Method for reconstructing incomplete data of X-ray absorption contrast computed tomography based on deep learning
View Patent ↗The present invention discloses a method for reconstructing incomplete data of X-ray absorption contrast computed tomography (CT) based on deep learning (DL). The method includes the following steps: using a filtered back projection (FBP) algorithm to obtain an initial reconstructed image; forward projecting the initial reconstructed image to obtain artifact-contaminated complete projection sequences; using a DL technique to process the artifact-contaminated projection sequences to obtain artifact-free projection sequences; using the FBP algorithm to reconstruct the artifact-free projection sequences to obtain a final reconstructed image. Compared with the traditional incomplete data reconstruction methods, the examples of the present invention feature a simpler calculation process, fewer parameters to be manually set, a faster calculation speed and higher image quality.
1. A method for reconstructing incomplete data of X-ray absorption contrast computed tomography (CT) based on deep learning (DL), the method comprising:
a step 1 of using a filtered back projection (FBP) algorithm to reconstruct incomplete absorption contrast projection sequences obtained by an X-ray absorption contrast CT system to obtain an initial reconstructed image, wherein the initial reconstruction image in an initial reconstruction result of FBP comprises artifacts and noise due to the incomplete projection sequences;
a step 2 of using a forward projection operator to forward project the initial reconstructed image to obtain artifact-contaminated complete projection sequences, wherein the artifact-contaminated complete projection sequences are obtained by forward projecting image structure information and the artifacts into the projection sequences; a number of the sequences satisfies a complete condition, that is, a Nyquist sampling theorem;
a step 3 of using a DL technique to process the artifact-contaminated complete projection sequences to obtain artifact-free complete projection sequences, wherein the complete projection sequences obtained by processing the artifact-contaminated complete projection sequences by using the DL technique do not comprise the artifacts; a number of the sequences satisfies a complete condition; and
a step 4 of using the FBP algorithm to reconstruct the artifact-free complete projection sequences to obtain a final reconstructed image.
2. The method for reconstructing incomplete data of X-ray absorption contrast CT based on DL according to claim 1 , wherein
the incomplete projection sequences are incomplete data generated as a result of various imaging condition restrictions or special needs, and comprise sparse-view data and limited-view data.
3. The method for reconstructing incomplete data of X-ray absorption contrast CT based on DL according to claim 1 , wherein
in step 1, the FBP algorithm that is used to generate the initial reconstructed image is expressed by Formula (1):
β
(
r
,
θ
)
=
1
2
∫
0
2
π
1
U
2
P
(
ω
,
ϕ
)
D
D
2
+
ω
2
*
h
(
ω
)
d
ϕ
(
1
)
wherein, β(r,θ) represents a reconstruction result, (r,θ) represents polar coordinates, U represents a weight matrix of the imaging system, P(ω,ϕ) represents projection sequences, D represents a distance from a ray source to a rotation center of the imaging system, h represents inverse Fourier transform (IFT) of a filter, ω represents a position of a detection element on a detector, and ϕ represents a rotation angle of the imaging.
4. The method for reconstructing incomplete data of X-ray absorption contrast CT based on DL according to claim 1 , wherein
in step 2, the forward operator that is used to process the initial reconstructed image to produce a projection is expressed by Formula (2):
P (ω,ϕ)=∫ −∞ +∞ β( r ,θ) dl (2)
wherein, P(ω,ϕ) represents the artifact-contaminated complete projection sequences comprising image structure information and artifacts, the number of the sequences being the same as the complete data; β(r,θ) represents the initial reconstructed image; l represents a projection path.
5. The method for reconstructing incomplete data of X-ray absorption contrast CT based on DL according to claim 1 , wherein
in step 3, the DL technique used to process the artifact-contaminated complete projection sequences to obtain artifact-free complete projection sequences is expressed by Formulas (3) to (6):
P
^
(
ω
,
ϕ
)
=
F
(
Λ
(
f
(
P
(
ω
,
ϕ
)
)
)
)
+
P
(
ω
,
ϕ
)
(
3
)
f
(
P
(
ω
,
ϕ
)
)
=
W
T
·
P
(
ω
,
ϕ
)
+
Bias
(
4
)
Error
=
1
2
m
(
P
(
ω
,
ϕ
)
-
P
^
(
ω
,
ϕ
)
)
2
(
5
)
ω
j
t
+
1
=
ω
j
t
-
η
·
∂
Error
ω
j
t
(
6
)
wherein, {circumflex over (P)}(ω,ϕ) represents the artifact-free complete projection sequences; f represents an encoding network, which uses a convolutional neural network to extract features from the artifact-contaminated complete projection sequences {circumflex over (P)}(ω,ϕ); Λ represents a nonlinear mapping function; F represents a decoding network, which uses the convolutional neural network to analyze the artifact information from high-level features obtained from the encoding; Error represents a learning target of the DL technique in this step to measure a difference between an output value and a true value; W and Bias represent parameters that need to be learned in the convolutional neural network, wherein the parameters are updated by using a gradient descent algorithm by finding a partial derivative of the learning target to the parameters; η represents a learning rate; ωj t+1 represents a learned network parameter.
6. The method for reconstructing incomplete data of X-ray absorption contrast CT based on DL according to claim 1 , wherein
in step 3, the DL technique is used to process the artifact-contaminated complete projection sequences instead of the initial reconstruction result.