Vanishingly Sparse Matrices and Expander Graphs, With Application to Compressed Sensing

Compressed sensing (CS) is a technique that is suitable for compressing and recovering signals having sparse representations in certain bases. CS has been widely used to optimize the measurement process of bandwidth and power constrained systems like wireless body sensor network. The central issues with CS are the construction of measurement matrix and the development of recovery algorithm. In this paper, we propose a simple deterministic measurement matrix that facilitates the hardware implementation. To control the sparsity level of the signals, we apply a thresholding approach in the discrete cosine transform domain. We propose a fast and simple recovery algorithm that performs the proposed thresholding approach. We validate the proposed method by compressing and recovering electrocardiogram and electromyogram signals. We implement the proposed measurement matrix in a MSP-EXP430G2 LaunchPad development board. The simulation and experimental results show that the proposed measurement matrix has a better performance in terms of reconstruction quality compared with random matrices. Depending on the compression ratio, it improves the signal-to-noise ratio of the reconstructed signals from 6 to 20 dB. The obtained results also confirm that the proposed recovery algorithm is, respectively, 23 and 12 times faster than the orthogonal matching pursuit (OMP) and stagewise OMP algorithms.Index Terms-Compressed sensing (CS), deterministic measurement matrix, electrocardiogram (ECG), electromyogram (EMG), recovery algorithm.

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“…To overcome these limitations, sparse random matrices have been proposed [20]. Most of their entries are zero.…”

Section: B Related Workmentioning

confidence: 99%

Compressed Sensing: A Simple Deterministic Measurement Matrix and a Fast Recovery Algorithm

Ravelomanantsoa

Rabah

Rouane

2015

IEEE Trans. Instrum. Meas.

146

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“…The sparse binary matrix generated is the adjacency matrix of a random graph. Because any random graph with the right parameter is an expander graph with high probability, sparse binary matrix with proper value of a is an adjacency matrix of an expander graph with high probability [23]. Hence, in practice it is sufficient to use random graphs instead of expander graphs.…”

Section: Sparse Data Collection and Algorithm Descriptionmentioning

confidence: 99%

Compressed sensing and mobile agent based sparse data collection in wireless sensor networks

Wang

Shen

et al. 2015

2015 IEEE International Instrumentation and Measurement Technology Conference (I2MTC) Proceedings

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In the paper, we study how the theory of compressed sensing is applied in wireless sensor networks to capture sparse signals of interest. Traditional data collection and compressive data gathering separately use client/server paradigm and dense random matrix, leading high computation load and energy consumption. We adopt sparse binary matrix for the measurement matrix. A mobile agent based compressed sensing paradigm is proposed. In the paradigm, the sensed data are stored locally, and it doesn't require network topology as prior knowledge. For the routing of mobile agents, we formulate a Mobile Agent Path Design Algorithm(MAPDA), which is designed by greedy algorithm. Finally Orthogonal Matching Pursuit(OMP) algorithm is used for signal recovery. The experimental results show the proposed algorithm can save energy than client/server paradigm based on different sparse binary matrix and plain-CS. In addition, we observe that sparse binary matrix has the same reconstruction performance as Gaussian random matrix(dense random matrix).

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“…To overcome these limitations, sparse random matrices have been proposed [7]. Most of their entries are zero.…”

Section: B Deterministic Measurement Matrixmentioning

confidence: 99%

Fast and efficient signals recovery for deterministic compressive sensing: Applications to biosignals

Ravelomanantsoa¹,

Rabah²,

Rouane³

2015

2015 Conference on Design and Architectures for Signal and Image Processing (DASIP)

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Compressed sensing is a technique that is suitable for compressing and recovering signals having sparse representations in certain bases. Compressed sensing has been widely used to optimize the measurement process of power and bandwidth constrained systems like wireless body sensor network. The central issues with compressed sensing are mainly the construction of measurement matrices and the development of efficient recovery algorithms. In this paper, we proposed a simple and fast recovery algorithm which performed a thresholding in the discrete cosine transform domain. We validated it by recovering electrocardiogram and electromyogram signals taken from the Phyiobank database. The simulation and experimental results have shown that the proposed recovery algorithm was 25 and 12 times faster than orthogonal matching pursuit and stagewise orthogonal matching pursuit, respectively. In addition, depending on the compression ratio, the signal-to-noise ratio of recovered signals were improved up to 2 dB.

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Vanishingly Sparse Matrices and Expander Graphs, With Application to Compressed Sensing

Cited by 23 publications

References 27 publications

Compressed Sensing: A Simple Deterministic Measurement Matrix and a Fast Recovery Algorithm

Compressed Sensing: A Simple Deterministic Measurement Matrix and a Fast Recovery Algorithm

Compressed sensing and mobile agent based sparse data collection in wireless sensor networks

Fast and efficient signals recovery for deterministic compressive sensing: Applications to biosignals

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