Explicit calculation of singular integrals of tensorial polyadic kernels
| hal.structure.identifier | Laboratoire Ondes et Matière d'Aquitaine [LOMA] | |
| hal.structure.identifier | Université de Bordeaux [UB] | |
| dc.contributor.author | PERRIN, Mathias | |
| hal.structure.identifier | Laboratoire Georges Friedel [LGF-ENSMSE] | |
| hal.structure.identifier | Centre Sciences des Processus Industriels et Naturels [SPIN-ENSMSE] | |
| dc.contributor.author | GRUY, Frédéric | |
| dc.date.created | 2022 | |
| dc.date.issued | 2022 | |
| dc.identifier.issn | 0033-569X | |
| dc.description.abstractEn | The Riesz transform of u $u$ : $\mathcal{S}(\R^n) \rightarrow \mathcal{S'}(\R^n)$ is defined as a convolution by a singular kernel, and can be conveniently expressed using the Fourier Transform and a simple multiplier. We extend this analysis to higher order Riesz transforms, i.e. some type of singular integrals that contain tensorial polyadic kernels and define an integral transform for functions $\mathcal{S}(\R^n) \rightarrow \mathcal{S'}(\R^{ n \times n \times \dots n})$. We show that the transformed kernel is also a polyadic tensor, and propose a general method to compute explicitely the Fourier mutliplier. Analytical results are given, as well as a recursive algorithm, to compute the coefficients of the transformed kernel. We compare the result to direct numerical evaluation, and discuss the case n = 2, with application to image analysis. | |
| dc.language.iso | en | |
| dc.publisher | American Mathematical Society | |
| dc.title.en | Explicit calculation of singular integrals of tensorial polyadic kernels | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1090/qam/1629 | |
| dc.subject.hal | Mathématiques [math]/Analyse numérique [math.NA] | |
| dc.subject.hal | Informatique [cs]/Intelligence artificielle [cs.AI] | |
| dc.subject.hal | Informatique [cs]/Vision par ordinateur et reconnaissance de formes [cs.CV] | |
| dc.identifier.arxiv | 2209.01111 | |
| bordeaux.journal | Quarterly of Applied Mathematics | |
| bordeaux.page | 65 - 86 | |
| bordeaux.volume | 81 | |
| bordeaux.issue | 1 | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-03768198 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03768198v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Quarterly%20of%20Applied%20Mathematics&rft.date=2022&rft.volume=81&rft.issue=1&rft.spage=65%20-%2086&rft.epage=65%20-%2086&rft.eissn=0033-569X&rft.issn=0033-569X&rft.au=PERRIN,%20Mathias&GRUY,%20Fr%C3%A9d%C3%A9ric&rft.genre=article |
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