Compressive Sensing Measurement Matrix Research Articles

Multi-wavelength single-pixel non-line-of-sight imaging with a compressive sensing measurement matrix

Multi-wavelength single-pixel non-line-of-sight imaging with a compressive sensing measurement matrix

Design, implementation, and analysis of a compressed sensing photoacoustic projection imaging system.

Compressed sensing (CS) uses special measurement designs combined with powerful mathematical algorithms to reduce the amount of data to be collected while maintaining image quality. This is relevant to almost any imaging modality, and in this paper we focus on CS in photoacoustic projection imaging (PAPI) with integrating line detectors (ILDs). Our previous research involved rather general CS measurements, where each ILD can contribute to any measurement. In the real world, however, the design of CS measurements is subject to practical constraints. In this research, we aim at a CS-PAPI system where each measurement involves only a subset of ILDs, and which can be implemented in a cost-effective manner. We extend the existing PAPI with a self-developed CS unit. The system provides structured CS matrices for which the existing recovery theory cannot be applied directly. A random search strategy is applied to select the CS measurement matrix within this class for which we obtain exact sparse recovery. We implement a CS PAPI system for a compression factor of 4:3, where specific measurements are made on separate groups of 16 ILDs. We algorithmically design optimal CS measurements that have proven sparse CS capabilities. Numerical experiments are used to support our results. CS with proven sparse recovery capabilities can be integrated into PAPI, and numerical results support this setup. Future work will focus on applying it to experimental data and utilizing data-driven approaches to enhance the compression factor and generalize the signal class.

Real-Time Data Sensing for Microseismic Monitoring via Adaptive Compressed Sampling

The large amount of monitoring data has posed enormous challenges to the quick response and accurate analysis of microseismic events. Compressed sensing (CS) has the advantages of low resource cost, high efficiency, and excellent data compression ratio, over conventional sensing methods. However, there are still issues to be addressed for its applications: 1) The poor quality and complex signal structure significantly increased the difficulty of keeping satisfactory efficiency; 2) The systematic design of the sparse dictionary, and the measurement matrix for microseismic signal CS are still poor; 3) The conventional recovery algorithms also require prior knowledge of signal sparsity, which is hardly possible to know or estimate in practice. Therefore, an adaptive realtime sensing method for microseismic monitoring from the perspective of systematic design was proposed in this work. We first analyzed noise and signal structure characteristics to construct an over-complete learning dictionary. Secondly, according to the learned dictionary, we analyzed the key performance factors of random projection through comparison between different matrices. Thirdly, we explored the relationship between the signal sparsity and the residual energy decay during data recovery with the greedy pursuit algorithms, and then presented an energy-ratio based sparsity adaptive matching algorithm. Finally, we carried out the performance evaluation of the proposed realtime sensing method through synthetic signals and field monitoring data.

Deterministic Construction of Compressed Sensing Measurement Matrix with Arbitrary Sizes via QC-LDPC and Arithmetic Sequence Sets

It is of great significance to construct deterministic measurement matrices with good practical characteristics in Compressed Sensing (CS), including good reconstruction performance, low memory cost and low computing resources. Low-density-parity check (LDPC) codes and CS codes can be closely related. This paper presents a method of constructing compressed sensing measurement matrices based on quasi-cyclic (QC) LDPC codes and arithmetic sequence sets. The cyclic shift factor in each submatrix of QC-LDPC is determined by arithmetic sequence sets. Compared with random matrices, the proposed method has great advantages because it is generated based on a cyclic shift matrix, which requires less storage memory and lower computing resources. Because the restricted isometric property (RIP) is difficult to verify, mutual coherence and girth are used as computationally tractable indicators to evaluate the measurement matrix reconstruction performance. Compared with several typical matrices, the proposed measurement matrix has the minimum mutual coherence and superior reconstruction capability of CS signal according to one-dimensional (1D) signals and two-dimensional (2D) image simulation results. When the sampling rate is 0.2, the maximum (minimum) gain of peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) is up to 2.89 dB (0.33 dB) and 0.031 (0.016) while using 10 test images. Meanwhile, the reconstruction time is reduced by nearly half.

Exploiting 3D fractal cube and chaos for effective multi-image compression and encryption

At present, some image compression and encryption algorithms have been presented to protect digital images by combining chaos and compressed sensing (CS). However, some of them still suffer from security and efficiency shortcomings. To solve these issues, a multi-image compression and encryption based on 3D fractal cube, CS and chaos is introduced in this paper. Firstly, the multiple plain images are sparsified by the Haar Wavelet Transform (HWT), and measured by CS to obtain the measurement value matrices. Herein, a four-wing hyperchaotic system is adopted to generate the measurement matrix for CS. Subsequently, a 3D fractal cube (3D-FC) is defined and generated iteratively by constructing the initial 3D-FC. Based on it, the obtained measurement value matrices are shuffled to reduce the high correlation between the adjacent pixels. Next, the cipher images are obtained after the cipher-associated adaptive diffusion based on GF (28) is performed on the confused image. Moreover, we have conducted extensive experiments to verify the encryption efficiency, compression performance, and security. Both simulation results and performance analysis confirm that the present algorithm has satisfactory performance in these aspects.

Application of Compressive Sensing in the Presence of Noise for Transient Photometric Events

Compressive sensing is a simultaneous data acquisition and compression technique, which can significantly reduce data bandwidth, data storage volume, and power. We apply this technique for transient photometric events. In this work, we analyze the effect of noise on the detection of these events using compressive sensing (CS). We show numerical results on the impact of source and measurement noise on the reconstruction of transient photometric curves, generated due to gravitational microlensing events. In our work, we define source noise as background noise, or any inherent noise present in the sampling region of interest. For our models, measurement noise is defined as the noise present during data acquisition. These results can be generalized for any transient photometric CS measurements with source noise and CS data acquisition measurement noise. Our results show that the CS measurement matrix properties have an effect on CS reconstruction in the presence of source noise and measurement noise. We provide potential solutions for improving the performance by tuning some of the properties of the measurement matrices. For source noise applications, we show that choosing a measurement matrix with low mutual coherence can lower the amount of error caused due to CS reconstruction. Similarly, for measurement noise addition, we show that by choosing a lower expected value of the binomial measurement matrix, we can lower the amount of error due to CS reconstruction.

Compressed and Encrypted Acquisition of Transient Signals

A shockwave signal has the characteristics of short duration and wide dynamic range, so the wireless test system needs to collect it at a continuous high sampling rate, resulting in a short node life cycle and a large amount of redundant data during the test process. Moreover, test data with confidentiality, if it is still recorded and transmitted in plaintext, will challenge information security. Therefore, a compressed and encrypted acquisition framework based on hyperchaotic compressed sensing and semi-tensor is proposed in this paper. Firstly, a new four-dimensional hyperchaotic system is used to generate a compressed sensing measurement matrix to improve the encryption and anti-noise performance. Secondly, for saving memory space and improving computing efficiency, the semi-tensor product is introduced to reduce the dimension of the measurement matrix exponentially. The experimental results show that the proposed framework can realize the compressed and encrypted acquisition of transient signals with small memory space and low computational complexity. And the acquisition results can be directly transmitted to meet the requirements of real-time wireless transmission bandwidth and information security.

An Image Compression Encryption Algorithm Based on Chaos and ZUC Stream Cipher.

In order to improve the transmission efficiency and security of image encryption, we combined a ZUC stream cipher and chaotic compressed sensing to perform image encryption. The parallel compressed sensing method is adopted to ensure the encryption and decryption efficiency. The ZUC stream cipher is used to sample the one-dimensional chaotic map to reduce the correlation between elements and improve the randomness of the chaotic sequence. The compressed sensing measurement matrix is constructed by using the sampled chaotic sequence to improve the image restoration effect. In order to reduce the block effect after the parallel compressed sensing operation, we also propose a method of a random block of images. Simulation analysis shows that the algorithm demonstrated better encryption and compression performance.

A Compressed Sensing Measurement Matrix Construction Method Based on TDMA for Wireless Sensor Networks.

Compressed sensing theory has been widely used for data aggregation in WSNs due to its capability of containing much information but with light load of transmission. However, there still exist some issues yet to be solved. For instance, the measurement matrix is complex to construct, and it is difficult to implement in hardware and not suitable for WSNs with limited node energy. To solve this problem, a random measurement matrix construction method based on Time Division Multiple Access (TDMA) is proposed based on the sparse random measurement matrix combined with the data transmission method of the TDMA of nodes in the cluster. The reconstruction performance of the number of non-zero elements per column in this matrix construction method for different signals was compared and analyzed through extensive experiments. It is demonstrated that the proposed matrix can not only accurately reconstruct the original signal, but also reduce the construction complexity from to (), on the premise of achieving the same reconstruction effect as that of the sparse random measurement matrix. Moreover, the matrix construction method is further optimized by utilizing the correlation theory of nested matrices. A TDMA-based semi-random and semi-deterministic measurement matrix construction method is also proposed, which significantly reduces the construction complexity of the measurement matrix from to , and improves the construction efficiency of the measurement matrix. The findings in this work allow more flexible and efficient compressed sensing for data aggregation in WSNs.

Hyperspectral Acquisition Technology Based on Compressed Sampling in Spatial Domain

In the hyperspectral imaging device, the sensor detects the reflection or radiation intensity of the target at hundreds of different wavelengths, thus forming a spectral image composed of hundreds of continuous bands. The traditional processing method of sampling first and then compressing not only cannot fundamentally solve the problem of huge amount of data, but also causes waste of resources. To solve this problem, a spectral image reconstruction method based on compressed sampling in spatial domain and transform coding in spectral domain is designed by using the sparsity of single-band two-dimensional image and the spectral redundancy of spatial coded data. Based on Bayesian theory, a compressed sensing measurement matrix of adaptive projection is proposed. Combining these two algorithms, an adaptive Grouplet-FBCS algorithm is constructed to reconstruct the image using smooth projection Landweber. Experimental results show that, compared with existing image block compression sensing algorithms, this algorithm can significantly improve the quality of image signal reconstruction.

A compressive sensing measurement matrix for image signal

A compressive sensing measurement matrix for image signal

Neural network learning of improved compressive sensing sampling and receptive field structure

While the theory of compressive sensing (CS) in modern signal processing typically indicates that uniformly random sampling facilitates the efficient recovery of sparse signals, such measurements are infeasible in many engineering applications and are not well reflected by the constraints of natural systems, including neuronal networks in the brain. Uniformly random sampling also does not leverage the underlying structure of many classes of signals, and may therefore be suboptimal in these cases. We address these issues by formulating a novel neural network framework for learning improved CS sampling based on the intrinsic structure present in classes of training signals. Beyond sparsity in an appropriate domain, this approach does not assume knowledge of any specific signal statistics and is purely data-driven. The learning methodology is biologically realistic in that it utilizes (1) asymmetric feedback and feedforward connections in the neural network and (2) only information from adjacent layers in training the CS measurement matrix. Observing a broad spectrum of learned sampling paradigms that improve CS signal reconstructions relative to uniformly random sampling, our learned sampling is widely applicable across logistical constraints. Motivated by the receptive field structure of sensory systems, we specifically analyze natural scene inputs and demonstrate improved CS reconstruction as a result of training across several choices of penalization schemes on the sampling weights. Considering this learning is effective even under sparse and spatially localized constraints, as commonly observed in the brain, we hypothesize that neuronal connectivity may have manifested with the aim of providing a compressive encoding of data by leveraging its sparse structure, thereby achieving efficient signal transmission.

Adaptive Non-Uniform Compressive Sensing Using SOT-MRAM Multi-Bit Precision Crossbar Arrays

A Compressive Sensing (CS) approach is applied to utilize intrinsic computation capabilities of Spin-Orbit Torque Magnetic Random Access Memory (SOT-MRAM) devices for IoT applications wherein lifetime energy, device area, and manufacturing costs are highly-constrained while the sensing environment varies rapidly. In this manuscript, we propose the Adaptive Compressed-sampling via Multi-bit Crossbar Array (ACMCA) approach to intelligently generate the CS measurement matrix using a multi-bit SOT-MRAM crossbar array. SPICE circuit and MATLAB algorithm simulation results indicate that ACMCA reduces reconstruction error by up to 4dB using a 4-bit quantized CS measurement matrix while incurring a negligible increase in the energy consumption of generating the matrix. Additionally, we introduce an algorithm called Energy-aware Adaptive Sensing for IoT (EASI) which determines the frequency of measurement matrix updates within the energy budget of an IoT device.

Research and application of pseudorandom sequence based on Xor

Abstract In order to solve the problems of simple, low complexity and weak confidentiality in the generation of single chaotic sequence, a new chaotic sequence generation method based on xor was proposed by adding chaotic sequences generated by Logistic mapping and Chebyshev mapping. We analyze and study the chaotic sequences generated by the algorithm through computer simulation. The correlation, pseudo-randomness and balance of the new chaotic sequence generated by this method are studied and tested. Simulation results show that the generated chaotic sequences have a good pseudorandom performance, correlation performance, and balance performance. Therefore, the new chaotic sequence is suitable for the construction of compressive sensing measurement matrix, and the accurate reconstruction of one-dimension signal can be realized by the Mixed Chaotic - Bernoulli matrix (MCB).

Learning‐based design of random measurement matrix for compressed sensing with inter‐column correlation using copula function

In this work, a novel learning-based approach for the design of a compressed sensing measurement matrix is proposed. In contrast with the state-of-the-art methods, the suggested approach takes into account the correlation within entries of each column of the measurement matrix, namely, the inter-column correlation (ICC). The new method makes use of a rather small number of training sparse signal vectors in a recursive scheme to obtain their corresponding measurement vectors. The latter is exploited to estimate the copula function of measurements which, in turn, is used to generate an arbitrary number of measurement vector ensembles. By using the latter, the autocorrelation of the measurement vectors is estimated precisely and then, the ICC of measurement matrix under design is obtained from the autocorrelation. Given the resulting ICC, the measurement matrix columns are to be generated independently, e.g. by employing a proper random Gaussian vector generator. Performance evaluations using both synthetic and real-world data confirm the superiority of the proposed approach to the less recent methods.

Optimization Methods of Compressively Sensed Image Reconstruction Based on Single-Pixel Imaging

According to the theory of compressive sensing, a single-pixel imaging system was built in our laboratory, and imaging scenes are successfully reconstructed by single-pixel imaging, but the quality of reconstructed images in traditional methods cannot meet the demands of further engineering applications. In order to improve the imaging accuracy of our single-pixel camera, some optimization methods of key technologies in compressive sensing are proposed in this paper. First, in terms of sparse signal decomposition, based on traditional discrete wavelet transform and the characteristics of coefficients distribution in wavelet domain, a constraint condition of the exponential decay is proposed and a corresponding constraint matrix is designed to optimize the original wavelet decomposition basis. Second, for the construction of deterministic binary sensing matrices in the single-pixel camera, on the basis of a Gram matrix, a new algorithm model and a new method of initializing a compressed sensing measurement matrix are proposed to optimize the traditional binary sensing matrices via mutual coherence minimization. The gradient projection-based algorithm is used to solve the new mathematical model and train deterministic binary sensing measurement matrices with better performance. Third, the proposed optimization methods are applied to our single-pixel imaging system for optimizing the existing imaging methods. Compared with the conventional methods of single-pixel imaging, the accuracy of image reconstruction and the quality of single-pixel imaging have been significantly improved by our methods. The superior performance of our proposed methods has been fully tested and the effectiveness has also been demonstrated by numerical simulation experiments and practical imaging experiments.

Feature-Supervised Compressed Sensing for Microwave Imaging Systems

Traditional compressed sensing (CS) applications use sparse information for downsampling but ignore overall system objectives such as feature extraction. This article jointly designs the sensing and feature-extraction process to improve the efficiency of the microwave imaging systems in time, storage, and feature extraction. A feature-supervised CS (FsCS) is proposed for the cases where not all data contribute to feature extraction. Compared with the traditional spatial–spectral sweep and CS solutions, a feature constraint is added in designing the CS measurement matrix. More efficient sensing and feature extraction are achieved, because only the data contributing to feature extraction are sampled and reconstructed. To improve the time efficiency of CS reconstruction, an aligned spatial–spectral sensing (ASSS) is involved in FsCS to enable joint reconstruction. The proposed scheme is validated in an open-ended waveguide imaging system for low-energy impact damage feature detection. The experimental results demonstrate one order of magnitude improvement in time and two orders of improvement in the data compression ratio compared with the state-of-the-art method, while preserving the interested feature. This article can inspire the joint sensing-processing designs for more intelligent industrial processes.

Spatiotemporal Remote-Sensing Image Fusion With Patch-Group Compressed Sensing

Generally, it is difficult to acquire remote sensing data whose resolution is both highly spatial and highly temporal from a single satellite. In this paper, a novel compressed sensing (CS)-based spatiotemporal data fusion (CSBS) method is proposed to synthesize such high-spatiotemporal resolution images. With CSBS, a low-spatial resolution remote senisng image is treated as a sampling of the high-spatial resolution image. The down-sampling in the spatial domain of images is modeled as a CS measurement matrix in CSBS. Moreover, continuity constraints in the temporal domain are also introduced into the CSBS object function for CS reconstruction. To better represent the intrinsic features of the data, images are segmented into many small patches and clustered into several groups via K-means. Dictionary training, measurement matrix identification, and high-resolution prediction are carried out group-by-group. Based on features learned from patch groups, the transformational relationship between spatial-temporal images having different resolutions are easily identified. Compared with previous compressed sensing and dictionary learning methods, CSBS is characterized by: (1) the patch-group stratagem in dictionary learning and measurement matrix learning; (2) the combination of continuity in temporal domain and sparsity in spatial domain. The proposed method is then comprehensively compared with different methods using land-surface reflectance data. Experiment results validate the effectiveness and advancement of CSBS for spatiotemporal data fusion.

Exploiting joint sparsity for far-field microphone array sound source localization

The presence of far-field noise and reverberation poses significant challenges to the conventional microphone array sound source localization approaches. Consider the sparsity contained in the source direction vector, source localization can be transformed into a compressed sensing (CS) problem by constructing the redundancy frequency domain room impulse response (RIR) matrix as CS measurement matrix. In this paper a new sparse recovery model is derived by decomposing the RIR into delay response term and reverberation response term to facilitate reverberation mitigation via frequency domain accumulation. Furthermore, as the source direction vector of adjacent speech frames tends to exhibit similar sparse pattern, namely, the direction of source can be assumed to keep static within this short period, thus there exists substantial correlation of spatial sparsity among adjacent speech frames. In this paper, under the framework of distributed compressed sensing (DCS), multiple source direction vectors are treated as sparse solutions with common spatial support to derive a joint sparse recovery algorithm for far-field source localization. The experimental results obtained in the context of a uniform circle array (UCA) show that the proposed algorithm is capable of yielding better estimation performance compared with the traditional algorithms.

A High-Resolution Imaging Method for Strip-Map SAR With Missing Data

Due to the long aperture, the high-resolution imaging for strip-map SAR with missing data is a challenge, in which the range migration correction and phase error correction are challenging. In this paper, a high-resolution imaging method of this type of data based on compressed sensing (CS) is proposed, which divides the strip-map data into several sub-apertures restored by CS and recombined to the strip-map data. The basis matrix and the measurement matrix for CS are deduced. The sub-aperture data is autofocused by the Projection Approximation Subspace Tracking (PAST) algorithm to meet the sparse requirement for the reconstructed image and the intact phase error data is restored by CS in order to combine the sub-apertures. A high-resolution image of the restored data can be obtained by conventional imaging method which performs range migration and autofocus.