A Tutorial on Sparse Signal Reconstruction and Its Applications in Signal Processing

Stanković, Ljubiša; Sejdić, Ervin; Stanković, Srdjan; Daković, Miloš; Orović, Irena

doi:10.1007/s00034-018-0909-2

Cited by 63 publications

(44 citation statements)

References 105 publications

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“…B     denotes the B-bit quantization. These quantized 8-bit measurements are used as the basis of the CS reconstruction using the classical OMP algorithm from [8], [11], [12]. The number of available 8-bit measurements OMP M was varied from 8 to 128, with step 8.…”

Section:  mentioning

confidence: 99%

“…digital images are sparse in a two-dimensional discrete cosine transform domain. Similarly, signals appearing in telecommunications, radar technology, and biomedicine are commonly sparse in the Fourier transform domain, therefore making possible to apply the CS concepts and perform reconstructions based on the reduced sets of samples [12]. Generally speaking, the CS theory inherently assumes that the measurements are taken accurately.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of noise in complex-valued binary and bipolar sigmoid compressive sensing

et al. 2019

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Binary compressive sensing (CS) is a relatively new idea in the theory of sparse signal reconstruction. Under this framework, the signal is reconstructed based on the sign of the available measurements. This paper analyzes basic onebit CS concepts for the case of complex valued random Gaussian measurement matrices. The reconstruction is compared with the B-bit quantized measurements. The concept of binary CS-based reconstruction is generalized by applying a sigmoid function to the measurements. Noise influence is also considered. The reconstruction is performed using a simple iterative thresholding algorithm.

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Section:  mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of noise in complex-valued binary and bipolar sigmoid compressive sensing

et al. 2019

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“…In real applications, many signals are sparse or approximately sparse in a certain transformation domain. This makes the CS applicable in various fields of signal processing [14].…”

Section: Introductionmentioning

confidence: 99%

“…The numbers of quantized measurements M = 192, M = 170, and M = 128 are considered. Typical cases for the measurements quantization to B ∈ {4,6,8,10,12,14,16,18,20, 24} bits are analyzed.Signals with sparsity levels K ∈ {5, 10, 15, 20, 25, 30} are considered. The average statistical signal-to-nose ration SN R st and theoretical signal-to-noise ration SN R th values Reconstruction error with measurements quantized to fit the registers with B bits for various sparsities and the numbers of measurements.…”

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confidence: 99%

Quantization in Compressive Sensing: A Signal Processing Approach

et al. 2020

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Influence of the finite-length registers and quantization effects on the reconstruction of sparse and approximately sparse signals is analyzed in this paper. For the nonquantized measurements, the compressive sensing (CS) framework provides highly accurate reconstruction algorithms that produce negligible errors when the reconstruction conditions are met. However, hardware implementations of signal processing algorithms involve the finite-length registers and quantization of the measurements. An analysis of the effects related to the measurements quantization with an arbitrary number of bits is the topic of this paper. A unified mathematical model for the analysis of the quantization noise and the signal nonsparsity on the CS reconstruction is presented. An exact formula for the expected energy of error in the CS-based reconstructed signal is derived. The theory is validated through various numerical examples with quantized measurements, including the cases of approximately sparse signals, noise folding, and floating-point arithmetics.

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“…The only problem that remains is how to determine the proper signal support. Orthogonal Greedy Algorithms (OGAs) that belong to the family of the Compressed Sensing (CS) methods try to solve this issue [14]. They restore the signal x step-by-step in an iterative manner.…”

Section: Introductionmentioning

confidence: 99%

On a Sparse Approximation of Compressible Signals

Dziwoki

Kucharczyk

2019

Circuits Syst Signal Process

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Many physical phenomena can be modeled by compressible signals, i.e., the signals with rapidly declining sample amplitudes. Although all the samples are usually nonzero, due to practical reasons such signals are attempted to be approximated as sparse ones. Because sparsity of compressible signals cannot be unambiguously determined, a decision about a particular sparse representation is often a result of comparison between a residual error energy of a reconstruction algorithm and some quality measure. The paper explores a relation between mean square error (MSE) of the recovered signal and the residual error. A novel, practical solution that controls the sparse approximation quality using a target MSE value is the result of these considerations. The solution was tested in numerical experiments using orthogonal matching pursuit (OMP) algorithm as the signal reconstruction procedure. The obtained results show that the proposed quality metric provides fine control over the approximation process of the compressible signals in the mean sense even though it has not been directly designed for use in compressed sensing methods such as OMP.

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A Tutorial on Sparse Signal Reconstruction and Its Applications in Signal Processing

Cited by 63 publications

References 105 publications

Analysis of noise in complex-valued binary and bipolar sigmoid compressive sensing

Analysis of noise in complex-valued binary and bipolar sigmoid compressive sensing

Quantization in Compressive Sensing: A Signal Processing Approach

On a Sparse Approximation of Compressible Signals

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