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

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Ziran Wei ◽  
Jianlin Zhang ◽  
Zhiyong Xu ◽  
Yong Liu ◽  
Krzysztof Okarma
Keyword(s):  
Optimization Methods ◽  
Superior Performance ◽  
Gram Matrix ◽  
Sparse Signals ◽  
Two Dimensional ◽  
Measurement Matrix ◽  
Mutual Coherence ◽  
One Dimensional ◽  
Two Dimensional Image ◽  
Matrix Optimization

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.

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

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 329
Author(s):  
Renjie Yi ◽  
Chen Cui ◽  
Biao Wu ◽  
Yang Gong
Keyword(s):  
Compressed Sensing ◽  
New Method ◽  
Gram Matrix ◽  
Alternating Minimization ◽  
Measurement Matrix ◽  
Mutual Coherence ◽  
Matrix Optimization ◽  
Shrinkage Function ◽  
Reconstruction Performance ◽  
Method Of Measurement

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.

scholarly journals Determination of hard X-ray polarization from two-dimensional images

2020 ◽  
Vol 53 (6) ◽  
pp. 1559-1561
Author(s):  
Robert B. Von Dreele ◽  
Wenqian Xu
Keyword(s):  
Incident Beam ◽  
Beam Polarization ◽  
Two Dimensional ◽  
One Dimensional ◽  
X Ray ◽  
Dimensional Image ◽  
Two Dimensional Image ◽  
The Difference ◽  
Two Dimensional Images

An estimate of synchrotron hard X-ray incident beam polarization is obtained by partial two-dimensional image masking followed by integration. With the correct polarization applied to each pixel in the image, the resulting one-dimensional pattern shows no discontinuities arising from the application of the mask. Minimization of the difference between the sums of the masked and unmasked powder patterns allows estimation of the polarization to ±0.001.

Person Localization System Using Privacy-Preserving Sensor

2011 ◽  
Vol 103 ◽  
pp. 622-627 ◽  
Author(s):  
Shota Nakashima ◽  
Hui Min Lu ◽  
Kohei Miyata ◽  
Yuhki Kitazono ◽  
Serikawa Seiichi
Keyword(s):  
Low Cost ◽  
Video Camera ◽  
Brightness Distribution ◽  
Privacy Preserving ◽  
Two Dimensional ◽  
Texture Image ◽  
Localization System ◽  
One Dimensional ◽  
Two Dimensional Image ◽  
Simulation Results

A privacy-preserving sensor for person localization has been developed. In theory, the sensor can be constructed with a line sensor and cylindrical lens because only a one-dimensional brightness distribution is needed. However, a line sensor is expensive. In contrast, CMOS area sensors are low cost and are increasing in sensitivity according to recent rapid advancement in the technology. Therefore, we covered the CMOS area sensor physically so that it behaved as a line sensor, we substituted CMOS sensors for the line sensors in practice. The proposed sensor obtains a one-dimensional horizontal brightness distribution that is approximately equal to the integration value of each vertical pixel line of the two-dimensional image. It is impossible to restore the two-dimensional detail texture image from one-dimensional brightness distribution, although it obtains enough information to detect a person’s position and movement status. Thus, the privacy is protected. Moreover, the appearance of the proposed sensor is very different from the conventional video camera, so the psychological resistance of having a picture taken is reduced. In this work, we made the privacy preserving sensor practically, and verified whether a person’s state was able to be detected. The simulation results show that the proposed sensor can detect a present person’s state responsively without violating privacy.

scholarly journals Measurement Matrix Optimization for Compressed Sensing System with Constructed Dictionary via Takenaka–Malmquist Functions

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1229
Author(s):  
Qiangrong Xu ◽  
Zhichao Sheng ◽  
Yong Fang ◽  
Liming Zhang
Keyword(s):  
Compressed Sensing ◽  
Singular Values ◽  
Tight Frame ◽  
Gram Matrix ◽  
Signal Recovery ◽  
Measurement Matrix ◽  
Sensing Matrix ◽  
Matrix Optimization ◽  
Sensing System ◽  
Iterative Minimization

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.

scholarly journals Bayesian reconstruction ofP(r) directly from two-dimensional detector imagesviaa Markov chain Monte Carlo method

2013 ◽  
Vol 46 (2) ◽  
pp. 404-414 ◽  
Author(s):  
Sudeshna Paul ◽  
Alan M. Friedman ◽  
Chris Bailey-Kellogg ◽  
Bruce A. Craig
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Monte Carlo Method ◽  
Interatomic Distance ◽  
Scattering Data ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dimensional Image ◽  
Two Dimensional Image

The interatomic distance distribution,P(r), is a valuable tool for evaluating the structure of a molecule in solution and represents the maximum structural information that can be derived from solution scattering data without further assumptions. Most current instrumentation for scattering experiments (typically CCD detectors) generates a finely pixelated two-dimensional image. In continuation of the standard practice with earlier one-dimensional detectors, these images are typically reduced to a one-dimensional profile of scattering intensities,I(q), by circular averaging of the two-dimensional image. Indirect Fourier transformation methods are then used to reconstructP(r) fromI(q). Substantial advantages in data analysis, however, could be achieved by directly estimating theP(r) curve from the two-dimensional images. This article describes a Bayesian framework, using a Markov chain Monte Carlo method, for estimating the parameters of the indirect transform, and thusP(r), directly from the two-dimensional images. Using simulated detector images, it is demonstrated that this method yieldsP(r) curves nearly identical to the referenceP(r). Furthermore, an approach for evaluating spatially correlated errors (such as those that arise from a detector point spread function) is evaluated. Accounting for these errors further improves the precision of theP(r) estimation. Experimental scattering data, where no ground truth referenceP(r) is available, are used to demonstrate that this method yields a scattering and detector model that more closely reflects the two-dimensional data, as judged by smaller residuals in cross-validation, thanP(r) obtained by indirect transformation of a one-dimensional profile. Finally, the method allows concurrent estimation of the beam center andDmax, the longest interatomic distance inP(r), as part of the Bayesian Markov chain Monte Carlo method, reducing experimental effort and providing a well defined protocol for these parameters while also allowing estimation of the covariance among all parameters. This method provides parameter estimates of greater precision from the experimental data. The observed improvement in precision for the traditionally problematicDmaxis particularly noticeable.

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

2020 ◽  
Vol 10 (9) ◽  
pp. 3288 ◽  
Author(s):  
Ziran Wei ◽  
Jianlin Zhang ◽  
Zhiyong Xu ◽  
Yong Liu
Keyword(s):  
Image Reconstruction ◽  
Compressive Sensing ◽  
Imaging System ◽  
Optimization Methods ◽  
Superior Performance ◽  
Gram Matrix ◽  
Constraint Matrix ◽  
Single Pixel ◽  
Sensing Matrices

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.

FPGA Implementation of Laplacian of Gaussian Edge Detection Algorithm

2011 ◽  
Vol 282-283 ◽  
pp. 157-160 ◽  
Author(s):  
Feng Wang ◽  
Gui Tang Wang ◽  
Rui Huang Wang ◽  
Xiao Wu Huang
Keyword(s):  
Edge Detection ◽  
Detection Algorithm ◽  
Point Of View ◽  
Two Dimensional ◽  
Running Speed ◽  
Edge Detection Algorithm ◽  
One Dimensional ◽  
Absolute Value ◽  
System Generator ◽  
Two Dimensional Image

This paper introduces a design of gaussian Laplace edge detection algorithm model based on system generator which can be realized in FPGA.The data of a two- dimensional image was changed into a one-dimensional array，before line buffering in two Dual port RAM,the convolution of the image pixel data and the LOG template was carried out in the modules constituted of the component elements such as AddSub, Shift and Delay . After getting the absolute value with the modules of Slice，Negate and Mux ，the output was the image after edge-detection .The module function and the selecting principle was analyzed from the point of view of saving FPGA resources.The WaveScope and resource estimator showed that ：not only the detection result and the running speed was guaranteed but also the FPGA resources can be saved .

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