Edge-promoting reconstruction of absorption and diffusivity in optical tomography

Hannukainen, Antti; Harhanen, Lauri; Hyvönen, Nuutti; Majander, Helle

doi:10.1088/0266-5611/32/1/015008

Cited by 12 publications

(20 citation statements)

References 44 publications

(91 reference statements)

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“…(5. 21) We can see that the equalities hold when θ 1 = θ 2 in (5.21), that is, when the maximum is achieved for fixed r 1 and r 2 . Let us now fix θ 1 = θ 2 and r 1 in (5.21), we like to check again if the maximum of K 1 , which is a rational function of r 2 , is attained when r 2 ≈ r 1 .…”

Section: More About the Mutually Almost Orthogonality Propertymentioning

confidence: 85%

A Direct Sampling Method for Simultaneously Recovering Inhomogeneous Inclusions of Different Nature

Chow¹,

Han²,

Zou³

2020

Preprint

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In this work, we investigate a class of elliptic inverse problems and aim to simultaneously recover multiple inhomogeneous inclusions arising from two different physical parameters, using very limited boundary Cauchy data collected only at one or two measurement event. We propose a new fast, stable and highly parallelable direct sampling method (DSM) for the simultaneous reconstruction process. Two groups of probing and index functions are constructed, and their desired properties are analyzed. In order to identify and decouple the multiple inhomogeneous inclusions of different physical nature, we introduce a new concept of mutually almost orthogonality property that generalizes the important concept of almost orthogonality property in classical DSMs for inhomogeneous inclusions of same physical nature in [12,13,14,24,31]. With the help of this new concept, we develop a reliable strategy to distinguish two different types of inhomogeneous inclusions with noisy data collected at one or two measurement event. We further improve the decoupling effect by choosing an appropriate boundary influx. Numerical experiments are presented to illustrate the robustness and efficiency of the proposed method.

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Section: More About the Mutually Almost Orthogonality Propertymentioning

confidence: 85%

A Direct Sampling Method for Simultaneously Recovering Inhomogeneous Inclusions of Different Nature

Chow¹,

Han²,

Zou³

2020

Preprint

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“…We calculated the differential optical density on multiple detectors and plotted the differential optical density difference (ΔOD') curve between adjacent detectors. Gaussian curve fitting [20] was used to fit the differential optical density difference curve, and to obtain its characteristic parameters. The experimental results show that using the differential optical density difference curve, the characteristic parameters can be used to locate anomalies in uniform tissue quickly.…”

Section: Introductionmentioning

confidence: 99%

Fast localization method of an anomaly in tissue based on differential optical density

Wang

Ren

Zhao

et al. 2018

Biomed. Opt. Express

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Abstract:The position of the source-detector (S-D) relative to an anomaly has an important influence on the detection effect in non-invasive near-infrared spectroscopy-based methods. In this study, a single-source multi-detector structure was designed in order to realize the rapid localization of anomalies within tissue. This method uses finite element analysis of the optical density distribution for different horizontal positions, depths and diameters of anomalies. The difference in optical density between the detectors was then calculated. The simulation results show that the horizontal position of the anomaly in the tissue can be quickly located according to the differential optical density difference curves formed by the multiple detectors. The Gaussian fitting feature of these curves shows strong correlation with the horizontal positions, depths and diameters of the anomaly. Through the differential optical density difference curves, rapid localization within the region of interest can be achieved. This method provides an important reference for sources and detectors location for tumor detection, brain function optical imaging and other fields using near infrared spectroscopy, and improves its detection accuracy.

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“…The approach is based on iteratively combining a lagged diffusivity step and a linearisation of the measurement model of QPAT with priorconditioned LSQR. The algorithm is a modified version of the one introduced for inverse elliptic boundary value problems in [22,24]; see also [2] for the original ideas behind the technique. In particular, to facilitate the treatment of far greater amounts of data compared to [22,24], we implement a matrix-free technique for multiplying vectors by the Jacobian of the measurement map, rendering it possible to painlessly handle (full) Jacobians with, say, 10 5 rows and columns.…”

mentioning

confidence: 99%

“…The algorithm is a modified version of the one introduced for inverse elliptic boundary value problems in [22,24]; see also [2] for the original ideas behind the technique. In particular, to facilitate the treatment of far greater amounts of data compared to [22,24], we implement a matrix-free technique for multiplying vectors by the Jacobian of the measurement map, rendering it possible to painlessly handle (full) Jacobians with, say, 10 5 rows and columns. This is one of the few studies where QPAT is investigated in 3D; for previous works see [42,31,35].…”

mentioning

confidence: 99%

See 1 more Smart Citation

Efficient Inclusion of Total Variation Type Priors in Quantitative Photoacoustic Tomography

Hannukainen¹,

Hyvönen²,

Majander

et al. 2016

SIAM J. Imaging Sci.

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Abstract. Quantitative photoacoustic tomography is an emerging imaging technique aimed at estimating the distribution of optical parameters inside tissues from photoacoustic images, which are formed by combining optical information and ultrasonic propagation. This optical parameter estimation problem is ill-posed and needs to be approached within the framework of inverse problems. Photoacoustic images are three-dimensional and high-resolution. Furthermore, high-resolution reconstructions of the optical parameters are targeted. Therefore, in order to provide a practical method for quantitative photoacoustic tomography, the inversion algorithm needs to be able to perform successfully with problems of prominent size. In this work, an efficient approach for the inverse problem of quantitative photoacoustic tomography is proposed, assuming an edge-preferring prior for the optical parameters. The method is based on iteratively combining priorconditioned LSQR with a lagged diffusivity step and a linearisation of the measurement model, with the needed multiplications by Jacobians performed in a matrix-free manner. The algorithm is tested with three-dimensional numerical simulations. The results show that the approach can be used to produce accurate and high quality estimates of absorption and diffusion in complex three-dimensional geometries with moderate computation time and cost.

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Edge-promoting reconstruction of absorption and diffusivity in optical tomography

Cited by 12 publications

References 44 publications

A Direct Sampling Method for Simultaneously Recovering Inhomogeneous Inclusions of Different Nature

A Direct Sampling Method for Simultaneously Recovering Inhomogeneous Inclusions of Different Nature

Fast localization method of an anomaly in tissue based on differential optical density

Efficient Inclusion of Total Variation Type Priors in Quantitative Photoacoustic Tomography

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