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Brief review on learning-based methods for optical

tomography

Lin Zhang and Guanglei Zhang

Beijing Advanced Innovation Center for Biomedical Engineering

Beihang University

Beijing 100191, P. R. China

School of Biological Science and Medical Engineering

Beihang University

Beijing 100191, P. R. China

[email protected]

Received 2 February 2019

Accepted 13 July 2019

Published 19 August 2019

Learning-based methods have been proved to perform well in a variety of areas in the biomedical

¯eld, such as biomedical image segmentation, and histopathological image analysis. Deep

learning, as the most recently presented approach of learning-based methods, has attracted more

and more attention. For instance, massive researches of deep learning methods for image

reconstructions of computed tomography (CT) and magnetic resonance imaging (MRI) have

been reported, indicating the great potential of deep learning for inverse problems. Optical

technology-related medical imaging modalities including di®use optical tomography (DOT),

°uorescence molecular tomography (FMT), bioluminescence tomography (BLT), and photo-

acoustic tomography (PAT) are also dramatically innovated by introducing learning-based

methods, in particular deep learning methods, to obtain better reconst ruction results. This

review depicts the latest researches on learning-based optical tomography of DOT, FMT, BLT,

and PAT. According to the most recent studies, learning-based methods applied in the ¯eld of

optical tomography are categorized as kernel-based methods and deep learning methods. In this

review, the former are regarded as a sort of conventional learning-based methods and the latter

are subdivided into model-based methods, post-processing methods, and end-to-end methods.

Algorithm as well as data acquisition strategy are discussed in this revi ew. The evaluations of

these methods are summarized to illustrate the performance of deep learning-based

reconstruction.

Keywords: Optical imaging; tomography; inverse problem; machine learning; deep learning.

Corresponding author.

This is an Open Access article published by World Scienti¯c Publishing Company. It is distributed under the terms of the Creative

Commons Attribution 4.0 (CC BY) License which permits use, distribution and reproduction in any medium, provided the original

work is properly cited.

Journal of Innovative Optical Health Sciences

Vol. 12, No. 6 (2019) 1930011 (14 pages)

The Author(s)

DOI: 10.1142/S1793545819300118

1930011-1

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by 27.17.81.156 on 12/09/19. Re-use and distribution is strictly not permitted, except for Open Access articles.

1. Introduction

Di®use optical tomography (DOT), °uorescence

molecular tomography (FMT), together with bio-

luminescence tomography (BLT) are noninvasive

modalities for biomedical imaging.

–

Photons

propagating through biological tissues can be col-

lected in vivo by these modalities, indicating the

spatial optical properties like absorption coe±cient

and scattering coe±cient which can be obtained by

all the three methods, or the internal °uorophore

distribution which can be obtained by FMT and

BLT methods.

–

The optical coe±cients, as well as

the intensity and lifetime of °uorescence or biolu-

minescence, are generally in°uenced by oxygen

saturation, hemoglobin concentrations and other

situations of the tissue. Therefore, these modalities

of optical tomography are promising to be adopted

in tracing tumors and drug development, and have

been paid more and more attention.

1,9

The inverse problems of optical tomography are

ill-posed and sometimes nonlinear.

Therefore, it is

a challenge to obtain accurate and high-resolution

reconstructions by solving the inverse problems. A

mass of methods have been proposed to improve the

quantitative quality by developing novel e±cient

algorithms, and to reduce the time consumption by

developing accelerated algorithms or by rebuilding

the ¯nal results through limited-view and sparse

measurements.

11,12

Multi-modality technologies are

also utilized to obtain high-quality reconstructions

by introducing anatomical guidance from compu-

tational tomography (CT) or other modalities.

13,14

Coupled-physics biomedical imaging technologies,

such as photoacoustic imaging (PAI) or tomogra-

phy (PAT), are also developed to obtain the high-

quality reconstructions by bene¯cially combining

the high-contrast of optical imaging with the high-

spatial resolution of ultrasound imaging.

–

Regularization and optimization strategies with

iterative algorithms are generally employed to solve

the ill-posed and nonlinear inverse problems.

11,12,20

Learning-based methods have also been introduced

to solve inverse problems. One of the most recently

presented conventional learning-based methods is

kernel method, which can help make best of ana-

tomical information for reconstruction of multi-

modality imaging.

However, conventional princi-

ples of reconstruction for optical tomography have

been changed by the development of deep learning

technique.

Deep learning, as a new-raised part of

machine learning, has shown huge advantages in

computer vision, particularly in image classi¯cation

and other areas of pattern recognition.

Deep

neural networks can learn from the coupled samples

to generate a model mapping from the input to the

output. By introducing deep learning technologies,

the inverse problems in biomedical imaging can be

converted into data-driven problems.

Actually, deep learning technologies have been

widely adopted in solving biomedical problems.

Researchers have been utilizing deep neural net-

works in image segmentation and histopathological

image analysis, as well as in image reconstruction

for CT and magnetic resonance imaging (MRI),

etc.

–

Meanwhile, novel algorithms which are

based on deep learning have been consistently

employed into reconstruction issues of optical im-

aging and tomography. In order to obtain a com-

prehensive understanding of learning-based

methods, several state-of-the-art algorithms for

reconstructions of DOT, FMT, and BLT, together

with PAT or PAI will be reviewed here. Considering

the great potentiality in reconstruction of optical

tomography, this review will dramatically place

emphasis on deep learning-based algorithms. Ker-

nel-based methods, which are derived from machine

learning technology, are also novel approaches for

the reconstruction of optical tomography and will

be reviewed here as a contrast. All the deep learn-

ing-based algorithms mentioned here will be cate-

gorized into model-based methods, post-processing

methods, and end-to-end methods.

The rest of this review is organized as follows.

In Sec. 2, methodologies of kernel-based methods

for DOT and FMT are depicted. In Sec. 3, deep

learning-based methods including model-based

methods, post-processing methods, and end-to-end

methods are discussed, respectively. In Sec. 4, there

is an overall summary of the methods presented in

this review.

2. Kernel-Based Methods

Kernel-based method is one series of pattern anal-

ysis algorithms in machine learning, including the

most famous methods such as support vector ma-

chine (SVM), Gaussian process and so on, owing

the name to the utilization of kernel functions.

28,29

By mapping to high-dimension spaces described by

kernel functions, nonlinear problems can be

L. Zhang & G. Zhang

1930011-2

J. Innov. Opt. Health Sci. 2019.12. Downloaded from www.worldscientific.com

by 27.17.81.156 on 12/09/19. Re-use and distribution is strictly not permitted, except for Open Access articles.

changed into linear problems. In Wang's research, a

kernel-based method was introduced to positron

emission computed tomography (PET) to help the

image reconstruction.

Features obtained from

prior information are modeled and incorporated

into the forward function. Inspired by the well

performance of kernel-based method in PET re-

construction, similar approaches have been pro-

posed to improve reconstructions in optical

tomography in the last couple years.

Reconstructions in both DOT and FMT su®er

from the ill-posed and nonlinear inverse problems.

Anatomical guidance, as prior information, is of

great importance in improving the reconstruction

quality.

30,31

However, introducing anatomical in-

formation from other imaging modalities with high

spatial resolution calls for image segmentation and

registration ¯rst. Utilizing a kernel-based method,

optical absorption coe±cient at each ¯nite element

node is represented as a function of a set of features

obtained from anatomical images without any

preprocessing.

2.1. Kernel-based methods for DOT

As mentioned in Baikejiang et al.'s work, a Gauss-

ian kernel-based method was presented to involve

anatomical information in the forward model for the

DOT image reconstruction.

28,32

According to relative literatures, the theory of

Gaussian kernel-based reconstruction method for

DOT can be described as follows.

As DOT reconstruction is usually implemented

on ¯nite element method (FEM), the kernel func-

tion can be formulized as

m;n

exp

jjf

 f





; f

2 knn of f

;

0; otherwise;

ð1Þ

where f

and f

are feature vectors corresponding

to ¯nite element nodes m and n extracted from

anatomical image, respectively. Feature vector f

consists of all the values of the neighbor voxels

surrounding the ¯nite element node m. knn denotes

the k closest neighbors of f

and can be acquired by

K nearest neighbors (KNN) search algorithm.

Ignoring the optical scattering coe±cient, the

absorption coe±cient vector can be written as



¼ K; ð2Þ

where K is the kernel matrix de¯ned by the kernel

function k

m;n

. Vector  is the nth value of the vector

to be reconstructed.

In general, the objective function of inverse

problem for DOT can be written as

arg min F ð

Þ¼

jjy  W ð

Þjj

; ð3Þ

where W is the system matrix representing the

forward model. By combining Eqs. (2) and (3), the

inverse problem for DOT can be described as

arg min F ðÞ¼

jjy  W ðKÞjj

: ð4Þ

Then, the inverse problem of DOT can be trans-

ferred into a minimized problem of vector  and the

prior information has been involved. Vector  is

then obtained by conventional iterative method

such as Tikhonov regularization, and the absorption

coe±cient can be obtained using Eq. (2).

In the numerical simulation of Baikejiang's work,

it was shown that the voxel number of each corre-

sponding node and the number of nearest neighbors

had impact on the performance of kernel-based

method signi¯cantly. Di®erent values of k (16, 32,

or 64) and di®erent voxel numbers (3  3  3,

5  5  5, 7  7  7, or 9  9  9) were taken into

account to optimize the kernel-based method. Vol-

ume ratio (VR), Dice similarity coe±cient (Dice),

contrast-to-noise ratio (CNR), and mean square

error (MSE) are introduced as evaluation metrics.

Reconstruction results indicated that the kernel-

based method outperformed other cases whether

the value of k or the voxel number increased.

Then other three numerical experiments were

carried out to validate the performance of kernel-

based method. CT contrast e®ect in kernel-based

method for CT-guided DOT reconstruction, e®ect

of the false positive target in the kernel-based

method, and clinical breast CT image as anatomical

guidance were studied and compared to the

Laplacian-type soft prior method, respectively.

Numerical reconstruction results indicated that the

kernel-based method was robust to CT contrast and

the false positive targets in the guided CT image.

Although in some cases the reconstructions of ker-

nel-based method were not as good as that of soft

prior method, it still outperformed the method

without prior information and did not need seg-

mentation for the CT guidance.

Brief review on learning-based methods for optical tomography

1930011-3

J. Innov. Opt. Health Sci. 2019.12. Downloaded from www.worldscientific.com

by 27.17.81.156 on 12/09/19. Re-use and distribution is strictly not permitted, except for Open Access articles.

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