Binary Matrices for Compressed Sensing

Lu, Weizhi; Dai, Tao; Xia, Shu-Tao

doi:10.1109/tsp.2017.2757915

Cited by 41 publications

(28 citation statements)

References 23 publications

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“…For noisy signal recovery, additive Gaussian noise e is added to the original sparse signal x , where the signal-to-noise ratio (SNR) can be set. Therefore, given a sensing matrix Α , we have the measurement vector x x x (25) Note that if the original image x is a three-dimensional color image, the signal x is first converted to be a two-dimensional grayscale image signal F…”

Section: Simulation and Resultsmentioning

confidence: 99%

“…Both RIP [16][17][18][19] and coherence [9][10][11][12][13][20][21][22][23][24][25][26][27] are important tools to analyze the property of measurement matrices. In this paper, coherence will be adopted to analyze and illustrate the property of constructed measurement matrices, because it is easier to compute.…”

Section: Lemma 11mentioning

confidence: 99%

“…Although deterministic matrices may need a lot of complex mathematical operations during their construction, all elements of these matrices can be computed and generated on the fly only once, thus providing storage efficiency. Recently, many researchers have exploited some existing theories and techniques to construct deterministic measurement matrices, such as Euler Squares [9], extremal set theory [10], near orthogonal systems [12], chaotic systems [20][21][22], Legendre sequences [23], optimal codebooks [24], bipartite graph [25], low-density parity-check (LDPC) codes [13,14,26,28], equiangular tight frame theory [27], Reed-Muller sequences [29] and sparse fast Fourier transform [30]. In particular, Sasmal et al [11] proposed an optimal deterministic binary CS matrices by using a specialized composition rule which exploits the properties of existing binary matrices.…”

Section: Lemma 11mentioning

confidence: 99%

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Binary Sequence Family for Chaotic Compressed Sensing

2019

KSII TIIS

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It is significant to construct deterministic measurement matrices with easy hardware implementation, good sensing performance and good cryptographic property for practical compressed sensing (CS) applications. In this paper, a deterministic construction method of bipolar chaotic measurement matrices is presented based on binary sequence family (BSF) and Chebyshev chaotic sequence. The column vectors of these matrices are the sequences of BSF, where 1 is substituted with-1 and 0 is with 1. The proposed matrices, which exploit the pseudo-randomness of Chebyshev sequence, are sensitive to the initial state. The performance of proposed matrices is analyzed from the perspective of coherence. Theoretical analysis and simulation experiments show that the proposed matrices have limited influence on the recovery accuracy in different initial states and they outperform their Gaussian and Bernoulli counterparts in recovery accuracy. The proposed matrices can make the hardware implement easy by means of linear feedback shift register (LFSR) structures and numeric converter, which is conducive to practical CS.

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Section: Simulation and Resultsmentioning

confidence: 99%

Section: Lemma 11mentioning

confidence: 99%

Section: Lemma 11mentioning

confidence: 99%

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Binary Sequence Family for Chaotic Compressed Sensing

2019

KSII TIIS

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“…A method of fast super-resolution ultrasound imaging with CS reconstruction method and single plane wave transmission is proposed in [45]. In [46], a method of binary matrices for CS is proposed, it proposes a new performance parameter the minimal column degree d which performs better than the known coherence parameter, namely the maximum correlation between normalized columns; it has good recovery performance. It is also for sensing matrix A in formula y = Ax.…”

Section: B Greedy and Other Methodsmentioning

confidence: 99%

Marine Radar Image Processing of Compressed Sensing Based on Arbitrary Block Statistical Histogram and Dynamic Dictionary

Liu

Pang

Fu³

et al. 2019

IEEE Access

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In compressed sensing (CS), the absolute value of the inner product of signal and atom (or dictionary) is used to select atom (or dictionary); the atoms (or dictionaries) with larger absolute values of inner product are selected to decompose and reconstruct signals. This characteristic usually makes it impossible to distinguish the edges of objects (or targets) in some complex cases, especially when the density of objects is very high. For example: let signal, ψ 3 and ψ 4 denote several sparse basis matrices (i.e., sparse dictionaries);T are the sparse bases (i.e., atoms) from these sparse basis matrices (i.e., dictionaries), respectively. For signal x 1 , ψ 4l (or ψ 4 ) is selected instead of ψ 2j (or ψ 2 ); likewise, for x 2 , ψ 4l (or ψ 4 ) will be selected instead of ψ 3j (or ψ 3 ) and ψ 1i (or ψ 1 ). This causes the edge of the object to be unrecognizable. Another example is in l p regularization, it is not necessarily the optimal case: the smaller the value of −1 d x 0 , the better the sparse basis matrix (i.e., dictionary), or the larger the weighing parameter. At present, the inner product is used to process almost all signals in CS. Choosing the dictionary that matches the signal best rather than the dictionary with the maximum inner product value can reconstruct the signal more accurately. In order to overcome the above shortcoming, we propose a fully automatic radar image processing algorithm of CS based on arbitrary block statistical histogram and dynamic dictionary. We use arbitrary block statistical histogram to calculate the non-zero block numbers of different sizes, which can better choose the appropriate sparse base (or dictionary) for the signal. Furthermore, the better measurement vector y can be obtained, and the signal can be reconstructed more accurately than the state-of-the-art methods at the receiving end. To realize the proposed method, we construct objective functions and flow charts for noiseless and noisy signals, respectively. In our method, for noiseless signal, discarding the sub-images that do not contain objects can reduce running time; for noisy signal, according to the theory of wavelet, choosing the appropriate wavelet (i.e., wavelet basis) can usually suppress noise. Our proposed algorithm can overcome the above shortcoming of CS in using the absolute value of the inner product, reduce running time, suppressnoise, and improve the signal-tonoise ratio (SNR). The simulation results show that our method is superior to the state-of-the-art methods. INDEX TERMSCompressed sensing (CS), inner product, shortcoming, arbitrary block statistical histogram, dynamic dictionary, stagewise orthogonal matching pursuit algorithm (StOMP).

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“…In the last few years, various methods have been developed to design the sampling/measurement matrices. These methods are built based on random, binary, [36], [37], and structural matrices [38], [39]. However, these sampling matrices are all signal independent as well as non-optimal, due to the fact that they are unaware with the characteristics of the signal.…”

Section: A Challenges and State-of-the-artmentioning

confidence: 99%

DRCS-SR: Deep Robust Compressed Sensing for Single Image Super-Resolution

et al. 2020

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Compressed sensing (CS) represents an efficient framework to simultaneously acquire and compress images/signals while reducing acquisition time and memory requirements to process or transmit them. Specifically, CS is able to recover an image from a random measurements. Recently, deep neural networks (DNNs) are exploited not only to acquire and compress but also for recovering signals/images from a highly incomplete set of measurements. Super-resolution (SR) algorithms attempt to generate a single high resolution (HR) image from one or more low resolution (LR) images of the same scene. Despite the success of the existing SR networks to recover HR images with better visual quality, there are still some challenges that need to be addressed. Specifically, for many practical applications, the original images may be affected by various transformation effects including rotation, scaling, and translation. Moreover, in real-time transmissions, image compression is carried out first, followed by acquisition time reduction. To address this problem, we propose a novel robust deep CS framework that is able to mitigate the geometric transformation and recover HR images. Specifically, the proposed framework is able to perform two tasks. First, it is able to compress the transformed image with the help of an optimized generated measurement matrix. Second, the proposed framework is able not only to recover the original image from the compressed version but also to mitigate the transformation effects. The simulation results reported in this paper show that the proposed framework is able to achieve high level of robustness against different geometric transformations in terms of peak signal-to-noise-ratio (PSNR) and similar structure index measurements (SSIM). For the convenience of dissemination, we make our source codes available at GitHub a .

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Binary Matrices for Compressed Sensing

Cited by 41 publications

References 23 publications

Binary Sequence Family for Chaotic Compressed Sensing

Binary Sequence Family for Chaotic Compressed Sensing

Marine Radar Image Processing of Compressed Sensing Based on Arbitrary Block Statistical Histogram and Dynamic Dictionary

DRCS-SR: Deep Robust Compressed Sensing for Single Image Super-Resolution

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