Compressive Sensing Measurement Matrix Research Articles

Analytical Model for Photonic Compressive Sensing With Pulse Stretch and Compression

Compressive sensing (CS) with photonic technologies provides a promising way to acquire information with reduced measurement. Photonic CS with pulse stretch and compression has been proved to be capable of capturing wideband time-domain signals at extremely high equivalent sampling rate or images at high frame rate. In this approach, an input short pulse is first stretched by propagating through a dispersive medium and then the stretched pulse is modulated by a signal to be measured and a pseudorandom bit sequence (PRBS). The stretched pulse encoded with the signal and the PRBS is compressed in the time domain after passing a second dispersive medium with an opposite dispersion value. The time-domain compression of the stretched pulse was regarded as the integration function in the CS process (but it has never been proved), which is a key to realize time-domain downsampling or single-pixel imaging. In this paper, we fully investigate the theoretical framework of the photonic CS with optical pulse stretch and compression, and present an analytical model of the CS measurement matrix based on the analysis of the pulse stretch, modulation and compression, for the first time to our knowledge. Moreover, we prove the equivalence between the peak value of the compressed pulse and the integral value of the mixed signal, which is the basis of the analytical model. In addition, we further discuss the impact of the limited bandwidth of the employed photodetector on the measurement and the performance of signal reconstruction.

Secure and robust watermarking algorithm for remote sensing images based on compressive sensing

The aim of this paper is to improve the reconstruction accuracy and security when adopting Compressive Sensing (CS) in watermarking algorithm. Unlike classical CS-based watermark generation method, lifting wavelet transformation, partial Hadamard matrix, and ternary watermark sequence have been combined together to carry sufficient watermark information to ensure reconstruction accuracy and robustness. In the procedure of watermark embedding and extraction, watermark is embedded and extracted in CS measurement of remote sensing image. Hence the whole algorithm security is guaranteed by CS measurement matrix either in watermark generation or watermark embedding and extraction. Then, the CS-based watermarking algorithm for remote sensing images is proposed and demonstrated. Compared with other CS-based approaches, the improvements on reconstruction accuracy, security and robustness of the proposed algorithm have been verified by experiments.

Compressed Sensing With Approximate Message Passing Using In-Memory Computing

In-memory computing is a promising non-von Neumann approach where certain computational tasks are performed within resistive memory units by exploiting their physical attributes. In this paper, we propose a new method for fast and robust compressed sensing (CS) of sparse signals with approximate message passing recovery using in-memory computing. The measurement matrix for CS is encoded in the conductance states of resistive memory devices organized in a crossbar array. In this way, the matrix-vector multiplications associated with both the compression and recovery tasks can be performed by the same crossbar array without intermediate data movements at potential ${O}{(}{1}{)}$ time complexity. For a signal of size ${N}$ , the proposed method achieves a potential ${O}{(}{N}{)}$ -fold recovery complexity reduction compared with a standard software approach. We show the array-level robustness of the scheme through large-scale experimental demonstrations using more than 256k phase-change memory devices.

Demonstration of speckle-based compressive sensing system for recovering RF signals

We demonstrate measurement of RF signals in the 2-19 GHz band using a photonic compressive sensing (CS) receiver. The RF is modulated onto chirped optical pulses that then propagate through a multimode fiber that produces the random projections needed for CS via optical speckle. Our system makes 16 independent measurements per optical pulse and we demonstrate several calibration techniques to obtain the CS measurement matrix from these measurements. Then a standard penalized l1 norm method recovers amplitude, phase, and frequency of single-tone and two-tone RF signals with about 100 MHz resolution in a single 4.5 ns pulse. A novel subspace method recovers the frequency to about 20 kHz resolution over 100 pulses in a 2.8 microsecond time window. These experiments use discrete fiber-coupled optical components, but all necessary functions can be realized in photonic and electronic integrated circuits.

Single-Pixel Color Imaging Method with a Compressive Sensing Measurement Matrix

Compressive sensing theory has addressed the limitations of traditional methods in the field of information technology, and led to a revolution. On the basis of compressive sensing theory research, this study utilized the exterior determinacy and inherent randomness of chaotic sequences, designed a pseudo-random circulant measurement matrix based on chaotic sequence. Compared with other deterministic measurement matrices, the restoration effect of the designed measurement matrix remarkably improved and showed advantages in hardware and storage. Then, this study developed a single-pixel imaging scheme that could accurately obtain color information. The proposed improved measurement matrix combined with the hardware system could accurately reconstruct color images and had good robustness according to various experimental data.

Compressive sensing based secret signals recovery for effective image Steganalysis in secure communications

Conventional image steganalysis mainly focus on presence detection rather than the recovery of the original secret messages that were embedded in the host image. To address this issue, we propose an image steganalysis method featured in the compressive sensing (CS) domain, where block CS measurement matrix senses the transform coefficients of stego-image to reflect the statistical differences between the cover and stego- images. With multi-hypothesis prediction in the CS domain, the reconstruction of hidden signals is achieved efficiently. Extensive experiments have been carried out on five diverse image databases and benchmarked with four typical stegographic algorithms. The comprehensive results have demonstrated the efficacy of the proposed approach as a universal scheme for effective detection of stegography in secure communications whilst it has greatly reduced the numbers of features requested for secret signal reconstruction.

Low storage space for compressive sensing: semi-tensor product approach

Random measurement matrices play a critical role in successful recovery with the compressive sensing (CS) framework. However, due to its randomly generated elements, these matrices require massive amounts of storage space to implement a random matrix in CS applications. To effectively reduce the storage space of the random measurement matrix for CS, we propose a random sampling approach for the CS framework based on the semi-tensor product (STP). The proposed approach generates a random measurement matrix, where the dimensions of the random measurement matrix are reduced to a quarter (or 1/16, 1/64, and even 1/256) of the number of dimensions, which are used for conventional CS. We then estimate the values of the sparse vector with a modified iteratively re-weighted least-squares (IRLS) algorithm. The results of numerical simulations showed that the proposed approach can reduce the storage space of a random matrix to at least a quarter while maintaining quality of reconstruction. All results confirmed that the proposed approach significantly influences the physical implementation of the CS in images, especially on embedded system and field programmable gate array (FPGA), where storage is limited.

Securing image information using double random phase encoding and parallel compressive sensing with updated sampling processes

Recently, a new kind of image encryption approach using compressive sensing (CS) and double random phase encoding has received much attention due to the advantages such as compressibility and robustness. However, this approach is found to be vulnerable to chosen plaintext attack (CPA) if the CS measurement matrix is re-used. Therefore, designing an efficient measurement matrix updating mechanism that ensures resistance to CPA is of practical significance. In this paper, we provide a novel solution to update the CS measurement matrix by altering the secret sparse basis with the help of counter mode operation. Particularly, the secret sparse basis is implemented by a reality-preserving fractional cosine transform matrix. Compared with the conventional CS-based cryptosystem that totally generates all the random entries of measurement matrix, our scheme owns efficiency superiority while guaranteeing resistance to CPA. Experimental and analysis results show that the proposed scheme has a good security performance and has robustness against noise and occlusion.

A visually secure image encryption scheme based on compressive sensing

A novel visually secure image encryption scheme based on compressive sensing (CS) is proposed. Firstly, the plain image is transformed into wavelet coefficients, and then confused by a zigzag path and encrypted into a compressed cipher image using compressive sensing. Next, the cipher image is embedded into a carrier image, and finally a visually secure cipher image is obtained. SHA 256 hash function of the original image is generated to calculate the parameters for zigzag confusion and one-dimensional skew tent map, and the map is used to produce the measurement matrix for CS. Therefore, the proposed algorithm is highly sensitive to the plain image, and it can effectively withstand known-plaintext and chosen-plaintext attacks. Besides, our algorithm can achieve the image data security and image appearance security simultaneously, and the size of the cipher image and original image is equal, it does not require additional transmission bandwidth and storage space. Simulation results and performance analyses both demonstrate excellent encryption performance of the proposed encryption scheme.

Efficient distributed storage strategy based on compressed sensing for space information network

This article investigates the distributed data storage problem with compressed sensing in the space information network. Since there exists a performance-energy trade-off, most existing strategies focus only on improving the compressed sensing construction performance or reducing the energy consumption, respectively. In order to achieve a better balance, a novel and efficient strategy, referred to as distributed storage strategy based on compressed sensing, is proposed in this article. Unlike other strategies which require source packets visiting the entire network, the proposed strategy is a “one-hop” method since information exchange is only performed between neighbors. Therefore, the compressed sensing measurement matrix depends heavily on the degree of each space node. We prove that the proposed strategy guarantees the compressed sensing reconstruction performance under both sparse orthonormal basis and dense orthonormal basis. Simulation results validate that, compared with the representative CStorage strategy and compressive data persistence strategy, the proposed strategy consumes the least energy and computational overheads, while almost without sacrificing the compressed sensing reconstruction performance.

Multimode waveguide speckle patterns for compressive sensing.

Compressive sensing (CS) of sparse gigahertz-band RF signals using microwave photonics may achieve better performances with smaller size, weight, and power than electronic CS or conventional Nyquist rate sampling. The critical element in a CS system is the device that produces the CS measurement matrix (MM). We show that passive speckle patterns in multimode waveguides potentially provide excellent MMs for CS. We measure and calculate the MM for a multimode fiber and perform simulations using this MM in a CS system. We show that the speckle MM exhibits the sharp phase transition and coherence properties needed for CS and that these properties are similar to those of a sub-Gaussian MM with the same mean and standard deviation. We calculate the MM for a multimode planar waveguide and find dimensions of the planar guide that give a speckle MM with a performance similar to that of the multimode fiber. The CS simulations show that all measured and calculated speckle MMs exhibit a robust performance with equal amplitude signals that are sparse in time, in frequency, and in wavelets (Haar wavelet transform). The planar waveguide results indicate a path to a microwave photonic integrated circuit for measuring sparse gigahertz-band RF signals using CS.

A New Sparse Signal-Matched Measurement Matrix for Compressive Sensing in UWB Communication

Ultra wideband (UWB) technology is suitable for high data rate short range wireless communication, localization, and imaging techniques. However, UWB systems require high sampling rate and precise synchronization. In order to reduce the sampling rate, have precise synchronization, and for low power requirement, UWB systems are implemented using compressive or sub-Nyquist rate measured samples by exploiting the sparsity of the UWB signal. Compressive sensing (CS)-based UWB systems are being designed in two ways: 1) signal demodulation or detection is performed in the CS domain without full signal recovery at the front-end. Thus, demodulation or detection works on compressive measurements. However, system performance deteriorates in the CS domain as compared with full Nyquist rate sampling and 2) after, Nyquist rate signal is recovered using efficient algorithms at the front-end, the signal demodulation or detection is performed using the conventional receiver. Thus, one requires an efficient CS/sampling of signal measurement at the front-end for better system performance for both the cases stated earlier. In this paper, we propose a deterministic (partial) UWB waveform-matched measurement matrix. The proposed measurement matrix has a circulant structure and is sparse in nature. The proposed matrix is easy to implement in hardware and is operationally time efficient as needed in a practical system. The bit error rate performance of the corresponding UWB system and the operational time complexity with the proposed measurement matrix are better as compared with the existing measurement matrices in the CS domain for both the above receiver designs. The efficacy of the proposed measurement matrix is verified through extensive simulations in both the additive white Gaussian noise and multipath communication environments. In addition, we have also compared other desirable properties of the proposed measurement matrix with the existing measurement matrices.

Compressive Sensing Based Beamforming forMillimeter-Wave OFDM Systems

In this paper, we address codebook-based beamforming for multi-antenna orthogonal frequency division multiplexing (OFDM) systems operating in 60-GHz millimeter-wave band. Given a pre-specified codebook, the task of the beamforming process is to identify the best transmit and receive beam vectors to maximize the spectral efficiency. By properly modeling the multipath structure in 60-GHz channels, we transform the above task into the estimation of several sparse signal vectors. Furthermore, we tailor compressive sensing (CS) technology to efficiently estimate such sparse signals, wherein the CS measurement matrix is specifically designed by minimizing the inner products between different columns of the CS effective dictionary. As a result, CS-based iterative and non-iterative beamforming schemes are proposed. Due to the ability to judiciously exploit multipath sparsity inherent in 60-GHz channels, the proposed schemes significantly outperform the existing counterparts in terms of training overhead and success probability, which is confirmed by theoretical analysis and extensive simulations.

基于m序列的压缩感知测量矩阵构造

测量矩阵作为压缩感知理论的核心内容，对信号的测量和重构会产生重大影响。本文主要基于m序列构造压缩感知测量矩阵。首先，给出一种压缩率为0.5的测量矩阵构造方法，利用该方法构造的测量矩阵元素取值集合较小，具有一定的循环特性。其次，结合有限域的理论，对利用m序列构造的测量矩阵做进一步改进，改进后测量矩阵的压缩率取值范围增大加。仿真结果表明：本文构造的测量矩阵的重构性能优于同大小的Gause测量矩阵，避免了随机性测量矩阵的不确定性，具有一定实用价值。 The measurement matrix as the core of the compressed sensing theory, will have a significant im-pact on the measurement and reconstruction. This paper produces a method of compressed sensing measurement matrix through the m sequences. First of all, it gives a method to construct the measurement matrix with compression rate is 0.5; this measurement matrix has small element set and certain cycle characteristics. Secondly, for combining the theory of finite fields, the measure-ment matrix based on m sequence is further improved. The compression rate of the matrix mea-surement range is greatly increased. The simulation results show that the measurement matrix is constructed in this paper which is better than Gause measurement matrix reconstruction perfor-mance of the same size, avoids the random measurement matrix uncertainty and has a certain practical value.

Compressive sensing measurement matrix construction based on improved size compatible array LDPC code

ISC-array LDPC code matrix is evolved from SC-array LDPC code matrix to improve compressive sensing performance for large-size sparse signal. When q is a prime number, no repetitive row occurs in the shift index of SC-array LDPC code matrix, ISC-array LDPC code matrix performs comparably with SC-array LDPC code matrix. When q is a non-prime number, some repetitive rows will appear in the shift index of SC-array LDPC code matrix, which results in more 4-cycles and decreases the compressive sensing performance. ISC-array LDPC code matrix outperforms SC-array LDPC code matrix by effectively reducing or even eliminating the repetitive rows according to their distribution rule, 4-cycles are removed to the maximum extent. ISC-array LDPC code matrix qualifies for compressive sensing because of satisfying RIP well. It also has good quasi-cyclic structure and supports arbitrary code lengths. The simulations verify that the optimised ISC-array LDPC code matrix is advantageous in the image reconstruction quality, the robustness to noise performance and the algorithm complexity.

Compressive Sensing Measurement Matrix Generator Based on Improved SC-Array LDPC Code

We construct and implement a compressive sensing measurement matrix based on improved size-compatible (ISC)-array low-density parity-check (LDPC) code. First, we propose an improved measurement matrix from the array LDPC code matrix. The proposed measurement matrix retains suitable quasi-cyclic structures and supports arbitrary code lengths. It also achieves a high perfect recovery percentage compared with a Gaussian random matrix of the same size. Second, we propose a hardware scheme using cycle shift registers to design the compressive sensing measurement matrix generator. This provides simple circuit architecture during the generation of the measurement matrix. According to simulation verifications, the measurement matrix construction method is effective and entails fewer shift registers and a lower area overhead by using a simplified hardware implementation scheme. The compressive sensing measurement matrix generator can generate all of the required elements in the ISC-array LDPC code matrix with an acceptable hardware overhead. Therefore, it can be widely applied to large-scale sparse signal compressive sensing.

Design and Analysis of Compressive Data Persistence in Large-Scale Wireless Sensor Networks

This paper addresses the data persistence problem in wireless sensor networks (WSNs) where static sinks are not present and the sensed data have to be temporarily but resiliently stored in the network. Based on the observation that sensor readings are correlated, we propose compressive data persistence (CDP) scheme that makes use of the compressive sensing (CS) theory. Each sensor node independently computes and stores a random projection of the sensed data, such that a mobile sink can recover the data with high probability after visiting a small and random portion of the network. As a prerequisite of distributed CS encoding, sensor readings from all nodes are disseminated within the network through random walk. Therefore, the CS measurement matrix depends heavily on how the random walk is performed. In this paper, we present an in-depth analysis on the interplay between random walk parameters and sensing data characteristics, and derive the conditions in successful CS data recovery. In addition, we discover that there is a trade-off between the number of random walk instances and steps in order to achieve the required data persistence performance. Experiments using real sensor data verify that the proposed CDP scheme achieves much lower decoding ratio than the state-of-the-art Fountain code based schemes or the decentralized erasure codes based schemes, and demonstrate that there exist energy-optimized random walk parameters for CDP.

Chaotic Compressed Sensing and Its Application to Magnetic Resonance Imaging

Fast image acquisition in magnetic resonance imaging (MRI) is important, due to the need to find ways that help relieve patient’s stress during MRI scans. Methods for fast MRI have been proposed, most notably among them are pMRI (parallel MRI), SWIFT (SWeep Imaging with Fourier Transformation), and compressed sensing (CS) based MRI. Although it promises to significantly reduce acquisition time, applying CS to MRI leads to difficulties with hardware design because of the randomness nature of the measurement matrix used by the conventional CS methods. In this paper, we propose a novel method that combines the above-mentioned three approaches for fast MRI by designing a compound measurement matrix from a series of single measurement matrices corresponding to pMRI, SWIFT, and CS. In our method, the CS measurement matrix is designed to be deterministic via chaotic systems. This chaotic compressed sensing (CCS) measurement matrix, while retaining most features of the random CS matrix, is simpler to realize in hardware. Several compound measurement matrices have been constructed and examined in this work, including CCS-MRI, CCS-pMRI, CCS-SWIFT, and CCS-pSWIFT. Simulation results showed that the proposed method allows an increase in the speed of the MRI acquisition process while not compromising the quality of the acquired MR images.

A Secure LFSR Based Random Measurement Matrix for Compressive Sensing

In this paper, a novel approach for generating the secure measurement matrix for compressive sensing (CS) based on linear feedback shift register (LFSR) is presented. The basic idea is to select the different states of LFSR as the random entries of the measurement matrix and normalize these values to get independent and identically distributed (i.i.d.) random variables with zero mean and variance \(\frac{1}{N}\), where N is the number of input samples. The initial seed for the LFSR system act as the key to the user to provide security. Since the measurement matrix is generated from the LFSR system, and memory overload to store the measurement matrix is avoided in the proposed system. Moreover, the proposed system can provide security maintaining the robustness to noise of the CS system. The proposed system is validated through different block-based CS techniques of images. To enhance security, the different blocks of images are measured with different measurement matrices so that the proposed encryption system can withstand known plaintext attack. A modulo division circuit is used to reseed the LFSR system to generate multiple random measurement matrices, whereby after each fundamental period of LFSR, the feedback polynomial of the modulo circuit is modified in terms of a chaotic value. The proposed secure robust CS paradigm for images is subjected to several forms of attacks and is proven to be resistant against the same. From experimental analysis, it is proven that the proposed system provides better performance than its counterparts.

Compressed Sensing Based Atomic Force Microscopy

The Atomic Force Microscope (AFM) is a powerful tool that has had a tremendous impact on the understanding of systems with nanometer-scale features. Efforts in improving the temporal resolution of the instrument have recently yielded high-speed AFMs with frame rates of approximately 10 frames per second. These instruments, however, achieve such speeds through various trade offs and as a result have limited imaging modes and scan sizes. In addition, despite these advances, typical commercial instruments continue to have frame rates well below one frame per second.This work develops and implements a novel sensing matrix for the application of compressed sensing (CS) to image acquisition in AFM, with the goal of improving the temporal resolution of the instrument by reducing the amount of data that needs to be acquired to create a high-quality image. In traditional CS, each measurement is, by design, a linear combination of the elements of the signal under study. In AFM however, the physics of the sensing process require that each measurement contains information about only a single point. The CS measurement matrix used here takes this into account and allows the user to balance image acquisition time against image quality. The proposed method is demonstrated through simulation. These simulations show faithful recovery with a reduction in imaging on the order of a factor of ten. By accepting a reduction in image reconstruction quality, additional gains in imaging time, up to a factor of twenty, were achieved.