A Novel Complex-Valued Gaussian Measurement Matrix for Image Compressed Sensing.

The measurement matrix used influences the performance of image reconstruction in compressed sensing. To enhance the performance of image reconstruction in compressed sensing, two different Gaussian random matrices were orthogonalized via Gram-Schmidt orthogonalization, respectively. Then, one was used as the real part and the other as the imaginary part to construct a complex-valued Gaussian matrix. Furthermore, we sparsified the proposed measurement matrix to reduce the storage space and computation. The experimental results show that the complex-valued Gaussian matrix after orthogonalization has better image reconstruction performance, and the peak signal-to-noise ratio and structural similarity under different compression ratios are better than the real-valued measurement matrix. Moreover, the sparse measurement matrix can effectively reduce the amount of calculation.

Video Compressive Sensing Reconstruction Using Unfolded LSTM.

Video compression sensing can use a few measurements to obtain the original video by reconstruction algorithms. There is a natural correlation between video frames, and how to exploit this feature becomes the key to improving the reconstruction quality. More and more deep learning-based video compression sensing (VCS) methods are proposed. Some methods overlook interframe information, so they fail to achieve satisfactory reconstruction quality. Some use complex network structures to exploit the interframe information, but it increases the parameters and makes the training process more complicated. To overcome the limitations of existing VCS methods, we propose an efficient end-to-end VCS network, which integrates the measurement and reconstruction into one whole framework. In the measurement part, we train a measurement matrix rather than a pre-prepared random matrix, which fits the video reconstruction task better. An unfolded LSTM network is utilized in the reconstruction part, deeply fusing the intra- and interframe spatial-temporal information. The proposed method has higher reconstruction accuracy than existing video compression sensing networks and even performs well at measurement ratios as low as 0.01.

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 O(MN) to O(d2N) (d≪M), 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 O(d2N) to O(dN), 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.

Image Encryption Scheme Based on Mixed Chaotic Bernoulli Measurement Matrix Block Compressive Sensing.

Many image encryption schemes based on compressive sensing have poor reconstructed image quality when the compression ratio is low, as well as difficulty in hardware implementation. To address these problems, we propose an image encryption algorithm based on the mixed chaotic Bernoulli measurement matrix block compressive sensing. A new chaotic measurement matrix was designed using the Chebyshev map and logistic map; the image was compressed in blocks to obtain the measurement values. Still, using the Chebyshev map and logistic map to generate encrypted sequences, the measurement values were encrypted by no repetitive scrambling as well as a two-way diffusion algorithm based on GF(257) for the measurement value matrix. The security of the encryption system was further improved by generating the Secure Hash Algorithm-256 of the original image to calculate the initial values of the chaotic mappings for the encryption process. The scheme uses two one-dimensional maps and is easier to implement in hardware. Simulation and performance analysis showed that the proposed image compression-encryption scheme can improve the peak signal-to-noise ratio of the reconstructed image with a low compression ratio and has good encryption against various attacks.

A Method of Constructing Measurement Matrix for Compressed Sensing by Chebyshev Chaotic Sequence.

In this paper, the problem of constructing the measurement matrix in compressed sensing is addressed. In compressed sensing, constructing a measurement matrix of good performance and easy hardware implementation is of interest. It has been recently shown that the measurement matrices constructed by Logistic or Tent chaotic sequences satisfy the restricted isometric property (RIP) with a certain probability and are easy to be implemented in the physical electric circuit. However, a large sample distance that means large resources consumption is required to obtain uncorrelated samples from these sequences in the construction. To solve this problem, we propose a method of constructing the measurement matrix by the Chebyshev chaotic sequence. The method effectively reduces the sample distance and the proposed measurement matrix is proved to satisfy the RIP with high probability on the assumption that the sampled elements are statistically independent. Simulation results show that the proposed measurement matrix has comparable reconstruction performance to that of the existing chaotic matrices for compressed sensing.

Measurement Matrix Construction for Large-area Single Photon Compressive Imaging.

We have developed a single photon compressive imaging system based on single photon counting technology and compressed sensing theory, using a photomultiplier tube (PMT) photon counting head as the bucket detector. This system can realize ultra-weak light imaging with the imaging area up to the entire digital micromirror device (DMD) working region. The measurement matrix in this system is required to be binary due to the two working states of the micromirror corresponding to two controlled elements. And it has a great impact on the performance of the imaging system, because it involves modulation of the optical signal and image reconstruction. Three kinds of binary matrix including sparse binary random matrix, m sequence matrix and true random number matrix are constructed. The properties of these matrices are analyzed theoretically with the uncertainty principle. The parameters of measurement matrix including sparsity ratio, compressive sampling ratio and reconstruction time are verified in the experimental system. The experimental results show that, the increase of sparsity ratio and compressive sampling ratio can improve the reconstruction quality. However, when the increase is up to a certain value, the reconstruction quality tends to be saturated. Compared to the other two types of measurement matrices, the m sequence matrix has better performance in image reconstruction.

A Regularized Weighted Smoothed L0 Norm Minimization Method for Underdetermined Blind Source Separation.

Compressed sensing (CS) theory has attracted widespread attention in recent years and has been widely used in signal and image processing, such as underdetermined blind source separation (UBSS), magnetic resonance imaging (MRI), etc. As the main link of CS, the goal of sparse signal reconstruction is how to recover accurately and effectively the original signal from an underdetermined linear system of equations (ULSE). For this problem, we propose a new algorithm called the weighted regularized smoothed L 0 -norm minimization algorithm (WReSL0). Under the framework of this algorithm, we have done three things: (1) proposed a new smoothed function called the compound inverse proportional function (CIPF); (2) proposed a new weighted function; and (3) a new regularization form is derived and constructed. In this algorithm, the weighted function and the new smoothed function are combined as the sparsity-promoting object, and a new regularization form is derived and constructed to enhance de-noising performance. Performance simulation experiments on both the real signal and real images show that the proposed WReSL0 algorithm outperforms other popular approaches, such as SL0, BPDN, NSL0, and L p -RLSand achieves better performances when it is used for UBSS.

Adaptive Single Photon Compressed Imaging Based on Constructing a Smart Threshold Matrix.

We demonstrate a single-photon compressed imaging system based on single photon counting technology and compressed sensing theory. In order to cut down the measurement times and shorten the imaging time, a fast and efficient adaptive sampling method, suited for single-photon compressed imaging, is proposed. First, the pre-measured rough images are transformed into sparse bases as a priori information. Then a smart threshold matrix is designed by using large sparse coefficients of the rough image in sparse bases. The adaptive measurement matrix is obtained by modifying the original Gaussian random matrix with the specially designed threshold matrix. Building the adaptive measurement matrix requires only one level of sparse representation, which means that adaptive imaging can be achieved quickly with very little computation. The experimental results show that the reconstruction effect of the image measured using the adaptive measurement matrix is obviously superior than that of the Gaussian random matrix under different measurement times and different reconstruction algorithms.

Calibration of a single-diode performance model without a short-circuit temperature coefficient.

We calibrate the seven parameters of a single-diode model (SDM) for photo-voltaic device performance using current-voltage (I-V) curves measured under controlled laboratory conditions over a matrix of nominal temperature and irradiance combinations. As described in previous modeling work, we do not use a short-circuit temperature coefficient parameter, which depends on the often unknown insolation spectrum and whose validity may be questionable. Alternatively, we employ a rigorous temperature-dependent extension of the spectral mismatch correction. This standard correction is routinely used by calibration laboratories to measure an effective irradiance ratio (i.e., a particular ratio of short-circuit currents) using a calibrated reference device, thereby compensating for spectral effects of the irradiance and for any difference in spectral response between the test device and reference device. The calibrated SDM predicts the device's current at any prescribed voltage, temperature, and effective irradiance, and thus can predicts power and energy production under prescribed conditions. Our approach aligns well with the matched reference cell approach to outdoor I-V curve measurements, while clarifying the requirements of a "matched" condition for the irradiance monitoring device(s). We find evidence for significant model discrepancy in the SDM, suggesting that model improvements and measurement intercomparisons are needed.

A 7.4 ps FPGA-Based TDC with a 1024-Unit Measurement Matrix.

In this paper, a high-resolution time-to-digital converter (TDC) based on a field programmable gate array (FPGA) device is proposed and tested. During the implementation, a new architecture of TDC is proposed which consists of a measurement matrix with 1024 units. The utilization of routing resources as the delay elements distinguishes the proposed design from other existing designs, which contributes most to the device insensitivity to variations of temperature and voltage. Experimental results suggest that the measurement resolution is 7.4 ps, and the INL (integral nonlinearity) and DNL (differential nonlinearity) are 11.6 ps and 5.5 ps, which indicates that the proposed TDC offers high performance among the available TDCs. Benefitting from the FPGA platform, the proposed TDC has superiorities in easy implementation, low cost, and short development time.

Measurement Matrix Optimization and Mismatch Problem Compensation for DLSLA 3-D SAR Cross-Track Reconstruction.

With a short linear array configured in the cross-track direction, downward looking sparse linear array three-dimensional synthetic aperture radar (DLSLA 3-D SAR) can obtain the 3-D image of an imaging scene. To improve the cross-track resolution, sparse recovery methods have been investigated in recent years. In the compressive sensing (CS) framework, the reconstruction performance depends on the property of measurement matrix. This paper concerns the technique to optimize the measurement matrix and deal with the mismatch problem of measurement matrix caused by the off-grid scatterers. In the model of cross-track reconstruction, the measurement matrix is mainly affected by the configuration of antenna phase centers (APC), thus, two mutual coherence based criteria are proposed to optimize the configuration of APCs. On the other hand, to compensate the mismatch problem of the measurement matrix, the sparse Bayesian inference based method is introduced into the cross-track reconstruction by jointly estimate the scatterers and the off-grid error. Experiments demonstrate the performance of the proposed APCs' configuration schemes and the proposed cross-track reconstruction method.

RBF-network based sparse signal recovery algorithm for compressed sensing reconstruction.

The approach of applying a cascaded network consisting of radial basis function nodes and least square error minimization block to Compressed Sensing for recovery of sparse signals is analyzed in this paper to improve the computation time and convergence of an existing ANN based recovery algorithm. The proposed radial basis function-least square error projection cascade network for sparse signal Recovery (RASR) utilizes the smoothed L0 norm optimization, L2 least square error projection and feedback network model to improve the signal recovery performance over the existing CSIANN algorithm. The use of ANN architecture in the recovery algorithm gives a marginal reduction in computational time compared to an existing L0 relaxation based algorithm SL0. The simulation results and experimental evaluation of the algorithm performance are presented here.