JOINT RIGID MOTION CORRECTION AND SPARSE-VIEW CT VIA SELF-CALIBRATING NEURAL FIELD Qing WuyXin LiyHongjiang WeizJingyi YuyYuyao Zhangy

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JOINT RIGID MOTION CORRECTION AND SPARSE-VIEW CT

VIA SELF-CALIBRATING NEURAL FIELD

Qing Wu†Xin Li†Hongjiang Wei‡Jingyi Yu†Yuyao Zhang†,?

†School of Information Science and Technology, ShanghaiTech University, Shanghai, China

‡School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai, China

ABSTRACT

Neural Radiance Field (NeRF) has widely received attention in

Sparse-View Computed Tomography (SVCT) reconstruction tasks

as a self-supervised deep learning framework. NeRF-based SVCT

methods represent the desired CT image as a continuous function

of spatial coordinates and train a Multi-Layer Perceptron (MLP) to

learn the function by minimizing loss on the SV sinogram. Ben-

eﬁting from the continuous representation provided by NeRF, the

high-quality CT image can be reconstructed. However, existing

NeRF-based SVCT methods strictly suppose there is completely

no relative motion during the CT acquisition because they require

accurate projection poses to model the X-rays that scan the SV

sinogram. Therefore, these methods suffer from severe performance

drops for real SVCT imaging with motion. In this work, we pro-

pose a self-calibrating neural ﬁeld to recover the artifacts-free image

from the rigid motion-corrupted SV sinogram without using any

external data. Speciﬁcally, we parametrize the inaccurate projection

poses caused by rigid motion as trainable variables and then jointly

optimize these pose variables and the MLP. We conduct numerical

experiments on a public CT image dataset. The results indicate

our model signiﬁcantly outperforms two representative NeRF-based

methods for SVCT reconstruction tasks with four different levels of

rigid motion.

Index Terms—Sparse-View CT Reconstruction, Rigid Motion

Correction, Neural Radiance Field, Self-Supervised Learning.

1. INTRODUCTION

Sparse-View Computed Tomography (SVCT) can signiﬁcantly re-

duce the radiation dose and shorten the scanning time by decreasing

the number of radiation views. However, the insufﬁcient projection

measurement (i.e., SV sinogram) in SVCT will suffer from severe

streaking artifacts if applying conventional analytical reconstruction

algorithms such as Filtered Back-Projection (FBP) [1], which signif-

icantly degrades image quality.

Recently, several self-supervised SVCT methods [2–6] based

on Neural Radiance Field (NeRF) [7] have been emerged. Differ-

ent from supervised deep learning models [8,9], these NeRF-based

methods can recover the high-quality CT image from the SV sino-

gram without using any external data. Speciﬁcally, NeRF-based

methods ﬁrst represent the unknown CT image as a continuous func-

tion that maps coordinates to intensities and then train a Multi-Layer

Perceptron (MLP) to learn the function by minimizing prediction er-

rors on the SV sinogram. Beneﬁting from the implicit continuous

prior imposed by the function and the neural network prior [10–12],

the function can be approximated well, and thus the desired high-

quality CT image will be reconstructed.

Existing NeRF-based SVCT methods [2–6] suppose there is

completely no relative motion during the CT acquisition process,

which beneﬁts that the accurate projection poses can be accessi-

ble for modeling the X-rays that scan the SV sinogram. However,

relative motion, especially rigid motion, is common and even in-

evitable [13–16] during the real CT acquisition process due to

various factors (e.g., imaging subject’s movement and CT scanner’s

system error, etc.). Therefore, this overly strict assumption will re-

sult in severe model performance drops in real SVCT reconstruction

with motion.

In this paper, we propose a self-calibrating neural ﬁeld that can

reconstruct the artifacts-free image from the rigid motion-corrupted

SV measurement without involving any external data. Like the pre-

vious works [2–6], our proposed model is also based on NeRF’s [17]

framework (i.e., using an MLP to learn the function of desired CT

image through minimizing loss on the SV sinogram). The major

novelty of our model is that it extra models the rigid motion in the

CT acquisition process and thus can produce robust and excellent

results for SVCT imaging with rigid motion. More speciﬁcally, we

ﬁrst parameterize inaccurate projection poses caused by rigid mo-

tion as three trainable variables (a rotation angle and two transla-

tion offsets). Then, we jointly optimize these pose variables and

the MLP representation. After the poses calibration and MLP opti-

mization, the ﬁnal high-quality CT image can be reconstructed. We

conduct numerical experiments on a public COVID-19 CT image

dataset [18]. Experimental results shows that the proposed model

signiﬁcantly outperforms the two representative NeRF-based meth-

ods [2,3] for SVCT reconstruction tasks with four different levels of

rigid motion. We also perform ablation study for the pose correction

module in our model. The results conﬁrm its effectiveness.

2. BACKGROUND

Formally, NeRF-based SVCT methods [2–6] represent the unknown

and high-quality CT image x∈RN×Nas a continuous function:

M:p→I, (1)

where p= (x, y)∈R2is any spatial coordinate in a normalized

2D Cartesian coordinates [−1,1] ×[−1,1] and I∈Rdenotes the

corresponding intensity value in the CT image x.

Given the acquired SV sinogram y∈RM×N, where Mand

Ndenote the number of projections and X-rays per projection, re-

spectively. NeRF-based methods leverage an MLP FΦto learn the

continuous function Mby optimizing the objective as below:

Φ∗= arg min

L(y,AFΦ),(2)

where A∈RN×Mrepresents a differentiable projection operator

(e.g., Radon transform for parallel X-ray beam CT acquisition) and

arXiv:2210.12731v2 [eess.IV] 6 Nov 2022

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摘要：

JOINTRIGIDMOTIONCORRECTIONANDSPARSE-VIEWCTVIASELF-CALIBRATINGNEURALFIELDQingWuyXinLiyHongjiangWeizJingyiYuyYuyaoZhangy;?ySchoolofInformationScienceandTechnology,ShanghaiTechUniversity,Shanghai,ChinazSchoolofBiomedicalEngineering,ShanghaiJiaoTongUniversity,Shanghai,ChinaABSTRACTNeuralRadianceField(Ne...

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