Optimized Measurement Matrix Research Articles

Visually secure encryption embedded with multiple types of images using semi-tensor product compressed sensing

An image encryption scheme with visual security is designed by combining the semi-tensor product compressed sensing (STP-CS) with multi-embedding strategy. Specifically, the optimized measurement matrix is firstly generated by chaotic system and singular value decomposition (SVD), and the optimized measurement matrix is used to obtain the measurement value matrix by STP-CS operation on the color image. Next, the reorganized measurement value matrix is scrambled and diffused with the key matrix generated by 2D Logistic-Sine-coupling map (2D-LSCM) to obtain the noise-like encrypted image. Finally, an image embedding method is introduced to embed the compressed noise-like encrypted image into a color or grayscale carrier image to obtain a visually secure color or grayscale encrypted image. SHA-256 is used to generate the initial values of chaotic systems, which are embedded into the carrier image to effectively reduce transmission and storage. The simulation results show that the visually secure encryption scheme is more reliable and outperforms other encryption algorithms.

Illumination pattern optimization in tomography based on the Kalman estimation filter and optimal experiment design

Tomography is widely used in medical imaging or industrial non-destructive testing applications. One costly and time consuming operation in any form of tomography is the process of data acquisition where a large number of measurements are made and collected data is used for image reconstruction. Data acquisition can slow down tomography to the point that the scanner cannot catch up with the speed of changes in the medium under test. By optimizing the information content of each measurement, we can reduce the number of measurements needed to achieve the target precision. Development of algorithms to optimize the information content of tomography measurements is the main goal of this article. Here, the dynamics of the medium and tomography measurements are formulated in the form of a Kalman estimation filter. A mathematical algorithm is developed to compute the optimal measurement matrix which minimizes the uncertainty left in the estimation of the distribution the tomography scanner is reconstructing. Results, as presented in the paper, show noticeable improvement is the quality of generated images when the medium is scanned by optimal measurements instead of traditional raster or random scanning protocols.

Color ghost imaging based on optimized random speckles and truncated singular value decomposition

The ambient noise always harms the image quality in ghost imaging. In this letter, we propose a scheme of color ghost imaging to reduce the noise impact. In addition to the method of truncated singular value decomposition (TSVD), the measurement matrix is optimized with low-pass filters. In experiment, four (Gaussian, averaging, circular averaging, and median) filters are applied to the patterns of random speckles, which reforms the measurement matrix. By using the TSVD method, the pseudo-inverse matrix of the optimized measurement matrix is obtained and used to reconstruct the images. With proper truncation rates, the mean square errors of the reconstructed images are greatly decreased. Therefore, the image quality in our scheme is greatly improved. Further simulation analysis shows that the point spread functions are greatly optimized after filtering the random speckles. Our technique strengthens the anti-noise ability of ghost imaging, especially in complex environment.

A novel method to repair missing vibration data in rolling bearing vibration signals based on improved optimized measurement matrix

Missing data, caused by many factors such as equipment short circuits or data cleaning, affect the accuracy of condition monitoring for rotating machinery. To improve the precision of missing data recovery, a compressed sensing-based vibration data repair method is developed. First, based on the Gaussian random matrix, an improved optimized measurement matrix (OMM) is proposed to accurately sample data. Then, a sparse representation of the vibration signal, through a discrete cosine transform, is utilized to make the noisy vibration signal sparse. Finally, the orthogonal matching pursuit algorithm is employed to reconstruct the missing signal. The effectiveness of the proposed method is verified by analyzing constant and variable speed time series of rolling bearings. Compared with other data repair methods, it is shown that the OMM has a higher repair precision at different loss rates.

Optimization of polarization parameters for an LCVR polarization spectrometer under non-oversampling.

The spectral polarization measurement can obtain not only the spectral information of the target but also its polarization information, which can improve the detection and identification of the measured target. In the polarization spectrometer based on a liquid crystal variable retarder (LCVR) and acousto-optic tunable filter (AOTF), the LCVR is a core device for achieving fast and high-precision polarization detection. The AOTF is a new, to the best of our knowledge, filter device for spectral tuning. To reduce the sensitivity of an LCVR-based Stokes polarization spectrometer system to errors and Gaussian noise, and to maintain the advantage of fast electrical tuning of the system for spectral polarization detection, the phase retardation and azimuth angle of the polarization device LCVR is calculated and analyzed optimally under the minimum number of samples N=4 of the Stokes vector measurement method in this paper. The optimization algorithm considers the constraints, such as the number of types of LCVR phase retardation and the number of adjustments, and the azimuth and phase retardation to be optimized are searched for optimality step by step. The simulation results show that the number of adjustments of the phase retardation δ of LCVRs is only three times when four Stokes parameters are obtained. The LCVRs' number of species is four kinds (2×2). The condition number of the optimized measurement matrix is 1.742, which converges to the ideal condition number, the optimal azimuth angle (θ 1,θ 2) is (18.9°, 41.9°), and the optimal phase retardation δ is (179.9°, 156.6°, 0.4°, 46.3°). Its corresponding tetrahedral volume is closer to the ideal value. The optimized system is less sensitive to errors and Gaussian noise.

Measurement Matrix Optimization Based on Target Prior Information for Radar Imaging

Radar target imaging can provide important information for target monitoring and recognition. In order to reduce the data amount and save radar resources, the target imaging methods based on compressed sensing have received extensive attention. In these methods, the measurement matrix will directly affect the target imaging quality and data down-sampling rate. However, most of the existing researches on measurement matrix optimization did not take into account the full use of target characteristic information and the internal consistency between the measurement matrix structure and the data sampling process, which makes it difficult to obtain the optimal imaging quality and down-sampling rate. To solve the above problems, this paper makes full use of the target imaging prior information, and takes the minimum dimension of the measurement matrix and the maximum similarity between the obtained image and expected image as the goal of measurement matrix optimization. On this basis, aims at the kind of signal which is composed of a group of sub-pulses with stepped frequency, a joint optimization model of measurement matrix and imaging performance based on the target imaging prior is established with the consideration of the 0-1 constraint of the measurement matrix structure caused by the physical observation process of the sparse stepped frequency signals. And then the corresponding sparse reconstruction algorithm is proposed. Thus, the optimal measurement matrix and high-resolution imaging results can be obtained, and the radar data down-sampling rate can be improved significantly. Simulation results indicate the effectiveness of the proposed method.

A unified framework of deep unfolding for compressed color imaging

Traditional iterative-based reconstruction algorithms for compressed color imaging often suffer from long reconstruction time and low reconstruction accuracy at extreme low-rate subsampling. This paper proposes a model-driven deep learning framework for compressed color imaging. In the training step, extract the image blocks at the same position of the R, G, and B channel images as the ground truth, and then, singular value decomposition is performed on the measurement matrix to obtain the optimized measurement matrix and low-dimensional measurements; afterward, the ground-truth and optimized measurements are utilized to construct a large amount of training data pairs to train an ‘end-to-end’ deep unfolding model for compressed color imaging. In the test step, the single pretrained model is used to reconstruct high-quality images from optimized low-dimensional compressed measurements for each channel and synthesize a color image. Numerical experiments demonstrate that our proposed unified framework can achieve high accuracy and real-time reconstruction for the color image at extremely low subsampling rate.

An improved measurement matrix of compressed sensing for synthetic aperture ultrasound imaging

Compressed sensing theory is a new signal processing theory proposed for high-speed data acquisition and large-capacity data storage in recent years. The application of compressed sensing technology can solve the data acquisition problem in ultrasound hardware system. The construction of the measurement matrix is one of the key steps, and its performance is directly related to the accuracy of signal reconstruction. Aiming at the problem of reconstruction efficiency and accuracy, this paper proposes an optimized measurement matrix for compressed sensing. According to the orthogonal basis linear representation principle, the proposed matrix is constructed with linear structure. Since the construction process of the proposed matrix is simple with high sparsity and no redundancy, the proposed matrix reduces the demand for hardware resources and is suitable for ultrasound acquisition system with limited hardware resources. The simulation experiments of scattering point targets, cyst phantoms, and geabr_0 data were conducted. The simulation results indicate that compared with several typical measurement matrices, the reconstruction error of the proposed measurement matrix is the smallest and the peak signal-to-noise ratio is the maximum, and it can accurately reconstruct ultrasound images with 30% of the sampled data.

New flexible deterministic compressive measurement matrix based on finite Galois field

Nowadays, the deterministic construction of sensing matrices is a hot topic in compressed sensing. The coherence of the measurement matrix is an important research area in the design of deterministic compressed sensing. To solve this problem, this paper proposes a novel sparse deterministic measurement matrix, which basically accesses the optimal low coherence of the measurement matrix. Firstly, a class of sparse square matrix is constructed based on finite fields' arithmetic. Then, the Hadamard matrix, or (discrete Fourier transform) DFT matrix, is nestled into the square matrix to construct an asymptotically optimal deterministic measurement matrix. That is, the relevant column vectors have orthogonal characteristics. Using this feature, the measurement matrix can be further optimized to reduce its mutual coherence, almost achieving the lower bound of the coherence (Welch bound). The two types of deterministic measurement matrices proposed are sparse with low mutual coherence and flexible measurement sizes. So, the proposed deterministic measurement matrices require less memory and time for the recovery as well as reducing the complexity due to their sparse structure. The simulation results show that compared with the existing (several typical) random matrices, the proposed method can reduce the mutual coherence and computational complexity of the measurement matrix.

Measurement Matrix Optimization for Compressed Sensing System with Constructed Dictionary via Takenaka-Malmquist Functions.

Compressed sensing (CS) has been proposed to improve the efficiency of signal processing by simultaneously sampling and compressing the signal of interest under the assumption that the signal is sparse in a certain domain. This paper aims to improve the CS system performance by constructing a novel sparsifying dictionary and optimizing the measurement matrix. Owing to the adaptability and robustness of the Takenaka–Malmquist (TM) functions in system identification, the use of it as the basis function of a sparsifying dictionary makes the represented signal exhibit a sparser structure than the existing sparsifying dictionaries. To reduce the mutual coherence between the dictionary and the measurement matrix, an equiangular tight frame (ETF) based iterative minimization algorithm is proposed. In our approach, we modify the singular values without changing the properties of the corresponding Gram matrix of the sensing matrix to enhance the independence between the column vectors of the Gram matrix. Simulation results demonstrate the promising performance of the proposed algorithm as well as the superiority of the CS system, designed with the constructed sparsifying dictionary and the optimized measurement matrix, over existing ones in terms of signal recovery accuracy.

A New Method of Measurement Matrix Optimization for Compressed Sensing Based on Alternating Minimization

In this paper, a new method of measurement matrix optimization for compressed sensing based on alternating minimization is introduced. The optimal measurement matrix is formulated in terms of minimizing the Frobenius norm of the difference between the Gram matrix of sensing matrix and the target one. The method considers the simultaneous minimization of the mutual coherence indexes including maximum mutual coherence μmax, t-averaged mutual coherence μave and global mutual coherence μall, and solves the problem that minimizing a single index usually results in the deterioration of the others. Firstly, the threshold of the shrinkage function is raised to be higher than the Welch bound and the relaxed Equiangular Tight Frame obtained by applying the new function to the Gram matrix is taken as the initial target Gram matrix, which reduces μave and solves the problem that μmax would be larger caused by the lower threshold in the known shrinkage function. Then a new target Gram matrix is obtained by sequentially applying rank reduction and eigenvalue averaging to the initial one, leading to lower. The analytical solutions of measurement matrix are derived by SVD and an alternating scheme is adopted in the method. Simulation results show that the proposed method simultaneously reduces the above three indexes and outperforms the known algorithms in terms of reconstruction performance.

Compression of Remotely Sensed Astronomical Image Using Wavelet-Based Compressed Sensing in Deep Space Exploration

Compression of remotely sensed astronomical images is an essential part of deep space exploration. This study proposes a wavelet-based compressed sensing (CS) algorithm for astronomical image compression in a miniaturized independent optical sensor system, which introduces a new framework for CS in the wavelet domain. The algorithm starts with a traditional 2D discrete wavelet transform (DWT), which provides frequency information of an image. The wavelet coefficients are rearranged in a new structured manner determined by the parent–child relationship between the sub-bands. We design scanning modes based on the direction information of high-frequency sub-bands, and propose an optimized measurement matrix with a double allocation of measurement rate. Through a single measurement matrix, higher measurement rates can be simultaneously allocated to sparse vectors containing more information and coefficients with higher energy in sparse vectors. The double allocation strategy can achieve better image sampling. At the decoding side, orthogonal matching pursuit (OMP) and inverse discrete wavelet transform (IDWT) are used to reconstruct the image. Experimental results on simulated image and remotely sensed astronomical images show that our algorithm can achieve high-quality reconstruction with a low measurement rate.

A Novel Optimization Method for Bipolar Chaotic Toeplitz Measurement Matrix in Compressed Sensing

In this paper, a bipolar chaotic Toeplitz measurement matrix optimization algorithm for alternating optimization is presented. The construction of measurement matrices is one of the key techniques for compressive sensing from theory to engineering applications. Recent studies have shown that bipolar chaotic Toeplitz matrices, constructed by combining the intrinsic determinism of bipolar chaotic sequences with the advantages of Toeplitz matrices, have significant advantages over other measurement matrices in terms of memory overhead, computational complexity, and hard implementation. However, problems such as strong correlation and large interdependence coefficients between measurement matrices and sparse dictionaries may still exist in practical applications. To address this problem, we propose a new bipolar chaotic Toeplitz measurement matrix alternating optimization algorithm. Firstly, by introducing the structure matrix, the optimization problem of the measurement matrix is transformed into the optimization problem of the generating sequence, thus ensuring that the optimization process does not destroy the structural properties of the matrix; then, constraints are added to the values of the generating sequence during the optimization process, so that the optimized measurement matrix still maintains the bipolar properties. Finally, the effectiveness of the optimization algorithm in this paper is verified by simulation experiments. The experimental results show that the optimized bipolar chaotic Toeplitz measurement matrix can effectively reduce the reconstruction error and improve the reconstruction probability.

Real-time and accurate pulsar time-of-arrival estimation using GA-optimized EMD-CS

For the estimation methods of the pulsar TOA (time-of-arrival) based on CS (compressed sensing), it is very important to construct the measurement matrix, which affects accuracy and computation load directly. Subjected to computational load, the matrix size is also an important performance indicator. To reduce the matrix size, we propose a pulsar TOA estimation method using GA (Genetic Algorithm)-optimized EMD (empirical mode decomposition)-CS. Firstly, the standard pulsar profile is decomposed by the EMD to get IMFs (Intrinsic Mode Function). After the decomposition and the phase shift, these IMFs are performed to obtain the set of IMFs with multiple phases. And then, we take the error of the pulsar TOA estimation as the optimization goal, and use the GA to select IMFs from this set. The IMFs selected by the GA forms the optimized measurement matrix. Finally, the CS with the GA-optimized measurement matrix is used to obtain the pulsar TOA estimation. Theoretical analysis and simulation results show that the GA-optimized EMD measurement matrix has unlimited dimensions and small size. The pulsar TOA estimation using GA-optimized EMD-CS has a high accuracy and small computational load.

Measurement Matrix Optimization via Mutual Coherence Minimization for Compressively Sensed Signals Reconstruction

For signals reconstruction based on compressive sensing, to reconstruct signals of higher accuracy with lower compression rates, it is required that there is a smaller mutual coherence between the measurement matrix and the sparsifying matrix. Mutual coherence between the measurement matrix and sparsifying matrix can be expressed indirectly by the property of the Gram matrix. On the basis of the Gram matrix, a new optimization algorithm of acquiring a measurement matrix has been proposed in this paper. Firstly, a new mathematical model is designed and a new method of initializing measurement matrix is adopted to optimize the measurement matrix. Then, the loss function of the new algorithm model is solved by the gradient projection-based method of Gram matrix approximating an identity matrix. Finally, the optimized measurement matrix is generated by minimizing mutual coherence between measurement matrix and sparsifying matrix. Compared with the conventional measurement matrices and the traditional optimization methods, the proposed new algorithm effectively improves the performance of optimized measurement matrices in reconstructing one-dimensional sparse signals and two-dimensional image signals that are not sparse. The superior performance of the proposed method in this paper has been fully tested and verified by a large number of experiments.

An Optimization Method for Measurement Matrix Based on Double Decomposition

This paper introduces a novel method of measurement matrix in compressed sensing. In order to overcome the difficulties associated with coherence of measurement matrix, we propose double optimization methods by eigenvalue decomposition and singular value decomposition under mild conditions. An efficient algorithm (SVD-EIG) is used to recover sparse inputs from the optimized measurement matrix, based on the adaptation of the optimized matrix by eigenvalue decomposition. Lastly, compared with the other methods as the same sampling rate, we demonstrate through simulations that SVD-EIG algorithm can improve accuracy and probability of the reconstruction.

Measurement matrix design for colocated MIMO radar imaging based on Compressive Sensing

Compressive Sensing (CS) is recently used in the colocated MIMO radar to reconstruct the high resolution range profiles (HRRPs) of the target. By exploiting the joint-block sparsity of the HRRPs, the reconstruction result is improved significantly. In this paper, a compressive measurement matrix is designed to reduce the amount of data. An objective for measurement matrix optimization is presented by considering the block sparsity of the HRRPs, and the Weighted Coherence Minimization algorithm is used to optimize the measurement matrix. Simulation results show that the optimized measurement matrix is superior to the Gaussians randomly measurement matrix which doesn’t utilize the block sparsity of the HRRPs.

Unevenly spaced continuous measurement approach for dual rotating-retarder Mueller matrix ellipsometry.

In order to efficiently extract the sample Mueller matrix by dual rotating-retarder ellipsometry, it is critical for the data reduction technique to achieve a minimal data processing burden while considering the ease of retarder control. In this paper, we propose an unevenly spaced sampling strategy to reach a globally optimal measurement matrix with minimum sampling points for continuous measurements. Taking into account the robustness to both systematic errors and detection noise, we develop multi-objective optimization models to identify the optimal unevenly spaced sampling points. A combined global search algorithm based on the multi-objective genetic algorithm is subsequently designed to solve our model. Finally, simulations and experiments are conducted to validate our approach as well as to provide near-optimal schemes for different design scenarios. The results demonstrate that significant improvement on error immunity performance can be achieved by applying an unevenly sampled measurement strategy compared to an evenly sampled one for our ellipsometer scenario.

Stokes polarimeter for the measurement of full linearly Stokes parameters with immunity to Gaussian and Poisson noise

The optimization of Stokes polarimeter to determine the full linearly Stokes parameters in the presence of additive Gaussian noise and signal-dependent Poisson shot noise is addressed. The measurement matrix to minimize the total measurement variance on the full linearly Stokes parameters is optimized. Compared with the previous measurement matrix, the optimal measurement matrix proposed in this paper can effectively improve the measurement precision of the full linearly Stokes parameters statistically. In addition, a practical configuration of Stokes polarimeter is optimized by a cost function to generate the optimal measurement matrix. For the Stokes polarimeter composed by a variable retarder and fixed polarizer, the optimal measurement matrix can be easily generated by a 179.28° retardation with a pair of azimuths ±78.84° and a 179.64° retardation with a pair of azimuths ±33.84°.

Software defined network inference with evolutionary optimal observation matrices

A key requirement for network management is the accurate and reliable monitoring of relevant network characteristics. In today’s large-scale networks, this is a challenging task due to the scarcity of network measurement resources and the hard constraints that this imposes. This paper proposes a new framework, called SNIPER, which leverages the flexibility provided by Software-Defined Networking (SDN) to design the optimal observation or measurement matrix that can lead to the best achievable estimation accuracy using Matrix Completion (MC) techniques. To cope with the complexity of designing large-scale optimal observation matrices, we use the Evolutionary Optimization Algorithms (EOA) which directly target the ultimate estimation accuracy as the optimization objective function. We evaluate the performance of SNIPER using both synthetic and real network measurement traces from different network topologies and by considering two main applications for per-flow size and delay estimations. Our results show that SNIPER can be applied to a variety of network performance measurements under hard resource constraints. For example, by measuring only 8.8% of all per-flow path delays in Harvard network [1], congested paths can be detected with probability of 0.94. To demonstrate the feasibility of our framework, we also have implemented a prototype of SNIPER in Mininet.