The research of Kronecker product-based measurement matrix of compressive sensing

Zhang, Baoju; Xiang, Tong; Wang, Wei; Xie, Jiazu

doi:10.1186/1687-1499-2013-161

Cited by 6 publications

(9 citation statements)

References 14 publications

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“…The experimental processes refer to the reference [13]. We select the discrete wavelet transform as the sparse algorithm and the OMP algorithm as the image reconstruction algorithm.…”

Section: Resultsmentioning

confidence: 99%

The Chaotic Measurement Matrix for Compressed Sensing

Yao

Wang

Shen

et al. 2015

Intelligent Computing Theories and Methodologies

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Abstract. How to construct a measurement matrix with good performance and easy hardware implementation is the core research problem in compressed sensing. In this paper, we present a 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. Simulation results demonstrate IRC matrix has a better performance than Gaussian random matrix, Bernoulli random matrix and other state-of-the-art measurement matrices. Thus it can efficiently work on both natural image and remote sensing image.

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“…The experimental processes refer to the reference [13]. We select the discrete wavelet transform as the sparse algorithm and the OMP algorithm as the image reconstruction algorithm.…”

Section: Resultsmentioning

confidence: 99%

The Chaotic Measurement Matrix for Compressed Sensing

Yao

Wang

Shen

et al. 2015

Intelligent Computing Theories and Methodologies

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show abstract

“…Further work remains in constructing the so-called independent identically distributed random matrix with fewer dimensions. Moreover, we shall attempt to optimize the matrix based on QR decomposition, which could help to improve the incoherence between the measurement matrix and the [15]. LDPC was obtained from a deterministic measurement matrix in [12] sparse basis.…”

Section: Discussionmentioning

confidence: 99%

“…In [15,16], low-dimensional orthogonal basis vectors or matrices were used to construct high-dimensional matrices according to the Kronecker product. The proposed algorithm effectively reduces the storage space of a measurement matrix.…”

Section: Introductionmentioning

confidence: 99%

Low storage space for compressive sensing: semi-tensor product approach

Wang

Ruan

et al. 2017

J Image Video Proc.

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Random measurement matrices play a critical role in successful recovery with the compressive sensing (CS) framework. However, due to its randomly generated elements, these matrices require massive amounts of storage space to implement a random matrix in CS applications. To effectively reduce the storage space of the random measurement matrix for CS, we propose a random sampling approach for the CS framework based on the semi-tensor product (STP). The proposed approach generates a random measurement matrix, where the dimensions of the random measurement matrix are reduced to a quarter (or 1/16, 1/64, and even 1/256) of the number of dimensions, which are used for conventional CS. We then estimate the values of the sparse vector with a modified iteratively re-weighted least-squares (IRLS) algorithm. The results of numerical simulations showed that the proposed approach can reduce the storage space of a random matrix to at least a quarter while maintaining quality of reconstruction. All results confirmed that the proposed approach significantly influences the physical implementation of the CS in images, especially on embedded system and field programmable gate array (FPGA), where storage is limited.

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“…Differentiating w.r.to φ r and equating the result to zero yields (9) Thus from (9) , the measurement matrix is decomposed into a product of an orthonormal and asymmetric matrix.…”

Section: A Formation Of Kronecker Product Of Hybrid 'L' Determimentioning

confidence: 99%

“…But, the random measurement matrix consumes more storage and complexity while implementing in hardware. Many literatures [7][8][9][10][11][12] have dealt with formation of structured deterministic measurement matrices for faithful reconstruction of image, speech and video signal with high probability of success rate and good PSNR value. Hence, still there is a quest for designing an optimum measurement matrix with low storage requirement and complexity.…”

Section: Introductionmentioning

confidence: 99%

Weak GPS Acquisition Via Compressed Differential Detection Using Structured Measurement Matrix

Elango

Sudha

2016

International Journal on Smart Sensing and Intelligent Systems

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Abstract-Quality of the acquisition algorithm is the main criteria for assessment of the GPS receiver.Compressed sensing has been used recently in the GPS signal acquisition process to improve the acquisition sensitivity and find visible satellites in the two dimensional search space. In this paper, strategies for constructing the GPS Dictionary matrix using different measurement matrices are analyzed for weak signal conditions. Conventional acquisition methods use pure random or Bernoulli measurement matrices requiring huge storage memory and resulting in high computational cost for faithful sparse signal representation. Based on the restricted isometry and coherence properties, the Kronecker product of hybrid 'L' deterministic measurement matrix has been proposed for fast calculation and easy hardware implementation of the GPS acquisition module. Simulation results for weak signals of C/N 0 25 dB-Hz show that the compressed sensing combined with post-correlation differential detection scheme has the ability to determine more number of visible satellites. It is inferred that using this approach, 92% probability of obtaining 1.2 times more visible satellites than the uncompressed data length of 8 msec is achieved with lower computation time and significant improvement in average post correlation SNR value of 0.84 dB is obtained for four visible satellites.

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The research of Kronecker product-based measurement matrix of compressive sensing

Cited by 6 publications

References 14 publications

The Chaotic Measurement Matrix for Compressed Sensing

The Chaotic Measurement Matrix for Compressed Sensing

Low storage space for compressive sensing: semi-tensor product approach

Weak GPS Acquisition Via Compressed Differential Detection Using Structured Measurement Matrix

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