norm minimization(MMV-ANM) technique based on compressive sensing (CS) and sparse Bayesian learning (SBL) technique based on Bayesian Inference. CS techniques have been employed in identifying the tonal frequency components. It is now well-known from the theory of CS that a high-dimensional signal can be recovered from a relatively small number of measurements as long as the desired signal is sparsely represented. MMV-ANM, an extended version of CS technique for solving the basis mismatch problem, has been proposed and shown better performance in terms of resolution and stability. On the other hand, tonal signals at passive sonar systems are also estimated with sparse Bayesian learning (SBL) using MMV. The prior source amplitudes are assumed independent zero-mean complex Gaussian distribution with the unknown variances (hyperparameters). The hyperparameters are derived by maximizing the probability of given passive data, which leads to sparse tonal signal frequencies. We compare performance of SBL and MMV-ANM in estimation of passive tonal signals with synthetic and in situ data. [*corresponding author Youngmin Choo]

Localization of Two Sound Sources Based on Compressed Matched Field Processing with a Short Hydrophone Array in the Deep Ocean

Passive multiple sound source localization is a challenging problem in underwater acoustics, especially for a short hydrophone array in the deep ocean. Several attempts have been made to solve this problem by applying compressive sensing (CS) techniques. In this study, one greedy algorithm in CS theory combined with a spatial filter was developed and applied to a two-source localization scenario in the deep ocean. This method facilitates localization by utilizing the greedy algorithm with a spatial filter at several iterative loops. The simulated and experimental data suggest that the proposed method provides a certain localization performance improvement over the use of the Bartlett processor and the greedy algorithm without a spatial filter. Additionally, the effects on the source localization caused by factors such as the array aperture, number of hydrophones or snapshots, and signal-to-noise ratio (SNR) are demonstrated.