Stability estimates for the local Radon transform

被引：1

作者：

Andersson, Joel ^{[1
]}

Boman, Jan ^{[1
]}

机构：

[1] Stockholm Univ, Dept Math, SE-10691 Stockholm, Sweden

来源：

INVERSE PROBLEMS | 2018年 / 34卷 / 03期

关键词：

radon transform; local injectivity; stability estimates; INVERSION-FORMULA;

D O I：

10.1088/1361-6420/aaa99c

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the inverse problem for the 2-dimensional local Radon transform R[f], where f is supported in y >= x(2) and R[f](xi, eta) = integral f (x, xi x + eta) dx is defined near (xi, eta) = (0, 0). We give logarithmic estimates of f in terms of R[f] for functions f that satisfy an a priori bound. For a certain class of smooth, positive weight functions m we give similar estimates for the weighted Radon transform R-m vertical bar f](xi, eta) = integral f (x, xi x + eta) m(xi, eta, x) dx.

引用

页数：23

共 50 条

[41] Wavelet transform and radon transform on the quaternion Heisenberg group [J].

He, Jian Xun ;

Liu, He Ping .

ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2014, 30 (04) :619-636

[42] Wavelet transform and radon transform on the quaternion Heisenberg group [J].

Jian Xun He ;

He Ping Liu .

Acta Mathematica Sinica, English Series, 2014, 30 :619-636

[43] Wavelet Transform and Radon Transform on the Quaternion Heisenberg Group [J].

Jian Xun HE ;

He Ping LIU .

ActaMathematicaSinica(EnglishSeries), 2014, 30 (04) :619-636

[44] Optical-flow estimation by means of local projection analysis with the Radon-Hermite transform [J].

Escalante-Ramírez, B ;

Silván-Cárdenas, JL .

MATHEMATICAL MODELING, BAYESIAN ESTIMATION, AND INVERSE PROBLEMS, 1999, 3816 :121-131

[45] STABILITY ESTIMATES FOR THE X-RAY TRANSFORM ON SIMPLE ASYMPTOTICALLY HYPERBOLIC MANIFOLDS [J].

Eptaminitakis, Nikolas .

PURE AND APPLIED ANALYSIS, 2022, 4 (03) :487-516

[46] UNITARIZATION AND INVERSION FORMULAE FOR THE RADON TRANSFORM BETWEEN DUAL PAIRS [J].

Alberti, Giovanni S. ;

Bartolucci, Francesca ;

De Mari, Filippo ;

De Vito, Ernesto .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2019, 51 (06) :4356-4381

[47] Isometry property and inversion of the Radon transform over a family of paraboloids [J].

Kim, Jeongmin ;

Moon, Sunghwan .

FILOMAT, 2024, 38 (23) :8047-8052

[48] A LOCAL UNIQUENESS THEOREM FOR WEIGHTED RADON TRANSFORMS [J].

Boman, Jan .

INVERSE PROBLEMS AND IMAGING, 2010, 4 (04) :631-637

[49] Pattern recognition by means of the Radon transform and the continuous wavelet transform [J].

Magli, E ;

Olmo, G ;

Lo Presti, L .

SIGNAL PROCESSING, 1999, 73 (03) :277-289

[50] The Generalized Radon Transform on the Plane, the Inverse Transform, and the Cavalieri Conditions [J].

D. A. Popov .

Functional Analysis and Its Applications, 2001, 35 :270-283

← 1 2 3 4 5 →