A fast hybrid DSC-GS-MLE approach for multiple sinusoids estimation

In this paper, we develop a novel hybrid method for estimation of frequencies of complex multiple sinusoids buried in noise. The algorithm applies two concepts of estimation statistics − data-supported optimization (DSO) and contracting grid search (CGS) to grid-search maximum likelihood estimator (...

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Bibliographic Details
Published in:Signal, image and video processing image and video processing, 2023-02, Vol.17 (1), p.165-172
Main Authors: Hussain, Md Shahnawaz, Pal, Srikanta
Format: Article
Language:English
Subjects:
Algorithms
Complexity
Computer Imaging
Computer Science
Cramer-Rao bounds
Image Processing and Computer Vision
Lower bounds
Maximum likelihood estimators
Multimedia Information Systems
Optimization
Original Paper
Pattern Recognition and Graphics
Signal,Image and Speech Processing
Sine waves
Vision
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Summary:In this paper, we develop a novel hybrid method for estimation of frequencies of complex multiple sinusoids buried in noise. The algorithm applies two concepts of estimation statistics − data-supported optimization (DSO) and contracting grid search (CGS) to grid-search maximum likelihood estimator (GS-MLE), which is an optimal estimator in terms of accuracy, compared to any other reported method. This hybrid data-supported contracting GS-MLE (DSC-GS-MLE) technique is observed to reduce the time complexity of computationally burdensome GS-MLE. The proposed algorithm has two variants − two-stage variant (DSC-GS-MLE-2) and three-stage variant (DSC-GS-MLE-3). Extensive Monte Carlo simulations show that DSC-GS-MLE-2 retains the optimality of GS-MLE for two and three sinusoids cases. On the other hand, DSC-GS-MLE-3 is suboptimal when compared to GS-MLE but proves to be even faster than DSC-GS-MLE-2 for two sinusoids case, although it does not produce reliable estimates for three sinusoids case. Moreover, they are verified to achieve the Cramér–Rao lower bound (CRLB) as GS-MLE does, even for the closely spaced sinusoids (comparative tables are being reported in Sect. 4 of this manuscript).
ISSN:1863-1703
1863-1711
DOI:10.1007/s11760-022-02218-y