Modifications of the Euclidean algorithm for isolating periodicities from a sparse set of noisy measurements

Casey, Stephen D.; Sadler, Brian M.

doi:10.1109/78.536682

Cited by 40 publications

(23 citation statements)

References 18 publications

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“…Euclid's algorithm finds application in the analysis of 1-dimensional signals, e.g., to determine the periodicity of signals from incomplete observations [20] [21]. This is equivalent to estimating the step size of a scalar quantizer, since the transform is trivially defined.…”

Section: Introductionmentioning

confidence: 99%

Transform coder identification

Tagliasacchi

Visentini-Scarzanella

Dragotti

et al. 2013

2013 IEEE International Conference on Acoustics, Speech and Signal Processing

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The widespread popularity of transform coding has made it central to a wide range of methods in forensics, quality assessment and digital restoration. However, most approaches require prior knowledge of the transform coding parameters. In this paper, we consider the challenging problem of identifying the transform matrix as well as the quantization step sizes of a transform coder, given a set of P non-overlapping N -dimensional vectors observed as its output. We formulate the problem in terms of finding the lattice with the largest determinant that contains all observed vectors and we propose an algorithm that is able to find the optimal solution. Our experimental analysis shows that the probability of success of the algorithm quickly approaches 1 for small values of (P − N ). The complexity of the proposed algorithm grows linearly with the dimensionality N .

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Section: Introductionmentioning

confidence: 99%

Transform coder identification

Tagliasacchi

Visentini-Scarzanella

Dragotti

et al. 2013

2013 IEEE International Conference on Acoustics, Speech and Signal Processing

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“…i.) Developed computationally straightforward techniques for spectral analysis of a very broad class of periodic processes, including procedures so that estimates achieve the Cramer-Rao bound [21,22,23,24,41,43]. Our techniques of parameter estimation fit models of currently deployed sonar, radar, and communication systems.…”

Section: Introduction: An Overview Of Resultsmentioning

confidence: 99%

“…Modifications of the Euclidean algorithm were presented for determining the period from a sparse set of noisy measurements in [22], [23]. The elements of the set were assumed to be the noisy occurrence times of a periodic event with (perhaps very many) missing measurements.…”

Section: Recent Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Number Theoretic Methods in Parameter Estimation

Casey¹

1998

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“…While in this section we assume knowledge of the first quantisation step size ∆ 1 , it is possible to retrieve it with existing methods such as [12].…”

Section: Algorithmic Solutionsmentioning

confidence: 99%