Compressive Signal Processing Research Articles

Waveform Optimization of Compressed Sensing Radar without Signal Recovery

Radar signal processing mainly focuses on target detection, classification, estimation, filtering, and so on. Compressed sensing radar (CSR) technology can potentially provide additional tools to simultaneously reduce computational complexity and effectively solve inference problems. CSR allows direct compressive signal processing without the need to reconstruct the signal. This study aimed to solve the problem of CSR detection without signal recovery by optimizing the transmit waveform. Therefore, a waveform optimization method was introduced to improve the output signal-to-interference-plus-noise ratio (SINR) in the case where the target signal is corrupted by colored interference and noise having known statistical characteristics. Two different target models are discussed: deterministic and random. In the case of a deterministic target, the optimum transmit waveform is derived by maximizing the SINR and a suboptimum solution is also presented. In the case of random target, an iterative waveform optimization method is proposed to maximize the output SINR. This approach ensures that SINR performance is improved in each iteration step. The performance of these methods is illustrated by computer simulation.

An Efficient Wideband Spectrum Sensing Algorithm for Unmanned Aerial Vehicle Communication Networks

With increasingly smaller size, more powerful sensing capabilities and higher level of autonomy, multiple unmanned aerial vehicles (UAVs) can form UAV networks to collaboratively complete missions more reliably, efficiently, and economically. While UAV networks are promising for many applications, there are many outstanding issues to be resolved before large scale UAV networks are practically used. In this paper we study the application of cognitive radio (CR) technology for UAV communication networks, to provide high capacity and reliable communication with opportunistic and timely spectrum access. Compressive sensing is applied in the CR to boost the performance of spectrum sensing. However, the performance of existing compressive spectrum sensing schemes is constrained with nonstrictly sparse spectrum. In addition, the reconstruction process applied in existing schemes has unnecessarily high computational complexity and low energy efficiency. We proposed a new compressive signal processing algorithm, called iterative compressive filtering, to improve the UAV network communication performance. The key idea is using orthogonal projection as a bandstop filter in compressive domain. The components of primary users in the recognized subchannels are adaptively eliminated in compressive domain, which can directly update the measurement for further detection of other active users. Experiment results showed increased efficiency of the proposed algorithm over existing compressive spectrum sensing algorithms. The proposed algorithm achieved higher detection probability in identifying the occupied subchannels under the condition of nonstrictly sparse spectrum with large computational complexity reduction, which can provide strong support of reliable and timely communication for UAV networks.

Phased Fractional Lower-Order Cyclic Moment Processed in Compressive Signal Processing

In signal processing research, cyclostationarity and fractional lower-order statistics (FLOS) are two important solutions to non-stationary signals and non-Gaussian noises, respectively. In the last five years, many methodologies combining the two technologies were proposed to achieve the two tasks simultaneously. Unfortunately, these methodologies need to be based on the Shannon/Nyquist sampling theorem. As phased fractional lower-order cyclic moment (PFLOCM) theoretically cooperates with compressive signal processing (CSP), this paper studies PFLOCM to apply in CSP at sub-Nyquist sampling rates. Using this technical foundation, a complete procedure is novelly proposed to rebuild phased fractional lower-order cyclic moment spectrum (PFLOCMS), which functions as a crucial factor in signal detection, system identification, parameter estimation, and other applications. In addition, various experiments verify the performance of the proposed procedure. It is believed that this paper will have implications for non-stationary and non-Gaussian signal processing at sub-Nyquist sampling rates.

Reconstruction of apertured Fourier Transform Hologram using compressed sensing

Fourier Transform Holography (FTH) encodes object information as the Fourier spectrum in an interference pattern with the help of a reference point source. Hence, a single Fourier transform (FT) operation is capable to provide a complete object from a digitally reconstructed FTH. However, high intensity values in the central region of the FTH demands central blocking due to the limited dynamic range of a detector in a variety of applications. The central blocking causes the loss of frequency content and hence affects the reconstruction result. Still, it can be properly recovered using signal processing techniques such as Compressive Sensing (CS) or Sparse signal processing. This paper investigates the role of CS for centrally blocked FTH using various kind of beam stops and provide a detailed comparison between usual FT reconstruction and technique equipped with CS. We also provide a detail procedure to apply the CS reconstruction in the FTH and compared the results with and without CS. It is established that an object can be recovered from limited size of a recorded hologram with the constraint that object has to be sparse in known basis. Quantitative analysis has been carried out to compare the quality of reconstruction using inverse Fourier transform (IFT) and CS techniques. Quality of reconstruction is assessed by evaluating measures such as the overall visibility, efficiency and PSNR of reconstruction. The finding highlights that the CS reconstruction is better than that of IFT reconstruction. Both simulation and experimental results demonstrate the effectiveness and robustness of the CS-based approach.

Compressive sensing-based electrostatic sensor array signal processing and exhausted abnormal debris detecting

Abstract When faults happen at gas path components of gas turbines, some sparsely-distributed and charged debris will be generated and released into the exhaust gas. The debris is called abnormal debris. Electrostatic sensors can detect the debris online and further indicate the faults. It is generally considered that, under a specific working condition, a more serious fault generates more and larger debris, and a piece of larger debris carries more charge. Therefore, the amount and charge of the abnormal debris are important indicators of the fault severity. However, because an electrostatic sensor can only detect the superposed effect on the electrostatic field of all the debris, it can hardly identify the amount and position of the debris. Moreover, because signals of electrostatic sensors depend on not only charge but also position of debris, and the position information is difficult to acquire, measuring debris charge accurately using the electrostatic detecting method is still a technical difficulty. To solve these problems, a hemisphere-shaped electrostatic sensors’ circular array (HSESCA) is used, and an array signal processing method based on compressive sensing (CS) is proposed in this paper. To research in a theoretical framework of CS, the measurement model of the HSESCA is discretized into a sparse representation form by meshing. In this way, the amount and charge of the abnormal debris are described as a sparse vector. It is further reconstructed by constraining l1-norm when solving an underdetermined equation. In addition, a pre-processing method based on singular value decomposition and a result calibration method based on weighted-centroid algorithm are applied to ensure the accuracy of the reconstruction. The proposed method is validated by both numerical simulations and experiments. Reconstruction errors, characteristics of the results and some related factors are discussed.

Restricted Isometry Property of Subspace Projection Matrix Under Random Compression

Structures play a significant role in the field of signal processing. As a representative of structural data, low rank matrix along with its restricted isometry property (RIP) has been an important research topic in compressive signal processing. Subspace projection matrix is a kind of low rank matrix with additional structure, which allows for further reduction of its intrinsic dimension. This leaves room for improving its own RIP, which could work as the foundation of compressed subspace projection matrix recovery. In this work, we study the RIP of subspace projection matrix under random orthonormal compression. Considering the fact that subspace projection matrices of $s$ dimensional subspaces in $\mathbb{R}^N$ form an $s(N-s)$ dimensional submanifold in $\mathbb{R}^{N\times N}$, our main concern is transformed to the stable embedding of such submanifold into $\mathbb{R}^{N\times N}$. The result is that by $O(s(N-s)\log N)$ number of random measurements the RIP of subspace projection matrix is guaranteed.

Signal Compression Reconstruction with Narrow-Band Interference

Compressive sensing (CS) implements sampling and compression to sparse or compressible signals simultaneously. Compressive signal processing is a new signal processing scheme base on compressive sensing theory. In this paper, the problem of signal compressive reconstruction base on narrow-band interference is researched. The reconstruction performance of BP, MP, and OMP algorithms with narrow-band interference is analyzed by computer simulations.

New analysis of manifold embeddings and signal recovery from compressive measurements

Compressive Sensing (CS) exploits the surprising fact that the information contained in a sparse signal can be preserved in a small number of compressive, often random linear measurements of that signal. Strong theoretical guarantees have been established concerning the embedding of a sparse signal family under a random measurement operator and on the accuracy to which sparse signals can be recovered from noisy compressive measurements. In this paper, we address similar questions in the context of a different modeling framework. Instead of sparse models, we focus on the broad class of manifold models, which can arise in both parametric and non-parametric signal families. Using tools from the theory of empirical processes, we improve upon previous results concerning the embedding of low-dimensional manifolds under random measurement operators. We also establish both deterministic and probabilistic instance-optimal bounds in ℓ2 for manifold-based signal recovery and parameter estimation from noisy compressive measurements. In line with analogous results for sparsity-based CS, we conclude that much stronger bounds are possible in the probabilistic setting. Our work supports the growing evidence that manifold-based models can be used with high accuracy in compressive signal processing.

Concentration of Measure for Block Diagonal Matrices With Applications to Compressive Signal Processing

Theoretical analysis of randomized, compressive operators often depends on a concentration of measure inequality for the operator in question. Typically, such inequalities quantify the likelihood that a random matrix will preserve the norm of a signal after multiplication. Concentration of measure results are well established for unstructured compressive matrices, populated with independent and identically distributed (i.i.d.) random entries. Many real-world acquisition systems, however, are subject to architectural constraints that make such matrices impractical. In this paper we derive concentration of measure bounds for two types of block diagonal compressive matrices, one in which the blocks along the main diagonal are random and independent, and one in which the blocks are random but equal. For both types of matrices, we show that the likelihood of norm preservation depends on certain properties of the signal being measured, but that for the best case signals, both types of block diagonal matrices can offer concentration performance on par with their unstructured, i.i.d. counterparts. We support our theoretical results with illustrative simulations as well as analytical and empirical investigations of several signal classes that are highly amenable to measurement using block diagonal matrices. We also discuss applications of these results in ensuring stable embeddings for various signal families and in establishing performance guarantees for solving various signal processing tasks (such as detection and classification) directly in the compressed domain.

Congestion-aware, loss-resilient bio-monitoring sensor networking for mobile health applications

Many elder patients have multiple health conditions such as heart attacks (of various kinds), brain problems (such as seizure, mental disorder, etc.), high blood pressure, etc. Monitoring those conditions needs different types of sensors for analog signal data acquisition, such as electrocardiogram (ECG) for heart beats, electroencephalogram (EEG) for brain signals, and electromyogram (EMG) for muscles motions. To reduce mobile-health (m-health) cost, the above sensors should be made in tiny size, low memory, and long-term battery operations. We have designed a series of medical sensors with wireless networking capabilities. In this paper, we report our work in three aspects: (1) networked embedded system design, (2) network congestion reduction, and (3) network loss compensation. First, for networked embedded system design, we have designed an integrated wireless sensor network hardware / software platform for multi-condition patient monitoring. Such a system integrates ECG/EEG/other sensors with Radio Frequency Identification (RFID) into a Radio Frequency (RF) board through a programmable interface chip, called PSoc. Second, for network congestion reduction, the interface chip can use compressive signal processing to extract bio-signal feature parameters and only transmit those parameters. This provides an alternative approach to sensor network congestion reduction that aims to alleviate ?hot spot? issues. Third, for network loss compensation, we have designed wireless loss recovery schemes for different situations as follows. (1) If original sensor data streams are transmitted, network congestion will be a big concern due to the heavy traffic. A receiver-only loss prediction will be a good solution. (2) If the signal parameters are transmitted, the transmission loss mandates a 100% recovery rate. We have comprehensively compared the performance of those schemes. The proposed mechanisms for m-health system have potentially significant impacts on today's elder nursing home management and other mobile patient monitoring applications.

The Identification of Frequency Hopping Signal Using Compressive Sensing

Compressive sensing (CS) creates a new framework of signal reconstruction or approximation from a smaller set of incoherent projection compared with the traditional Nyquist-rate sampling theory. Recently, it has been shown that CS can solve some signal processing problems given incoherent measurements without ever reconstructing the signals. Moreover, the number of measurements necessary for most compressive signal processing application such as detection, estimation and classification is lower than that necessary for signal reconstruction. Based on CS, this paper presents a novel identification algorithm of frequency hopping (FH) signals. Given the hop interval, the FH signals can be identified and the hopping frequencies can be estimated with a tiny number of measurements. Simulation results demonstrate that the method is effective and efficient.