Construction of Measurement Matrix Based on Cyclic Direct Product and QR Decomposition for Sensing and Reconstruction of Underwater Echo
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TLDR
The results clearly show the advantage of this method in terms of reconstruction accuracy, signal-to-noise ratio (SNR) enhancement, and construction time, by comparison with Gaussian matrix, Bernoulli matrix, partial Hadamard matrix and Toeplitz matrix.Abstract:
Compressive sensing is a very attractive technique to detect weak signals in a noisy background, and to overcome limitations from traditional Nyquist sampling. A very important part of this approach is the measurement matrix and how it relates to hardware implementation. However, reconstruction accuracy, resistance to noise and construction time are still open challenges. To address these problems, we propose a measurement matrix based on a cyclic direct product and QR decomposition (the product of an orthogonal matrix Q and an upper triangular matrix R). Using the definition and properties of a direct product, a set of high-dimensional orthogonal column vectors is first established by a finite number of cyclic direct product operations on low-dimension orthogonal “seed” vectors, followed by QR decomposition to yield the orthogonal matrix, whose corresponding rows are selected to form the measurement matrix. We demonstrate this approach with simulations and field measurements of a scaled submarine in a freshwater lake, at frequencies of 40 kHz–80 kHz. The results clearly show the advantage of this method in terms of reconstruction accuracy, signal-to-noise ratio (SNR) enhancement, and construction time, by comparison with Gaussian matrix, Bernoulli matrix, partial Hadamard matrix and Toeplitz matrix. In particular, for weak signals with an SNR less than 0 dB, this method still achieves an SNR increase using less data.read more
Citations
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Direct Under-Sampling Compressive Sensing Method for Underwater Echo Signals and Physical Implementation
TL;DR: The method proposed provides an effective way for compressed sensing theory to move toward practical field applications that use underwater echo signals, and it is shown that DUS-CS works well when the SNR is 3 dB, 0 dB, −3 dB, and −5 dB and the compression ratio is 50%, 20%, and 10%.
Journal ArticleDOI
Floating Point Implementation of the Improved QRD and OMP for Compressive Sensing Signal Reconstruction
TL;DR: The experimental results show that the optimization of floating point unit offers significant resource optimization in QR decomposition, and also better performance of high peak signal-to-noise ratio of 32.99 dB, which outperforms all other fixed point Orthogonal Matching Pursuit systems.
Efficient Recovery of Block Sparse Signals by an Improved Algorithm of Block-StOMP
Boxue Huang,Tong Zhou +1 more
TL;DR: In this paper, an improved version of the block stagewise orthogonal matching pursuit (Block-StOMP) algorithm is proposed, which uses the estimated TDR (true discovery rate) to prune support sets of each stage.
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Analysis of the Measurement Matrix in Directional Predictive Coding for Compressive Sensing of Medical Images
TL;DR: The experimental result shows that the spatially directional predictive coding (SDPC) with Laplace measurement matrices performs better compared to scalar quantization (SQ) and differential pulse code modulation (DPCM) methods.
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Posted Content
Near Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
Emmanuel J. Candès,Terence Tao +1 more
TL;DR: In this article, it was shown that if the objects of interest are sparse or compressible in the sense that the reordered entries of a signal $f \in {\cal F}$ decay like a power-law, then it is possible to reconstruct $f$ to within very high accuracy from a small number of random measurements.
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