Evaluation of temporal moments and Fourier transformed data in time-domain diffuse optical tomography

Meghdoot Mozumder; Tanja Tarvainen; Tanja Tarvainen

doi:10.1364/JOSAA.405541

Journal of the Optical Society of America A
Vol. 37,
Issue 12,
pp. 1845-1856
(2020)
•https://doi.org/10.1364/JOSAA.405541

Evaluation of temporal moments and Fourier transformed data in time-domain diffuse optical tomography

Meghdoot Mozumder and Tanja Tarvainen

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Meghdoot Mozumder and Tanja Tarvainen, "Evaluation of temporal moments and Fourier transformed data in time-domain diffuse optical tomography," J. Opt. Soc. Am. A 37, 1845-1856 (2020)

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Abstract

Time-domain diffuse optical tomography (TD-DOT) uses near-infrared pulsed lasers as light sources to measure time-varying exitance on the boundary of the target. These are used to estimate optical properties of the imaged target. Several integral-transform-based moments of the time-resolved data have been utilized in TD-DOT, the most common being the mean time of flight and variance. Recently, it has been shown that Fourier transforming the time-domain data to frequency domain enables utilization of these data at one or several frequencies, producing equally as good estimates as the whole time-domain data. In this work, we present a systematic comparison of the usage of the temporal moments and Fourier transformed data in TD-DOT. Both absolute and difference imaging are evaluated using numerical simulations. The simulations show that utilizing temporal moments and Fourier transformed data in TD-DOT provides good quality reconstructions with a good estimation accuracy. These estimates are improved if more than one data type is used. Furthermore, the simulations show that the frequency-domain computations enable computationally cheaper and straightforward implementation of the inverse solver when compared to the temporal moments.

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Equations (54)

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Ref.	Moment	Reconstructed Parameters	Application
[8]	E	Difference $μ_{a}$	Cylindrical phantom
[27]	$⟨ t ⟩$ , $c_{2}$ , LT	Difference and absolute $μ_{a}, μ_{s}^{'}$	Cylindrical phantom
[10]	$⟨ t ⟩$ , $c_{2}$ , LT	Absolute $μ_{a}, μ_{s}^{'}$	Cylindrical phantom
[28]	$⟨ t ⟩$	Difference and absolute $μ_{a}, μ_{s}^{'}$	Human forearm movement
[29]	$⟨ t ⟩$	Difference $μ_{a}, μ_{s}^{'}$	Infant brain hemorrhage
[16]	Whole data, E, $⟨ t ⟩$ , $c_{2}$ , $c_{3}$ .	Absolute $μ_{a}, μ_{s}^{'}$	Simulations
[23]	Fourier transform	Difference $μ_{a}, μ_{s}^{'}$	Infant brain cortical response
[30]	Fourier transform	Absolute $μ_{a}, μ_{s}^{'}$	Cylindrical phantom
[31]	$⟨ t ⟩$	Difference $μ_{a}, μ_{s}^{'}$	Infant brain oxygenation
[32]	Whole data	Difference $μ_{a}$	Liquid phantom tank
[22]	$⟨ t ⟩$	Absolute $μ_{a}$	Cylindrical phantom
[26]	Mellin–Laplace transform	Absolute $μ_{a}, μ_{s}^{'}$	Simulations
[17]	Whole data	Difference $μ_{a}, μ_{s}^{'}$	Simulations
[33]	Mellin–Laplace transform	Difference $μ_{a}$	Cuboid phantom
[15]	E	Absolute $μ_{a}$	Breast cancer phantom
[34]	Temporal windows	Absolute $μ_{a}$	Simulations

	Target 1		Target 2		Target 3		Target 4
Type	$E_{μ_{a}}$	$E_{μ_{s}^{'}}$	$E_{μ_{a}}$	$E_{μ_{s}^{'}}$	$E_{μ_{a}}$	$E_{μ_{s}^{'}}$	$E_{μ_{a}}$	$E_{μ_{s}^{'}}$
$⟨ t ⟩$	16	13	29	20	23	17	18	12
$c_{2}$	15	14	24	17	22	18	17	13
$⟨ t ⟩, c_{2}$	14	12	19	15	20	16	16	11
${F T}_{N_{ω} = 1}$	15	12	22	18	21	16	17	12
${F T}_{N_{ω} = 5}$	14	11	20	17	19	15	16	11

	Target 1		Target 2		Target 3		Target 4
Type	$E_{δ μ_{a}}$	$E_{δ μ_{s}^{'}}$	$E_{δ μ_{a}}$	$E_{δ μ_{s}^{'}}$	$E_{δ μ_{a}}$	$E_{δ μ_{s}^{'}}$	$E_{δ μ_{a}}$	$E_{δ μ_{s}^{'}}$
$⟨ t ⟩$	89	85	101	81	86	68	78	56
$c_{2}$	80	78	91	96	67	141	76	67
$⟨ t ⟩, c_{2}$	75	79	79	91	81	72	70	61
${F T}_{N_{ω} = 1}$	82	83	83	81	69	60	63	57
${F T}_{N_{ω} = 5}$	74	78	73	83	68	58	63	53

	$⟨ t ⟩$	$c_{2}$	( $⟨ t ⟩, c_{2}$ )	${F T}_{N_{ω} = 1}$	${F T}_{N_{ω} = 5}$
$T_{d i f f}$	11	26	35	3	7
$T_{a b s}$	49	187	162	8	52
$N_{i t e r}$	6	8	5	5	5

Ref.	Moment	Reconstructed Parameters	Application
[8]	E	Difference $μ_{a}$	Cylindrical phantom
[27]	$⟨ t ⟩$ , $c_{2}$ , LT	Difference and absolute $μ_{a}, μ_{s}^{'}$	Cylindrical phantom
[10]	$⟨ t ⟩$ , $c_{2}$ , LT	Absolute $μ_{a}, μ_{s}^{'}$	Cylindrical phantom
[28]	$⟨ t ⟩$	Difference and absolute $μ_{a}, μ_{s}^{'}$	Human forearm movement
[29]	$⟨ t ⟩$	Difference $μ_{a}, μ_{s}^{'}$	Infant brain hemorrhage
[16]	Whole data, E, $⟨ t ⟩$ , $c_{2}$ , $c_{3}$ .	Absolute $μ_{a}, μ_{s}^{'}$	Simulations
[23]	Fourier transform	Difference $μ_{a}, μ_{s}^{'}$	Infant brain cortical response
[30]	Fourier transform	Absolute $μ_{a}, μ_{s}^{'}$	Cylindrical phantom
[31]	$⟨ t ⟩$	Difference $μ_{a}, μ_{s}^{'}$	Infant brain oxygenation
[32]	Whole data	Difference $μ_{a}$	Liquid phantom tank
[22]	$⟨ t ⟩$	Absolute $μ_{a}$	Cylindrical phantom
[26]	Mellin–Laplace transform	Absolute $μ_{a}, μ_{s}^{'}$	Simulations
[17]	Whole data	Difference $μ_{a}, μ_{s}^{'}$	Simulations
[33]	Mellin–Laplace transform	Difference $μ_{a}$	Cuboid phantom
[15]	E	Absolute $μ_{a}$	Breast cancer phantom
[34]	Temporal windows	Absolute $μ_{a}$	Simulations

Abstract

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Figures (6)

Tables (4)

Equations (54)

Journal of the Optical Society of America A