# Reconstruction Formula For Photoacoustic Tomography With Cylindrical Detectors

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### Simultaneous Reconstructions of Absorption Density and Wave

The literature on reconstruction formulas and back-projection algorithms for photoacoustic imaging is vast. Wang et al. developed reconstruction formulas for cylindrical, spherical, and planar measurement geometries in a series of pa-pers [30, 29, 28, 31], and recently many more algorithms based on reconstruction 2

### EXTERIOR/INTERIOR PROBLEM FOR THE CIRCULAR MEANS TRANSFORM

very similar problem arises in the photoacoustic tomography with integrating line detectors, and the derivation presented below can be found in the corresponding literature (see, for example [4]). Let us assume that the acoustic wave is measured by in nitely long transducers placed on the surface of a cylindrical catheter of radius R

### Full eld inversion in photoacoustic tomography with variable

this paper, we present a two-step reconstruction method for full eld detection photoacoustic tomography that takes variable speed of sound into account. In the rst step, by applying the inverse Radon transform, the pressure distribution at the measurement time is reconstructed point-wise from the projection data.

### On the determination of a function from cylindrical Radon

On the determination of a function from cylindrical Radon transforms Sunghwan Moon Abstract This paper is devoted to a Radon-type transform arising in Photoacoustic Tomography that uses integrating line detectors. We consider two situations: when the line detectors are tangent

### Universal back-projection algorithm for photoacoustic

We report results of a reconstruction algorithm for three-dimensional photoacoustic computed tomography. A universal back-projection formula is presented for three types of imaging geometries: planar, spherical, and cylindrical surfaces. A solid-angle weighting factor is introduced in the back-projection formula to compensate

### Exact Series Reconstruction in Photoacoustic Tomography with

Exact Series Reconstruction in Photoacoustic Tomography with Circular Integrating Detectors Gerhard Zangerl∗ Otmar Scherzer† Markus Haltmeier‡ January 30, 2009 Abstract. A method for photoacoustic tomography is presented that uses circular integrals of the acoustic wave for the reconstruction of a three-dimensional image. Image

### Boundary conditions in photoacoustic tomography and image

this depth limit. Photoacoustic tomography has ﬁlled this void by combining high ultrasonic resolution and strong optical contrast in a single modality. However, it has been assumed in reconstruction of photoacoustic tomography until now that ultrasound propagates in a boundary-free inﬁnite medium. We present the boundary conditions

### Boundary conditions in photoacoustic tomography and image

this depth limit. Photoacoustic tomography has Þlled this void by combining high ultrasonic resolution and strong optical contrast in a single modality. However, it has been assumed in reconstruction of photoacoustic tomography until now that ultrasound propagates in a boundary-free inÞnite medium. We present the boundary conditions

### Reconstructions in limited-view thermoacoustic tomography

Key words: thermoacoustic tomography, photoacoustic tomography, optoacoustic tomography, local tomography, limited view, incomplete data I. INTRODUCTION A correlation between the electromagnetic absorption of a biological tissue and its physiological and pathological fea-tures is reported.1 4 To employ this contrast mechanism,

### AppliedMathematics - Universität Innsbruck

Technikerstraße 13 - 6020 Innsbruck - Austria Tel.: +43 512 507 53803 Fax: +43 512 507 53898 https://applied-math.uibk.ac.at AppliedMathematics

### applicationstointravascularimaging

the feasibility of tomography-like reconstruction in IVPA and IVUS, which can be obtained by the techniques proposed here. The rest of the paper is organized as follows: In Section 1 we discuss an exact inversion formula for the CMT in the exterior and interior/exterior problem. We then present an algorithm based on

### Mathematical Methods for Photoacoustical Imaging

the object (over time) and are used for reconstruction of Inverse Problem of Photoacoustic Tomography I Given: p 3.Taking into account semi cylindrical detectors

### Analytic explanation of spatial resolution related to

In cylindrical recording geometry, it is assumed that the measurement surface is a circular cylindrical surface r0 5(r0,w0,z0) in the circular cylindrical coordinates r 5(r,w,z). The sample lies in the cylinder, i.e., A(r) 5A(r,w,z) when r,r0, and A(r)50 when r.r0. The rigorous reconstruction formula for A(r) can be written as @9,11#

### Spatial Resolution in Photoacoustic Tomography: Eﬀects of

the data Lφ,wf leads to a blurred reconstruction. The laser beam, however, can be made very thin, suggesting that the one dimension approximation with approximate line detectors gives less blurred images than the zero dimension approximation with approximate point detectors.1 Theorem 1.3. Let D⊂ R2, let Φθ∞ c (Ω), and let φ,w: R→

### AppliedMathematics - Universität Innsbruck

Both reconstruction problems are essential for the novel hybrid imaging methods photoacoustic tomography(PAT) andthermoacoustictomography(TAT). The standardsetups in PAT/TAT using point-like detectors require the inversion of the wave equation in three spatial dimensions [1, 2].

### On reconstruction formulas and algorithms for the

Oct 01, 2020 raphy (TAT) (also called photoacoustic tomography and optoacoustic to-mography and abbreviated as TCT, PAT, or OAT) [1 8]. Major progress has been made recently in developing the mathematical foundations of TAT, including proving uniqueness of reconstruction, obtain-ing range descriptions for the relevant operators, deriving inversion formulas

### Analysis of Spatial Resolution in Thermo- and Photoacoustic

Photoacoustic tomography (PAT) PAT with integrating line detectors Mathematical model Classical approach Classical approach: Ideal point detectors 1 Assume point-wise data on ∂B Data = (W3D f)(z,t), for (z,t) ∈ ∂B ×(0,∞). Function f can be reconstructed uniquely and stably. 2 Exact inversion formula in case of ball B R: f(x) = 1 2R Z

### arXiv:0809.2052v3 [math.NA] 21 Jan 2009

arXiv:0809.2052v3 [math.NA] 21 Jan 2009 Exact Series Reconstruction in Photoacoustic Tomography with Circular Integrating Detectors Gerhard Zangerl∗ Otmar Scherzer† Markus Haltmeier‡ January

### Thermoacoustic Tomography with Integrating Area and Line

coustic or photoacoustic tomography, is an emerging proposed tomography method as the reconstruction algo- the focusing properties for cylindrical lens detectors are

### MathematicalChallengesArisingin

To obtain high resolution the size of the detectors has to be taken into account when modeling the corresponding forward operator. Exact recon-struction formulas incorporating the detector size have been derived for large planar detectors in spherical geometry [9] and line detectors with cylindrical circular recording geometry [5, 19].

### Impact of sensor apodization on the tangential resolution in

Photoacoustic tomographic (PAT) image reconstruction with apodized sensors is dis-cussed. A Gaussian function was used to model axisymmetric apodization of sensors and its full width at half maximum (FWHM) was varied to investigate the role of apodization on the PAT image reconstruction. The well known conventional delay-and-sum (CDAS) and re-

### EXACT SERIES RECONSTRUCTION IN PHOTOACOUSTIC TOMOGRAPHY WITH

Abstract. A method for photoacoustic tomography is presented that uses circular integrals of the acoustic wave for the reconstruction of a three-dimensional image. Image reconstruction is a two-step process: In the ﬁrst step data from a stack of circular integrating detectors are used to reconstruct the circular projection of the source

### Simultaneous Reconstructions of Absorption Density and Wave

The literature on reconstruction formulas and back-projection algorithms for photoacoustic imaging is vast. Wang et al. developed reconstruction formulas for cylindrical, spherical, and planar measurement geometries in a series of pa-pers [27, 26, 25, 28], and recently many more algorithms based on reconstruction 2

### Weight factors for limited angle photoacoustic tomography

Experimental evaluation of reconstruction algorithms for limited view photoacoustic tomography with line detectors G Paltauf, R Nuster, M Haltmeier et al.-Temporal back-projection algorithms for photoacoustic tomography with integrating line detectors P Burgholzer, J Bauer-Marschallinger, H Grün et al.-Photoacoustic tomography and sensing in

### PROCEEDINGS OF SPIE

heywords: Back-projection, algorithm, photoacoustic computed tomography 1. INTolDUCTflN Photoacoustic (PA) computed tomography is based on the reconstruction of an internal PA source distribution from measurements acquired by scanning small-aperture ultrasound detectors over a surface that encloses the source under study [1].

### Reconstructions in limited-view thermoacoustic tomography

problems have been studied extensively in X-ray tomography,19 diffraction tomography,20 and reflectivity tomography,21 to the best of our knowledge, no results on the limited-view TAT have been published. In the methods section, a formula for the forward problem is presented. In

### Exact Reconstruction in Photoacoustic Tomography with

Exact Reconstruction in Photoacoustic Tomography with Circular Integrating Detectors II: Spherical Geometry Gerhard Zangerl1 Otmar Scherzer1,2 1Department of Mathematics 2Radon Institute of Computational University of Vienna and Applied Mathematics Nordbergstr. 15 Altenberger Str. 69 1090 Wien, Austria 4040 Linz, Austria

### Reconstruction in thermoacoustic tomography

May 16, 2019 The paper contains an analytic reconstruction formula in thermoacoustic and photoacoustic tomography. It works for any geometry of point detectors placement along a closed surface and for variable sound speed satisfying a non-trapping condition. It is shown how this formula leads in particular to

### Improving tangential resolution with a modified delay‑and‑sum

virtual point detectors. Here, we have implemented a modified delay-and-sum reconstruction method, which takes into account the large aperture of the detector, leading to more than fivefold improvement in the tangential resolution in photoacoustic (and thermoacoustic) tomography. Three different types of numerical phantoms were

### 8 On Reconstruction Formulas and Algorithms for the

89 8On Reconstruction Formulas and Algorithms for the Thermoacoustic Tomography Mark Agranovsky Bar-Ilan University Peter Kuchment Texas A&M University Leonid Kunyansky

### DENSITY AND WAVE SPEED WITH PHOTOACOUSTIC

The literature on reconstruction formulas and back-projection algorithms for photoacoustic imaging is vast. Wang and colleagues developed reconstruction for-mulas for cylindrical, spherical, and planar measurement geometries in a series of papers [30, 29, 28, 31], and recently, many more algorithms based on reconstruc-