OperA: Operator-Based Annihilation for Finite-Rate-of-Innovation Signal Sampling

Seelamantula, Chandra Sekhar

doi:10.1007/978-3-319-19749-4_13

Cited by 4 publications

(5 citation statements)

References 42 publications

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“…Remark 2.2. Special generalized sampling schemes for the shift operator and the differential operator have also been proposed by Seelamantula [23], but without considering the relations between these operators. However, a rigorous investigation of rank properties of the involved matrices has not been given in [23].…”

Section: Generalization 2: Changing the Sampling Schemementioning

confidence: 99%

“…Special generalized sampling schemes for the shift operator and the differential operator have also been proposed by Seelamantula [23], but without considering the relations between these operators. However, a rigorous investigation of rank properties of the involved matrices has not been given in [23]. The representation of Prony's method as an approach to reconstruct expansions into eigenfunctions of linear operators has been given already in [13].…”

Section: Generalization 2: Changing the Sampling Schemementioning

confidence: 99%

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The Generalized Operator Based Prony Method

Stampfer

Plonka

2020

Constr Approx

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The generalized Prony method introduced in [13] is a reconstruction technique for a large variety of sparse signal models that can be represented as sparse expansions into eigenfunctions of a linear operator A. However, this procedure requires the evaluation of higher powers of the linear operator A that are often expensive to provide.In this paper we propose two important extensions of the generalized Prony method that simplify the acquisition of the needed samples essentially and at the same time can improve the numerical stability of the method. The first extension regards the change of operators from A to ϕ(A), where ϕ is an analytic function, while A and ϕ(A) possess the same set of eigenfunctions. The goal is now to choose ϕ such that the powers of ϕ(A) are much simpler to evaluate than the powers of A. The second extension concerns the choice of the sampling functionals. We show, how new sets of different sampling functionals F k can be applied with the goal to reduce the needed number of powers of the operator A (resp. ϕ(A)) in the sampling scheme and to simplify the acquisition process for the recovery method.

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Section: Generalization 2: Changing the Sampling Schemementioning

confidence: 99%

Section: Generalization 2: Changing the Sampling Schemementioning

confidence: 99%

The Generalized Operator Based Prony Method

Stampfer

Plonka

2020

Constr Approx

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“…where this variation of Prony's method is called Operator based Annihilation. The difference to the present thesis is that in [43] this idea is only used for exponential eigenfunctions.…”

Section: Prony's Method: the Operator Waymentioning

confidence: 92%

“…Remark 2.1.1. The idea of using the product of suitable linear polynomial factors (λ j − z) in combination with the differential operator to annihilate the signal at hand can be found in [43],…”

Section: Prony's Method: the Operator Waymentioning

confidence: 99%

“…Although the examples concerning the differential and the difference operators with arbitrary starting points are also developed in [43], the connection between these two schemes was not given. Moreover, in [43] only point evaluation functionals were taken into account and the results therein were already implied by the Generalized Prony Method of Peter & Plonka [32].…”

Section: Prony's Method: the Operator Waymentioning

confidence: 99%

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