Reconstruction of finite rate of innovation signals in a noisy scenario: a robust, accurate estimation algorithm

The paradigmatic example of signals with finite rate of innovation (FRI) is a linear combination of a finite number of Diracs per time unit, a.k.a. spike sequence. Many researchers have investigated the problem of estimating the innovative part of a spike sequence, i.e., time instants t k s and weig...

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Vydáno v:Signal, image and video processing Ročník 14; číslo 8; s. 1707 - 1715
Hlavní autoři: Najjarzadeh, Meisam, Sadjedi, Hamed
Médium: Journal Article
Jazyk:angličtina
Vydáno: London Springer London 01.11.2020
Springer Nature B.V
Témata:
Algorithms
Computer Imaging
Computer Science
Image Processing and Computer Vision
Innovations
Maximum likelihood estimation
Multimedia Information Systems
Noise
Original Paper
Parameter estimation
Particle swarm optimization
Pattern Recognition and Graphics
Reconstruction
Robustness (mathematics)
Signal,Image and Speech Processing
Spikes
Vision
Maximum likelihood estimation
Modified particle swarm optimization
Sampling and reconstruction
Finite rate of innovation signals
Spike sequence
ISSN:1863-1703, 1863-1711
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Shrnutí:The paradigmatic example of signals with finite rate of innovation (FRI) is a linear combination of a finite number of Diracs per time unit, a.k.a. spike sequence. Many researchers have investigated the problem of estimating the innovative part of a spike sequence, i.e., time instants t k s and weights c k s of Diracs and proposed various deterministic or stochastic algorithms, particularly while the samples were corrupted by digital noise. In the presence of noise, maximum likelihood estimation method proved to be a powerful tool for reconstructing FRI signals, which is inherently an optimization problem. Wein and Srinivasan presented an algorithm, namely IterML, for reconstruction of streams of Diracs in noisy situations, which achieved promising reconstruction error and runtime. However, IterML is prone to limited resolution of search grid for t k , so as to avoid a phenomenon known as the curse of dimensionality, that makes it an inappropriate algorithm for applications that require highly accurate reconstruction of time instants. In order to overcome this shortcoming, we introduce a novel modified local best particle swarm optimization (MLBPSO) algorithm aimed at maximizing likelihood estimation of innovative parameters of a sparse spike sequence given noisy low-pass filtered samples. We demonstrate via extensive simulations that MLBPSO algorithm outperforms the IterML in terms of robustness to noise and accuracy of estimated parameters while maintaining comparable computational cost.
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ISSN:1863-1703
1863-1711
DOI:10.1007/s11760-020-01712-5