Measurement Matrix In Compressed Research Articles

Flexible deterministic compressive measurement matrix based on two finite fields

Flexible deterministic compressive measurement matrix based on two finite fields

Optimization of the Compressive Measurement Matrix in a Massive MIMO System Exploiting LSTM Networks

Massive multiple-input multiple-output (MIMO) technology, which is characterized by the use of a large number of antennas, is a key enabler for the next-generation wireless communication and beyond. Despite its potential for high performance, implementing a massive MIMO system presents numerous technical challenges, including the high hardware complexity, cost, and power consumption that result from the large number of antennas and the associated front-end circuits. One solution to these challenges is the use of hybrid beamforming, which divides the transceiving process into both analog and digital domains. To perform hybrid beamforming efficiently, it is necessary to optimize the analog beamformer, referred to as the compressive measurement matrix (CMM) here, that allows the projection of high-dimensional signals into a low-dimensional manifold. Classical approaches to optimizing the CMM, however, are computationally intensive and time consuming, limiting their usefulness for real-time processing. In this paper, we propose a deep learning based approach to optimizing the CMM using long short-term memory (LSTM) networks. This approach offers high accuracy with low complexity, making it a promising solution for the real-time implementation of massive MIMO systems.

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.

Construction of compressive measurement matrix based on sinusoidal function called Sinusoidal Sensing Matrix (SSM)

Compression sensing theory enables a safe reconstruction of signals under certain conditions. Random measurement (sensing) matrix Φ is one of the necessary conditions which give a strong impact on the behavior of the method used to reconstruct the signal. A deterministic method is therefore proposed to construct a new matrix called Sinusoidal Sensing Matrix (SSM) for compressing sensing theorem. The SSM matrix depends on its built upon generating equation used both Sin and Cos function depend upon the number of compressed samples. This new matrix is very simple and easy to create but very effective and can be generated in transmission and distention end without a need to send it, only need in Rx side knowledge of signal length. The new matrix interval meets the Restricted Isometry Property (RIP) characteristic with high probability.The simulation experiments of one- and two- dimensional signals, using a new matrix show a superior in evaluating recovered signals with parameters and the visual effect of the restored images.

Feature fusion via dual-resolution compressive measurement matrix analysis for spectral image classification

In the compressive spectral imaging (CSI) framework, different architectures have been proposed to recover high-resolution spectral images from compressive measurements. Since CSI architectures compactly capture the relevant information of the spectral image, various methods that extract classification features from compressive samples have been recently proposed. However, these techniques require a feature extraction procedure that reorders measurements using the information embedded in the coded aperture patterns. In this paper, a method that fuses features directly from dual-resolution compressive measurements is proposed for spectral image classification. More precisely, the fusion method is formulated as an inverse problem that estimates high-spatial-resolution and low-dimensional feature bands from compressive measurements. To this end, the decimation matrices that describe the compressive measurements as degraded versions of the fused features are mathematically modeled using the information embedded in the coded aperture patterns. Furthermore, we include both a sparsity-promoting and a total-variation (TV) regularization terms to the fusion problem in order to consider the correlations between neighbor pixels, and therefore, improve the accuracy of pixel-based classifiers. To solve the fusion problem, we describe an algorithm based on the accelerated variant of the alternating direction method of multipliers (accelerated-ADMM). Additionally, a classification approach that includes the developed fusion method and a multilayer neural network is introduced. Finally, the proposed approach is evaluated on three remote sensing spectral images and a set of compressive measurements captured in the laboratory. Extensive simulations show that the proposed classification approach outperforms other approaches under various performance metrics.

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.

Construction of compressive measurement matrix based on convolution of fractional chaos and cyclic matrix

A method is proposed to construct an improved measurement matrix—chaotic cyclic convolution measurement matrix (CCCMM). It is constructed by convoluting the fractional order Lorenz chaotic sequences and the cyclic matrix; since cyclic matrix is easy to implement on hardware, accurate reconstructed signal can be obtained by using fractional order chaos with pseudorandomness and convoluting them makes computing results smooth. Meanwhile, CCCMM is proved to have the high probability to satisfy the restricted isometry property. Then, the one-dimensional signals and two-dimensional images are simulated by the CCCMM and other methods, and the results show that the CCCMM is more superior in evaluating recovered signals with parameters and the visual effect of the restored images.

A Novel Compressed Sensing Technique for Traffic Matrix Estimation of Software Defined Cloud Networks

Traffic Matrix estimation has always caught attention from researchers for better network management and future planning. With the advent of high traffic loads due to Cloud Computing platforms and Software Defined Networking based tunable routing and traffic management algorithms on the Internet, it is more necessary as ever to be able to predict current and future traffic volumes on the network. For large networks such origin-destination traffic prediction problem takes the form of a large under-constrained and under-determined system of equations with a dynamic measurement matrix. In this work, we present our Compressed Sensing with Dynamic Model Estimation (CS-DME) architecture suitable for modern software defined networks. Our main contributions are: (1) we formulate an approach in which measurement matrix in the compressed sensing scheme can be accurately and dynamically estimated through a reformulation of the problem based on traffic demands. (2) We show that the problem formulation using a dynamic measurement matrix based on instantaneous traffic demands may be used instead of a stationary binary routing matrix which is more suitable to modern Software Defined Networks that are constantly evolving in terms of routing by inspection of its Eigen Spectrum using two real world datasets. (3) We also show that linking this compressed measurement matrix dynamically with the measured parameters can lead to acceptable estimation of Origin Destination (OD) Traffic flows with marginally poor results with other state-of-art schemes relying on fixed measurement matrices. (4) Furthermore, using this compressed reformulated problem, a new strategy for selection of vantage points for most efficient traffic matrix estimation is also presented through a secondary compression technique based on subset of link measurements.

Computational methods for underdetermined convolutive speech localization and separation via model-based sparse component analysis

In this paper, the problem of speech source localization and separation from recordings of convolutive underdetermined mixtures is addressed. This problem is cast as recovering the spatio-spectral speech information embedded in a microphone array compressed measurements of the acoustic field. A model-based sparse component analysis framework is formulated for sparse reconstruction of the speech spectra in a reverberant acoustic resulting in joint localization and separation of the individual sources. We compare and contrast the algorithmic approaches to model-based sparse recovery exploiting spatial sparsity as well as spectral structures underlying spectrographic representation of speech signals. In this context, we explore identification of the sparsity structures at the auditory and acoustic representation spaces. The audiory structures are formulated upon the principles of structural grouping based on proximity, autoregressive correlation and harmonicity of the spectral coefficients and they are incoporated for sparse reconstruction. The acoustic structures are formulated upon the image model of multipath propagation and they are exploited to characterize the compressive measurement matrix associated with microphone array recordings.Three approaches to sparse recovery relying on combinatorial optimization, convex relaxation and sparse Bayesian learning are studied and evaluated on thorough experiments. The sparse Bayesian learning method is shown to yield better perception quality while the interference suppression is also achieved using the combinatorial approach with the advantage of offering the most efficient computational cost. Furthermore, it is demonstrated that an average autoregressive model can be learned for speech localization while exploiting the proximity structure in the form of block sparse coefficients enables accurate localization and high quality speech separation. Throughout the extensive empirical evaluation, we confirm that a large and random placement of the microphones enables significant improvement in source localization and separation performance.

Chaotic compressive measurement and reconstruction of binary signals

Compressive sensing of binary signals is corresponding to the problem of binary symbol detection in the faster-than-Nyquist signaling systems, which has significant research value. Traditional compressive measurement of a binary signal is based on Gaussian matrix, and l1 minimization is a classic algorithm for signal reconstruction. However, stochastic matrix such as the Gaussian matrix can hardly be realized by a digital circuit, and the reconstruction performance of l1 minimization is not well enough for binary signals. Thus, it is of great meaning to construct a new kind of measurement matrix as well as a better reconstruction algorithm for binary signals. This paper constructs a chaotic circulant measurement matrix based on Cat chaotic map (CCMM), and proposes a brand new algorithm for binary signal reconstructionsmooth function approximation method (SFAM). Chaotic sequence has characteristics of both internal certainty and external randomness, while a circulant matrix requires less elements and can be realized through fast Fourier transform. CCMM conbines the advantages of both chaotic sequence and circulant matrix, so that it not only satisfies the RIPless property required by the compressive measurement matrix because of external randomness, but also has the power to resist the effect of low signaling efficiency and low SNR due to the internal certainty. Moreover, the circle structure gives CCMM the potential to be digital realized in the future. In SFAM, we first use a non-convex function to approximate the original discontinuous objective function, in order to transfer the original combinatorial optimization problem into an optimization problem with equality constraints which can be solved much easier. Then we use the interior point method to solve this optimization problem. Furthermore, sparse Bayesian learning algorithm is used to correct the reconstruction error for a more accurate result. Compressive measurement and reconstruction of binary signals in additive Gaussian white noise channel are operated. Result of numerical experiments shows that CCMM is much better than the traditional Gaussian matrix for compressive measurement, especially in the condition of low signaling efficiency and low SNR, and SFAM is much better than l1 minimization for binary signal reconstruction. At the end of this paper, we explain the essential reason why CCMM performs better than the traditional Gaussian matrix, through calculating the autocorrelation function of compressive measurement vector in various conditions.

A Bregman Matrix and the Gradient of Mutual Information for Vector Poisson and Gaussian Channels

A generalization of Bregman divergence is developed and utilized to unify vector Poisson and Gaussian channel models, from the perspective of the gradient of mutual information. The gradient is with respect to the measurement matrix in a compressive-sensing setting, and mutual information is considered for signal recovery and classification. Existing gradient-of-mutual-information results for scalar Poisson models are recovered as special cases, as are known results for the vector Gaussian model. The Bregman-divergence generalization yields a Bregman matrix, and this matrix induces numerous matrix-valued metrics. The metrics associated with the Bregman matrix are detailed, as are its other properties. The Bregman matrix is also utilized to connect the relative entropy and mismatched minimum mean squared error. Two applications are considered: 1) compressive sensing with a Poisson measurement model and 2) compressive topic modeling for analysis of a document corpora (word-count data). In both of these settings, we use the developed theory to optimize the compressive measurement matrix, for signal recovery and classification.

Construction of a circulant compressive measurement matrix based on chaotic sequence and RIPless theory

Construction of a compressive measurement matrix is one of the key technologies of compressive sensing. A circulant matrix corresponds to the discrete convolutions with a high-speed algorithm, which has been widely used in compressive sensing. This paper combines the advantages of chaotic sequence with circulant matrix to propose a circulant compressive measurement matrix based on the chaotic sequence. The elements of a chaotic circulant measurement matrix are generated by taking advantage of the chaotic internal certainty, i.e. the independent identically distributed randomness sequence can be produced by the chaotic mapping formula using the initial value and a certain sampling distance. At the same time, the external randomness of chaotic sequence can satisfy the stochastic requirements of compressive measurement matrix. This paper presents the method of constructing chaotic circulant measurement matrix using a Cat chaotic map and the test method for RIPless property of the matrix. Measurement results of one-dimensional and two-dimensional signals using the chaotic circulant measurement matrix are studied and are compared with the results of conventional circulant measurement matrix. It can be shown that the chaotic circulant measurement matrix has good recovery results for both one-dimensional and two-dimensional signals. Moreover, it may get better results than the traditional matrix for the two-dimensional signal. From the point of view of phase diagram, the essential reason of chaotic circulant measurement matrix outperforms the conventional one is its integration of internal certainty with the external randomness of the chaotic sequence.