Compressive Sensing Theory Research Articles

Compressive Sensing Hyperspectral Imaging by Spectral Multiplexing with Liquid Crystal.

Hyperspectral (HS) imaging involves the sensing of a scene’s spectral properties, which are often redundant in nature. The redundancy of the information motivates our quest to implement Compressive Sensing (CS) theory for HS imaging. This article provides a review of the Compressive Sensing Miniature Ultra-Spectral Imaging (CS-MUSI) camera, its evolution, and its different applications. The CS-MUSI camera was designed within the CS framework and uses a liquid crystal (LC) phase retarder in order to modulate the spectral domain. The outstanding advantage of the CS-MUSI camera is that the entire HS image is captured from an order of magnitude fewer measurements of the sensor array, compared to conventional HS imaging methods.

Echo Preprocessing to Enhance SNR for 2D CS-Based ISAR Imaging Method.

A new CS-based inverse synthetic aperture radar (ISAR) imaging framework is proposed to enhance both the image performance and the robustness at a low SNR. An ISAR echo preprocessing method for enhancing the ISAR imaging quality of compressed sensing (CS) based algorithms is developed by implementing matched filtering, echo denoising and matrix optimization sequentially. After the preprocessing, the two-dimensional (2D) SL0 algorithm is applied to reconstruct an ISAR image in the range and cross-range plane through a series of 2D matrices using the 2D CS theory, rather than converting the 2D convex optimization problem to the one-dimensional (1D) problem in the image reconstruction process. The proposed preprocessing framework is verified by simulations and experiment. Simulations and experimental results show that the ISAR image obtained by the 2D sparse recovery algorithm with our proposed method has a better performance.

Fragile watermarking for copyright authentication and tamper detection of medical images using compressive sensing (CS) based encryption and contourlet domain processing

With the rapid growth in communication and computing technologies, transmission of digital images and medical images over the Internet is on the rise. In such scenario, there is a special need to meet the security and privacy issues and challenges of an individual and Intellectual Property (IP) owners. It is highly important for an individual to keep his/her personal images against invalid manipulation by the impostors. Hence developments of authentication and tamper detection techniques are the need of the hour. In this paper, a new hybrid non-blind fragile watermarking technique is proposed for tamper detection of images and for securing the copyrights of sensitive images. A combination of Compressive Sensing (CS) theory, Discrete Wavelet Transform (DWT), and Non-Subsampled Contourlet Transform (NSCT) are employed to achieve security, high embedding capacity, and authenticity. In this technique, the requirements are achieved by inserting encrypted watermark in lower frequency contourlet coefficients of cover images. The experimental results prove that this proposed technique provides high security, high imperceptibility, authenticity and tamper detection of various common signal processing and geometrical attacks.

Single‐pixel compressive imaging based on motion compensation

Compressive sensing (CS) theory enables single-pixel compressive imaging (SPCI) popular in optical remote sensing imaging, since single-pixel imager not only realises the acquisition and recovery of sparse images at the sampling rates significantly below the classical Nyquist rate, but also makes use of special detectors to improve sensitivity, dynamic range, spectral range and so on. However, its requirement of static imaging condition for the time-sequential measurements makes it difficult to apply in remote sensing, since the imaging platform is always in motion relative to the imaging scene. In this study, the authors develop a new method for SPCI on moving platform in optical remote sensing. Instead of ignoring the motion during sampling, the proposed method first builds the compressive sampling model based on motion compensation during sampling, and then reconstructs the image by frame-by-frame recovery method and joint recovery method, respectively, in the framework of CS theory, where the recovery condition is also analysed. To validate the basic principle and the physical feasibility of motion compensation, the authors implement the numerical simulations and optical experiments, where different conditions are exploited sufficiently. In addition, the proposed method for SPCI can be also extended into other applications, such as 360° annular imaging, multi-pixel compressive imaging as well as super-resolution imaging.

A Reversed Visible Light Multitarget Localization System via Sparse Matrix Reconstruction

A reversed indoor multitarget localization system employing compressive sensing (CS) theory is proposed for the first time in terms of visible light positioning (VLP). Unlike conventional VLP systems, where targets process the received light signals to localize themselves, our system works reversely by using multiple photodiodes (PDs) mounted on the ceiling to localize mobile targets that carry light emitting diodes. By utilizing its nature of sparsity, the problem of multitarget localization is formulated as a problem of sparse matrix reconstruction, and a 3-step workflow is developed to solve the problem. In this workflow, first, a sensing matrix is redesigned by using QR decomposition to enable CS theory. Next, the conventional l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -minimization (l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> M) algorithm which is highly vulnerable to noise in solving a localization problem is theoretically analyzed and subsequently improved by adopting a reweighted l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> M approach. Finally, a subgrid localization algorithm is proposed to overcome a common unpractical assumption of on-grid locations, tackle the false peak problem in sparse matrix reconstruction, and ultimately improve the localization precision. The feasibility of our system and supporting algorithms is verified through extensive simulations. Our system demonstrates a good positioning accuracy of 7.4 cm by using 25 PDs when SNR = 20 dB. We also investigate the impact of various factors on the positioning performance, and the obtained results provide an insightful reference paving the way to a practical system design.

Radar pulse completion and high‐resolution imaging with SAs based on reweighted ANM

In actual condition, array elements deficiency or transmission errors lead to incomplete data, which is called sparse aperture (SA) data. In inverse synthetic aperture radar (ISAR) imaging, this large-gaped data produces poor-quality ISAR images when using traditional range–Doppler algorithm. Recently, imaging algorithms based on compressed sensing (CS) theory alleviate this problem effectively because CS theory indicates that sparse signal can be reconstructed from incomplete measurements. However, the basis mismatch problem in CS-based algorithms may degrade the ISAR image. In this study, a reweighted atomic-norm minimisation (ANM) (RAM)-based imaging method is proposed. RAM is a gridless sparse method, which can enhance sparsity and resolution. RAM formulates an optimisation problem and iteratively carries out ANM with a sound reweighting strategy. By reformulating the RAM as a semi-definite programme, the echoes with full aperture (FA) are reconstructed from SA data. After that, ISAR imaging with the reconstructed FA data is achieved via the conventional azimuth compression method. Simulated and real data results demonstrate the effectiveness and superiority of the proposed method.

Measurement matrix design for sparse spatial spectrum estimation in Khatri-Rao subspace

Compressive (or namely compressed) sensing (CS) exhibits superior performance in sparse spatial spectrum estimation from a predefined vandermonde based dictionary. The CS theory requires that dictionary is as incoherent (orthogonal) as possible since the number of atoms is generally much more than observation vectors, and, namely, the dictionary is over-complete or redundant. Previous researches focus on designing sensing matrix to reduce the mutual coherence of dictionary. However, according to Grassmannian frames, it is still a problem that the coherence of a given dictionary is hard to break through an equiangular tight frame (ETF). To address the problem, we proposed and proved a KR-KSVD method to break through the original lower bound of mutual coherence. In the Khatri-Rao subspace, measurement matrix is designed by minimizing the cost function between the Gram matrix of the equivalent dictionary and an identity matrix with the KSVD method. Simulations demonstrate that the method can produce a better performance in terms of mutual coherence property and sparse recovery accuracy.Compressive (or namely compressed) sensing (CS) exhibits superior performance in sparse spatial spectrum estimation from a predefined vandermonde based dictionary. The CS theory requires that dictionary is as incoherent (orthogonal) as possible since the number of atoms is generally much more than observation vectors, and, namely, the dictionary is over-complete or redundant. Previous researches focus on designing sensing matrix to reduce the mutual coherence of dictionary. However, according to Grassmannian frames, it is still a problem that the coherence of a given dictionary is hard to break through an equiangular tight frame (ETF). To address the problem, we proposed and proved a KR-KSVD method to break through the original lower bound of mutual coherence. In the Khatri-Rao subspace, measurement matrix is designed by minimizing the cost function between the Gram matrix of the equivalent dictionary and an identity matrix with the KSVD method. Simulations demonstrate that the method can produce a better...

Pilot design for sparse MIMO-OFDM channel estimation with generalized shift invariance property

Compressed sensing (CS) based channel estimation is greatly bound by the measurement matrix according to CS theory. We design pilot patterns by minimizing the mutual coherence of the measurement matrix with the generalized shift invariance property (GSIP). GSIP and a corollary are firstly proposed. Then two pilot pattern design schemes termed pilot design with GSIP (PDGSIP) and tradeoff pilot design with GSIP (TPDGSIP) are put forward to design orthogonal pilot patterns based on GSIP for a multiple-input multiple-output orthogonal frequency division multiplexing system. In PDGSIP, a collection of pilot patterns are firstly obtained and then pilot patterns having large mutual coherence are replaced with new ones generated with optimal pilot patterns. TPDGSIP directly produces new pilot patterns based on GSIP to fully exploit the pilot distance of the obtained pilot pattern as soon as one pilot pattern is obtained. Simulation results have shown that, the proposed pilot pattern design schemes are able to obtain the best pilot patterns in comparison to existing methods from the perspective of mutual coherence. Channel estimation performance using pilot patterns designed by proposed schemes precedes that using pilot patterns designed by existing schemes in terms of normalized mean square error and bit error rate.

Detection Efficiency of Signal with Unknown Non-Power Parameter Using Algorithms Based on the Compressive Sensing Theory

The problem of detecting quasi-deterministic signals against the background of noise during the digital processing has been considered. In this case, at the specified detection efficiency, the minimum criterion of required arithmetic operations was used as a synthesis criterion for such algorithms. To this end, such algorithms were synthesized based on concepts of the compressive sensing theory. The computer simulation was used to check the efficiency of developed algorithms making it possible to determine the manner in which the total probability of detection errors depends on the signal-to-noise ratio and the compression ratio (ratio of the number of elements in the sufficient statistic vectors before and after “compression”). The detection efficiency losses of proposed algorithms were determined in comparison with the classical optimal algorithm in accordance with the maximum likelihood method at different values of signal-to-noise ratio and compression ratio. At the same time, the paper indicates the gain in the number of used arithmetic operations of proposed algorithms as compared to the classical one. The presented results allow us to make a sound choice of detection algorithm depending on the available hardware resources and admissible degradation of the detection efficiency.

Sub-Nyquist Sampling and Parameters Estimation of Wideband LFM Signals Based on FRFT

Last years, most sub-Nyquist sampling and parameters estimation methods for linear frequency modulated (LFM) signals are based on compressed sensing (CS) theory. However, nearly all CS reconstruction algorithms are with high computational complexity and difficult to be implemented in hardware. In this paper, a novel framework of sub-Nyquist sampling and low-complexity parameters estimation for LFM signals is proposed. The incoherent sampling in CS theory is introduced into the construction of sub-Nyquist sampling system, but no CS reconstruction algorithm is employed in the estimation of parameters. Based on the energy aggregation of LFM signals in the proper fractional Fourier transform (FRFT) domain, the chirp rate and center frequency can be estimated by linear operations. Accordingly, the proposed estimation method is easily realized compared with existing estimation methods based on CS. Simulation results verify its effectiveness and accuracy.

Accurate Sparse Recovery of Rayleigh Wave Characteristics Using Fast Analysis of Wave Speed (FAWS) Algorithm for Soft Soil Layers

This paper presents a novel fast analysis of wave speed (FAWS) algorithm from the waveforms recorded by a random-spaced geophone array based on a compressive sensing (CS) platform. Rayleigh-type seismic surface wave testing is excited by a hammer source and conducted to develop the phase velocity characteristics of the subsoil layers in Shenyang Metro line 9. Data are filtered by a bandpass filter bank to pursue the dispersive profiles of phase velocity at various frequencies. The Rayleigh-type surface-wave dispersion curve for the soil layers at each frequency is conducted by the ℓ1-norm minimization algorithm of CS theory. The traditional frequency-wavenumber transform technique and in-site downhole observation are employed as the comparison of the proposed technique. The experimental results indicate the proposed FAWS algorithm has a good agreement with both the results of conventional even-spaced geophone array and the in-site measurements, which provides an effective and efficient way for accurate non-destructive evaluation of the surface wave dispersion curve of the soil.

WBAN node sleep strategy and energy conservation method based on data compression

Wireless Body Area Network (WBAN) node is usually powered by batteries, which is energy limited and not easy to change frequently. A data compression energy-saving method is proposed to reduce the energy consumption of WBAN node, adopting Sparse Representation Classification (SRC) algorithm to identify the normal signal, using Compressed Sensing (CS) theory for signal compression sampling, and the compressed signal is sent to the base station for reconstruction. When the physiological signals collected by WBAN nodes are in the normal range, need not to transmit normal signals, and make nodes convert into a sleep state to prolong the sleep time of nodes and reduce the amount of transmitting data, thus the node energy consumption can be reduced. The simulation and analysis have been implemented on Electrocardiogram (ECG) signal, the results shows that the ECG signal after compression, has good recognition performance and reconstruction performance, and reduces the amount of data acquisition and transmission, effectively reduce the energy consumption of WBAN nodes.

Analysis of the Reconstruction of Sparse Signals in the DCT Domain Applied to Audio Signals

Sparse signals can be reconstructed from a reduced set of signal samples using compressive sensing (CS) methods. The discrete cosine transform (DCT) can provide highly concentrated representations of audio signals. This property implies the DCT as a good sparsity domain for the audio signals. In this paper, the DCT is studied within the context of sparse audio signal processing using the CS theory and methods. The DCT coefficients of a sparse signal, calculated with a reduced set of available samples, can be modeled as random variables. It has been shown that the statistical properties of these variables are closely related to the unique reconstruction conditions. The main result of this paper is in an exact formula for the mean-square reconstruction error in the case of approximately sparse and nonsparse noisy signals reconstructed under the sparsity assumption. Based on the presented analysis, a simple and computationally efficient reconstruction algorithm is proposed. The presented theoretical concepts and the efficiency of the reconstruction algorithm are verified numerically, including examples with synthetic and recorded audio signals with unavailable or corrupted samples. Random disturbances and disturbances simulating clicks or inpainting in audio signals are considered. Statistical verification is done on a dataset with experimental signals. Results are compared with some classical and recent methods used in similar signal and disturbance scenarios.

Compressive Sensing Based Multilevel Fast Multipole Acceleration for Fast Scattering Center Extraction and ISAR Imaging.

In recent years, Compressive Sensing (CS) theory has been very popular in the data sensing and process area as it utilizes the sparsity and measurement matrix to reconstruct the compressible signal from limited samples successfully. In this paper, CS is introduced into an efficient numerical method, multilevel fast multipole acceleration (MLFMA), for the electromagnetic (EM) scattering problem over a wide incident angle. This allows composition of a new kind of incident wave, which obtains efficient and reliable data for scattering centers extraction with low complexity. The resulting data from CS-based MLFMA are processed for ISAR) imaging. Simulation results show the received data for ISAR imaging from MLFMA with CS can outperform the data from MLFMA, which achieves a similar quality of ISAR imaging. Additionally, the computation complexity is improved by CS through the reduced matrix computation for fewer incident waves. It makes ISAR imaging using real data feasible and meaningful.

Energy Efficient GNSS Signal Acquisition Using Singular Value Decomposition (SVD).

A significant challenge in global navigation satellite system (GNSS) signal processing is a requirement for a very high sampling rate. The recently-emerging compressed sensing (CS) theory makes processing GNSS signals at a low sampling rate possible if the signal has a sparse representation in a certain space. Based on CS and SVD theories, an algorithm for sampling GNSS signals at a rate much lower than the Nyquist rate and reconstructing the compressed signal is proposed in this research, which is validated after the output from that process still performs signal detection using the standard fast Fourier transform (FFT) parallel frequency space search acquisition. The sparse representation of the GNSS signal is the most important precondition for CS, by constructing a rectangular Toeplitz matrix (TZ) of the transmitted signal, calculating the left singular vectors using SVD from the TZ, to achieve sparse signal representation. Next, obtaining the M-dimensional observation vectors based on the left singular vectors of the SVD, which are equivalent to the sampler operator in standard compressive sensing theory, the signal can be sampled below the Nyquist rate, and can still be reconstructed via minimization with accuracy using convex optimization. As an added value, there is a GNSS signal acquisition enhancement effect by retaining the useful signal and filtering out noise by projecting the signal into the most significant proper orthogonal modes (PODs) which are the optimal distributions of signal power. The algorithm is validated with real recorded signals, and the results show that the proposed method is effective for sampling, reconstructing intermediate frequency (IF) GNSS signals in the time discrete domain.

An Energy-Efficient Compressive Image Coding for Green Internet of Things (IoT).

Aimed at a low-energy consumption of Green Internet of Things (IoT), this paper presents an energy-efficient compressive image coding scheme, which provides compressive encoder and real-time decoder according to Compressive Sensing (CS) theory. The compressive encoder adaptively measures each image block based on the block-based gradient field, which models the distribution of block sparse degree, and the real-time decoder linearly reconstructs each image block through a projection matrix, which is learned by Minimum Mean Square Error (MMSE) criterion. Both the encoder and decoder have a low computational complexity, so that they only consume a small amount of energy. Experimental results show that the proposed scheme not only has a low encoding and decoding complexity when compared with traditional methods, but it also provides good objective and subjective reconstruction qualities. In particular, it presents better time-distortion performance than JPEG. Therefore, the proposed compressive image coding is a potential energy-efficient scheme for Green IoT.

Enhancing the image resolution in a single-pixel sub-THz imaging system based on compressed sensing

Compressed sensing (CS) techniques allow for faster imaging when combined with scan architectures, which typically suffer from speed. This technique when implemented with a subterahertz (sub-THz) single detector scan imaging system provides images whose resolution is only limited by the pixel size of the pattern used to scan the image plane. To overcome this limitation, the image of the target can be oversampled; however, this results in slower imaging rates especially if this is done in two-dimensional across the image plane. We show that by implementing a one-dimensional (1-D) scan of the image plane, a modified approach to CS theory applied with an appropriate reconstruction algorithm allows for successful reconstruction of the reflected oversampled image of a target placed in standoff configuration from the source. The experiments are done in reflection mode configuration where the operating frequency is 93 GHz and the corresponding wavelength is λ = 3.2 mm. To reconstruct the image with fewer samples, CS theory is applied using masks where the pixel size is 5 mm × 5 mm, and each mask covers an image area of 5 cm × 5 cm, meaning that the basic image is resolved as 10 × 10 pixels. To enhance the resolution, the information between two consecutive pixels is used, and oversampling along 1-D coupled with a modification of the masks in CS theory allowed for oversampled images to be reconstructed rapidly in 20 × 20 and 40 × 40 pixel formats. These are then compared using two different reconstruction algorithms, TVAL3 and l1-MAGIC. The performance of these methods is compared for both simulated signals and real signals. It is found that the modified CS theory approach coupled with the TVAL3 reconstruction process, even when scanning along only 1-D, allows for rapid precise reconstruction of the oversampled target.

Application of Adaptive Recovery CAMP Reconstruction Algorithm in Compressing Sensing Radar Signal Processing

Compressive Sensing (CS) theory uses the sparsity property in pulsed radar signal to reduce the number of measurements needed for digital acquisition, which causes reduction in the size, weight, power consumption, and cost [1-3]. A proposed adaptive recovery Complex Approximate Massage Passing (CAMP) reconstruction algorithm was introduced by the authors in [4] to enhance the detection performance of pulsed radar receiver compared to the traditional CAMP algorithm. In the present work, this proposed algorithm is used in pulsed radar receiver to resolve the limitation of the number of detected targets in the traditional CAMP algorithm with a remarkable reduction in time complexity.

Scattering Estimation for Cone-Beam CT Using Local Measurement Based on Compressed Sensing

Cone-beam computed tomography (CBCT) plays a critical role in both medical imaging and industrial nondestructive testing with high efficiency and precision. However, scattering poses a significant limitation to image quality. In order to get the complete scattering information when the object is scanned, a simple scattering correction method based on compressed sensing (CS) is proposed, which is based on the assumption that the object scattering (OS) is eliminated by the lead collimator. In the process, the additional scattering from shadow area is first estimated, and then the OS is obtained by using the information in the irradiated area (with the strips pattern) extracted from the primary projection (without the strips pattern). Then, the estimated scatterings are subtracted from each primary projection data to yield an estimate for CBCT reconstruction, and the scattering-corrected CBCT volume is reconstructed by using an alternating direction method of multipliers algorithm. Finally, experimental studies are performed to evaluate the performance of the proposed schemes which has reduced the scattering artifacts. For an aluminum sample, the average gradient (AG) and contrast-to-noise ratio (CNR) were increased by 60% and 80%; for titanium, the AG and signal-to-noise ratio (SNR) were increased by 60% and 20%; and for iron, the AG, CNR, and SNR were increased by 30%–50%. Moreover, this paper studies long-span information sensing by replacing the interpolation algorithm with CS theory; it can provide a certain theoretical guidance for the sparse data recovery and mining.

Performance Improvement of Wireless Multimedia Sensor Networks Using MIMO and Compressive Sensing

Wireless Multimedia Sensor Networks (WMSN) are designed to transmit audio and video streams, still images, and scalar data. Multimedia transmission over wireless sensor networks has many applications, such as video surveillance, object tracking, telemedicine, theft control systems, and traffic monitoring. Researchers face many challenges, such as higher data rates, lower energy consumption, reliability, signal detection and estimation, uncertainty in network topology, quality of service (QoS), and security-and privacy-related issues to accomplish various applications of WMSN. This paper presents multiple input multiple output (MIMO) along with compressive sensing (CS) properties to improve system performance in terms of energy consumption and QoS in deep fade environments. The CS theory model has been proposed to reduce energy consumption by taking fewer measurements of the original signal or information and reconstructing it with acceptable image quality at the receiver side. The transmission and processing energy can be reduced by transmitting fewer measurements from the sensor side itself. The MIMO model and CS algorithm have been simulated, and results show that CS performs well on images.