Image Restoration in Optical-Acoustic Tomography

Попов, Д. А.; Sushko, D. V.

doi:10.1023/b:prit.0000044261.87490.05

Cited by 17 publications

(37 citation statements)

References 3 publications

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“…Projections (R [f O ]) (t, ω) of function f O (x) with ω parametrized in spherical coordinates (i.e., ω = (sin ϕ cos θ, sin ϕ sin θ, cos ϕ)) are shown in figure 4(c) for a fixed value of ϕ = ϕ 0 ≈ 53 • . Symmetries expressed by equations (34) and (37) can be clearly seen in this figure. A magnified image of projections restricted to the region (t, θ) ∈ [−1, 0] × [0, π/2] with ϕ = ϕ 0 is shown in figure 4(d).…”

Section: Boundary Of An Octet In 3dmentioning

confidence: 86%

Inversion of the spherical means transform in corner-like domains by reduction to the classical Radon transform

Kunyansky

2015

Inverse Problems

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We consider an inverse problem arising in thermo-/photo-acoustic tomography that amounts to reconstructing a function f from its circular or spherical means with the centers lying on a given measurement surface. (Equivalently, these means can be expressed through the solution u(t, x) of the wave equation with the initial pressure equal to f .) An explicit solution of this inverse problem is obtained in 3D for the surface that is the boundary of an open octet, and in 2D for the case when the centers of integration circles lie on two rays starting at the origin and intersecting at the angle equal to π/N , N = 2, 3, 4, .... Our formulas reconstruct the Radon projections of a function closely related to f , from the values of u(t, x) on the measurement surface. Then, function f can be found by inverting the Radon transform.

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Section: Boundary Of An Octet In 3dmentioning

confidence: 86%

Inversion of the spherical means transform in corner-like domains by reduction to the classical Radon transform

Kunyansky

2015

Inverse Problems

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“…This did not prevent practitioners from the reconstructions, since good approximate inversion formulas (parametrices) could be developed, followed by an iterative improvement of the reconstruction (see, e.g. the reconstruction procedures in [128,129,[132][133][134], and especially [106,107]). The first set of exact inversion formulas of filtered backprojection type was discovered in [38].…”

Section: Filtered Backprojection Methodsmentioning

confidence: 99%

Mathematics of thermoacoustic tomography

Kuchment

Kunyansky

2008

Eur. J. Appl. Math.

305

312

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“…The enormous growth in the application areas of the Radon transform and the fact that digital computations are often required, has led to the development of the discrete Radon transform (DRT). The Radon transform (RT) is a widely studied algorithm used to perform image pattern extraction in fields such as computer graphics and several others digital signal and image processing applications [23][24][25][26][27][28][29][30][31][32].…”

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confidence: 99%