On the Errors in Randomly Sampled Nonsparse Signals Reconstructed With a Sparsity Assumption

Stanković, Ljubiša; Daković, Miloš; Stanković, Isidora; Vujovic, Stefan

doi:10.1109/lgrs.2017.2768664

Cited by 14 publications

(10 citation statements)

References 17 publications

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“…For simplicity reasons it is assumed that number of sinusoids M is known in advance. There are several available algorithms for this purpose [9,10], with the main obstacle that it is assumed that sinusoidal frequency belongs to the grid. The signal model without this limitation is considered in this paper.…”

Section: Signal Modelmentioning

confidence: 99%

“…Development of the signal processing field was closely related to sinusoids and such interest is lasting. Recently, the emerging field of compressive sensing signal processing handling the signals sampled below the Nyquist criterion has attracted significant attention of the scientific community [9][10][11]. Reconstruction of an undersampled and non-uniformly sampled sum of sinusoids has importance in various applications.…”

Section: Introductionmentioning

confidence: 99%

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Estimation of parameters of a sum of sinusoids sampled below the Nyquist rate with frequencies away from the grid

Djurović

2021

Journal of Electrical Engineering

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We are witnessing a growing interest in processing signals sampled below the Nyquist rate. The main limitation of current approaches considering estimation of multicomponent sinusoids parameters is the assumption of frequencies on the frequency grid. The sinusoids away from the frequency grid are considered in this paper. The proposed procedure has three stages. In the first two, a rough estimation of signal components is performed while in the third refinement in estimation is achieved in a component-by-component manner. We have tested the developed technique on an extended set of simulation examples showing excellent accuracy. Three scenarios are considered in experiments: missing samples, noisy environment, and non-uniform sampling below the Nyquist rate.

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Section: Signal Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Estimation of parameters of a sum of sinusoids sampled below the Nyquist rate with frequencies away from the grid

Djurović

2021

Journal of Electrical Engineering

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“…The same value is obtained for other considered random matrices. The variance σ 2 µ of µ(k i , k) is presented in Table I for various measurement matrices [6], [13]- [15].…”

Section: A Initial Estimatementioning

confidence: 99%

“…Moreover, the problem of the physical unavailability of measurements, or the problem of a significant signal corruption, are also potentially solvable within the CS framework. Since the establishment of CS, the phenomena related to the reduced sets of measurements and sparse signal reconstruction have been supported by the fundamental theory and well-defined mathematical framework, while the performance of the reconstruction processes have been continuously improved by newly introduced algorithms, often adapted to perform in a particular context, or to solve specific problems [10]- [15]. In real applications, many signals are sparse or approximately sparse in a certain transformation domain.…”

Section: Introductionmentioning

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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“…This case occurs often in application of some signal processing denoising techniques, such as the L-statistics [4]. During the last decade, the CS theory has been significantly developed, with various reconstruction methods and algorithms being introduced [8]- [13].…”

Section: Introductionmentioning

confidence: 99%

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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On the Errors in Randomly Sampled Nonsparse Signals Reconstructed With a Sparsity Assumption

Cited by 14 publications

References 17 publications

Estimation of parameters of a sum of sinusoids sampled below the Nyquist rate with frequencies away from the grid

Estimation of parameters of a sum of sinusoids sampled below the Nyquist rate with frequencies away from the grid

Quantization in Compressive Sensing: A Signal Processing Approach

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

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