Reconstruction from limited data of arc means

V. P. Palamodov

doi:10.1007/bf02510116

Reconstruction from limited data of arc means

V. P. Palamodov^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

49 Scopus citations

Abstract

Let f be a function in a Euclidean plane with compact support in a half disc H. The problem of reconstruction of the function from the data of its integrals over half circles A ⊂ H with centers at the diameter of H is studied. An explicit formula and a microlocal analysis of stability of the reconstruction are given.

Original language	English
Pages (from-to)	25-42
Number of pages	18
Journal	Journal of Fourier Analysis and Applications
Volume	6
Issue number	1
DOIs	https://doi.org/10.1007/bf02510116
State	Published - 2000

Keywords

Arc mean transform
Audible zone
Energy
Factorization property
Interpolation
Microlocal estimate
Plancherel-type theorem
Reconstruction

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10.1007/bf02510116

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abstract = "Let f be a function in a Euclidean plane with compact support in a half disc H. The problem of reconstruction of the function from the data of its integrals over half circles A ⊂ H with centers at the diameter of H is studied. An explicit formula and a microlocal analysis of stability of the reconstruction are given.",

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AB - Let f be a function in a Euclidean plane with compact support in a half disc H. The problem of reconstruction of the function from the data of its integrals over half circles A ⊂ H with centers at the diameter of H is studied. An explicit formula and a microlocal analysis of stability of the reconstruction are given.

KW - Arc mean transform

KW - Audible zone

KW - Energy

KW - Factorization property

KW - Interpolation

KW - Microlocal estimate

KW - Plancherel-type theorem

KW - Reconstruction

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Reconstruction from limited data of arc means

Abstract

Keywords

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