Bernoulli Random Matrix Research Articles

Efficient measurement matrix for speech compressive sampling

Signal sampling is an important concern for compressive sensing framework. The use of efficient sampling may enhance the overall performance by collecting informative samples. The work done in this paper is aimed to propose the efficient sampling matrix for speech compressive sensing by reviewing the reconstruction results obtained via conventionally used measurement matrices. Recently used measurement matrices are either randomly structured or deterministic in nature. Therefore, the prime objective of this work is to analyse speed and reconstruction performance of l1-norm minimization algorithm when samples are provided by the concerned sampling matrix. The speed and accuracy analysis is intended to propose efficient sampling matrix which can facilitate faithful signal reconstruction process for speech compressive sensing. The sampling matrices chosen for this work are Bernoulli random matrix, Gaussian random matrix, Hadamard matrix and Toeplitz matrix. The observed matrices are carefully adjusted to provide different range of sampling ratios for signal recovery process. In this work, the number of input samples are changed (from 10% to 40%) to search for the efficient sampling matrix which can survive the least possible number of samples. The performances of the sampling matrices are compared on the basis of Root Mean Squared Error (RMSE) values and reconstruction time (in seconds) is obtained via l1 minimization method.

Incoherence Analysis of RD-AIC-Based Observation Matrix and Its Application in Power Quality Disturbance Signal

In the theory of compressed sensing, restricted isometry property (RIP) decides the universality and reconstruction robustness of an observation matrix. At present, an observation matrix based on RD-AIC (RD-AIC-based observation matrix) can compress sparse continuous signals with a simple structure, but RIP analysis of this matrix is lack and challenging to prove. In this paper, this problem is relaxed. Instead, we demonstrate the incoherence analysis process, derive the orthogonality and nonsingularity of the matrix, propose the generalized relevance calculation steps of the matrix, and propose the hardware parameter design principles to improve the incoherence of the matrix. Moreover, compression and reconstruction experiments used in power quality disturbance signals are developed for testing the incoherence. The results show that the RD-AIC-based observation matrix has substantial incoherence under suitable hardware parameters, equivalent to the Gaussian random matrix and the Bernoulli random matrix.

An Arbitrarily Reconfigurable Extreme Learning Machine Inference Engine for Robust ECG Anomaly Detection

Extreme learning machine (ELM) has shown to be an effective and low-power approach for real-time electrocardiography (ECG) anomaly detection. However, prior ELM inference chips are noise-prone and lacking in reconfigurability. In this article, we present an arbitrarily reconfigurable ELM inference engine fabricated in 40-nm CMOS technology for robust ECG anomaly detection. By combining Adaptive boosting (Adaboost) and Eigenspace denoising with ELM (AE-ELM), robust classification under noisy conditions is achieved and saves the number of required multiplications by 95.9%. For chip implementation, a reconfigurable VLSI architecture is designed to support arbitrary complexity of AE-ELM, accounting for dynamic change in application requirements. On the other hand, we propose to construct the input weight matrix of ELM as a Bernoulli random matrix, which further reduces the number of multiplications by 55.2%. For real-time detection, parallel computing is exploited to reduce the latency by up to 86.8%. Overall, the 0.21-mm2 AE-ELM inference engine shows its robustness against noisy signals and achieves $1.83\times$ AEE compared with the state-of-the-art ELM design.

Wind Turbine Planetary Gearbox Condition Monitoring Method Based on Wireless Sensor and Deep Learning Approach

Condition monitoring for wind turbine (WT) planetary gearbox is of great significance to the reliable operation of WT. A novel condition monitoring method for WT planetary gearbox is proposed in this article. This method can identify and predict the fault in the initial stage. Raw vibration signals are gathered from WT planetary gearbox through an enhanced piezoelectric self-powered wireless sensor. First, after the data processing back-end receives the original samples transmitted by the wireless sensor, the high-dimensional raw vibration signals are compressed and collected by adopting a random Bernoulli matrix to obtain the compressed samples containing the characteristics of the raw signals by compressed sensing (CS). Moreover, the operation of reducing the signal dimension not only eliminates noise pollution but also greatly reduces the overall calculation. Second, the training part of compressed samples is first exploited to optimize the deep belief network (DBN) by the chaotic quantum particle swarm optimization (CQPSO) algorithm. In the optimization process, the CQPSO algorithm can avoid local optimal problem better compared with traditional quantum particle swarm optimization (QPSO) algorithm, which ensures that the optimized DBN architecture can extract distinguishing and deep features from compressed samples. Furthermore, the choice of compression ratio (CR) is realized in this process with the least-squares support vector machine (LSSVM) classifier. Third, testing samples are input into the DBN structure. A regression layer added on the last hidden layer, which stores extracted features, achieves the prediction of fault. In addition, LSSVM is exploited to distinguish fault types of features. The experimental results show that the modified wireless sensor can collect and transmit signals stably and achieve better performance in transmission interval and energy management. More importantly, the experimental results of prediction and diagnosis show that the proposed approach achieves excellent performance in terms of condition monitoring for the WT planetary gearbox.

Estimation of population column proportions of 1’s in survey type designs

Motivated by the nature of observed responses in real world situations, we propose an iterative algorithm for estimating population column proportions of a n × k Bernoulli random matrix (X) in survey type designs. The Perron-Frobenius theorem is used to establish the limiting form of the proposed estimator in the iteration process, where pj , is given by the row sum of the Perron projection of XtX or An asymptotic distribution of the proposed estimator is provided in this paper.

Indistinguishability and Energy Sensitivity of Gaussian and Bernoulli Compressed Encryption

The principle of compressed sensing (CS) can be applied in a cryptosystem by providing the notion of security. The Gaussian one-time sensing (G-OTS) CS-based cryptosystem employing a random Gaussian matrix and renewing the elements at each encryption is known to be perfectly secure, as long as each plaintext has constant energy. A random Bernoulli matrix can replace the Gaussian one for encrypting each plaintext efficiently in the Bernoulli one-time sensing (B-OTS) cryptosystem. In this paper, we analyze the security of G-OTS and B-OTS cryptosystems, respectively, where each cryptosystem may have unequal plaintext energy. By means of probability metrics, we study the indistinguishability of each CS-based cryptosystem, which formalizes the notion of computational security. Moreover, we investigate how much the indistinguishability is sensitive to energy variation of plaintexts in each cryptosystem. For the B-OTS cryptosystem, we analyze the indistinguishability and the energy sensitivity in a non-asymptotic manner for a finite plaintext length. In conclusion, this paper confirms that G-OTS and B-OTS cryptosystems can be strictly and asymptotically indistinguishable, respectively, as long as each plaintext has constant energy, but the indistinguishability is highly sensitive to energy variation of plaintexts.

Reconstruction of measurements in state estimation strategy against deception attacks for cyber physical systems

Without the known state equation, a new state estimation strategy is designed to be against malicious attacks for cyber physical systems. Inspired by the idea of data reconstruction, the compressive sensing (CS) is applied to reconstruction of residual measurements after the detection and identification scheme based on the Markov graph of the system state, which increases the resilience of state estimation strategy against deception attacks. First, the observability analysis is introduced to decide the triggering time of the measurement reconstruction and the damage level from attacks. In particular, the dictionary learning is proposed to form the over-completed dictionary by K-singular value decomposition (K-SVD), which is produced adaptively according to the characteristics of the measurement data. In addition, due to the irregularity of residual measurements, a sampling matrix is designed as the measurement matrix. Finally, the simulation experiments are performed on 6-bus power system. Results show that the reconstruction of measurements is completed well by the proposed reconstruction method, and the corresponding effects are better than reconstruction scheme based on the joint dictionary and the traditional Gauss or Bernoulli random matrix respectively. Especially, when only 29% available clean measurements are left, performance of the proposed strategy is still extraordinary, which reflects generality for five kinds of recovery algorithms.

Evaluation of Digital Compressed Sensing for Real-Time Wireless ECG System with Bluetooth low Energy.

In this paper, a wearable and wireless ECG system is firstly designed with Bluetooth Low Energy (BLE). It can detect 3-lead ECG signals and is completely wireless. Secondly the digital Compressed Sensing (CS) is implemented to increase the energy efficiency of wireless ECG sensor. Different sparsifying basis, various compression ratio (CR) and several reconstruction algorithms are simulated and discussed. Finally the reconstruction is done by the android application (App) on smartphone to display the signal in real time. The power efficiency is measured and compared with the system without CS. The optimum satisfying basis built by 3-level decomposed db4 wavelet coefficients, 1-bit Bernoulli random matrix and the most suitable reconstruction algorithm are selected by the simulations and applied on the sensor node and App. The signal is successfully reconstructed and displayed on the App of smartphone. Battery life of sensor node is extended from 55h to 67h. The presented wireless ECG system with CS can significantly extend the battery life by 22%. With the compact characteristic and long term working time, the system provides a feasible solution for the long term homecare utilization.

Research of incoherence rotated chaotic measurement matrix in compressed sensing

Measurement matrix construction is the hot issue of compressed sensing. How to construct a measurement matrix of good performance and easy hardware implementation is the main research problem in compressed sensing. In this paper, we present a novel simple and efficient measurement matrix named Incoherence Rotated Chaotic (IRC) matrix. We take advantage of the well pseudorandom of chaotic sequence, introduce the concept of the incoherence factor and rotation, and adopt QR decomposition to obtain the IRC measurement matrix which is suited for sparse reconstruction. The IRC matrix satisfies the Restricted Isometry Property criterion in sparse reconstruction and has a smaller RIP ratio. Simulations demonstrate IRC matrix has better performance than Gaussian random matrix, Bernoulli random matrix, Fourier matrix and can efficiently work on both natural image and remote sensing image. The peak signal-to-noise ratios of reconstructed images using IRC matrix are improved at 1.5 dB to 2.5 dB at least.

Compressive Sensing With Chaotic Sequence

Compressive sensing is a new methodology to capture signals at sub-Nyquist rate. To guarantee exact recovery from compressed measurements, one should choose specific matrix, which satisfies the Restricted Isometry Property (RIP), to implement the sensing procedure. In this letter, we propose to construct the sensing matrix with chaotic sequence following a trivial method and prove that with overwhelming probability, the RIP of this kind of matrix is guaranteed. Meanwhile, its experimental comparisons with Gaussian random matrix, Bernoulli random matrix and sparse matrix are carried out and show that the performances among these sensing matrix are almost equal.

Moderate Deviations in a Random Graph and for the Spectrum of Bernoulli Random Matrices

We prove the moderate deviation principle for subgraph count statistics of Erdös-Rényi random graphs. This is equivalent in showing the moderate deviation principle for the trace of a power of a Bernoulli random matrix. It is done via an estimation of the log-Laplace transform and the Gärtner-Ellis theorem. We obtain upper bounds on the upper tail probabilities of the number of occurrences of small subgraphs. The method of proof is used to show supplemental moderate deviation principles for a class of symmetric statistics, including non-degenerate U-statistics with independent or Markovian entries.