Reconstruction Error in Nonuniformly Sampled Approximately Sparse Signals

Stanković, Ljubiša; Brajović, Miloš; Stanković, Isidora; Ioana, Cornel; Daković, Miloš

doi:10.1109/lgrs.2020.2968137

Cited by 10 publications

(8 citation statements)

References 32 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%

“…However, the estimates ( 6), ( 8), (9), are only rough due to influence of other components. Therefore, we can proceed with the other algorithm stages.…”

Section: First Stage -Initial Parameter Estimationmentioning

confidence: 99%

“…Obtained results are similar to those in Figure 1 but it can be noted that here it is required approximately 25% more samples to achieve the same accuracy. The reason behind this is the higher variance in estimation caused by nonuniform sampling [9].…”

Section: Nonuniformly Subsampled Signalmentioning

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%

“…The Aboutanios-Mulgrew algo-rithm is used in the first and third stages [4]. In the second stage, the amplitudes and phases are re-estimated at once with a common technique forthe compressive sensing of sinusoids [9].…”

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%

“…However, the estimates ( 6), ( 8), (9), are only rough due to influence of other components. Therefore, we can proceed with the other algorithm stages.…”

Section: First Stage -Initial Parameter Estimationmentioning

confidence: 99%

Section: Nonuniformly Subsampled Signalmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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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High‐resolution passive imaging by electromagnetic vortex beams

Guo

Fan

et al. 2021

Micro & Optical Tech Letters

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A new scheme to achieve high resolution in passive millimeter wave imaging (PMMWI) using electromagnetic (EM) vortex beams is proposed in this article. The spatial resolution of the traditional PMMWI system based on the mechanically or electronically controlled scanning scheme is mainly limited by the beam width of the receiver. However, it is not practical to fabricate an antenna that is too large, another possible way to improve the resolution is to increase the sampling points but will increase the imaging time. In this article, the multimode EM vortex beam is applied to achieve high resolution with less sampling points. The imaging scene is first discretized into small grid cells, and then multimode measurements are conducted during the scanning process to construct equations to solve the unknown brightness distribution. The compress sensing method is applied to reduce the number of orbital angular momentum mode. Simulation results demonstrate that high resolution can be achieved by the proposed method.

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