Positron emission tomography image reconstruction method

1. A method, comprising:

1) injecting a positron emission tomography (PET) radioactive tracer into a biological tissue, scanning by a PET device, and detecting and counting coincidence photons to obtain an original protection data matrix Y;

2) establishing a measurement equation model according to a PET imaging principle:

Y=GX+R+S   (1);

wherein G is a system matrix, X is a real concentration distribution map of the radioactive tracer, R is a number of random photons during a measurement process, and S is a number of scattered photons during the measurement process;

3) Splitting a reconstruction problem into a first sub-problem and a second sub-problem,

X=F 1 ( Y )— F 2 ( R+S )  (2);

wherein the first sub-problem is to reconstruct the original projection data matrix Y to obtain a preliminarily reconstructed image F 1 (Y) containing noise; and the second sub-problem is to remove a noise F 2 (R+S) in the preliminarily reconstructed image F 1 (Y) to a PET reconstructed image X;

4) solving the first sub-problem by a filtered back-projection (FBP) layer, and solving the second sub-problem by an improved denoising convolutional neural network (DnCNN), wherein the filtered back-projection layer and the improved denoising convolutional neural network are connected in series to form a filtered back-projection network (FBP-Net);

5) in a training stage, inputting original projection data into the FBP-Net, and using an image obtained by a conventional reconstruction algorithm as a tag to adjust parameters of the FBP-Net to reduce an error between an output of the FBP-Net and the tag; and

6) in an estimation stage, inputting projection data to be reconstructed into the trained FBP-Net to obtain a desired reconstructed image;

wherein:

in 5), the training stage comprises:

5.1) initializing parameters of the FBP-Net, initializing all frequency-domain filters of the FBP layer by a ramp filter, and initializing parameters in the improved DnCNN by a truncated normal distribution;

5.2) inputting sinogram in a training set into the FBP-Net, calculating an output of each layer by a forward propagation formula, and obtaining a final output of the FBP-Net;

5.3) calculating a loss function between the output of the FBP-Net and the tag:

loss

=

1

N

⁢

∑

i

=

1

N

(

X

ˆ

(

i

)

-

X

⁡

(

i

)

)

2

;

(

4

)

wherein {circumflex over (X)}(i) is an estimated value of an i th sample output by the FBP-Net, and X(i) is a tag of the i th sample;

5.4) obtaining a partial derivative of the loss function, and updating learnable parameters in the FBP-Net by an Adam algorithm; and

5.5) repeating operations in 5.2) to 5.4) until a change in a numerical value of the loss value is less than 10 −5 .

2. The method of claim 1 , wherein in 4), PET projection data is input to the filtered back-projection layer to yield the preliminarily reconstructed image containing noise.

3. The method of claim 2 , wherein the filtered back-projection layer operates based on a filtered back-projection algorithm comprising frequency-domain filtering and back projection; the back projection uses a conventional filtered back-projection algorithm, the frequency-domain filtering involves a learnable filter, and the projection data of each angle corresponds to an independent one-dimensional frequency-domain filter.

4. The method of claim 1 , wherein in 4), the improved denoising convolutional neural network removes the noise in the preliminarily reconstructed image by residual learning.

5. The method of claim 4 , wherein the improved denoising convolutional neural network comprises eight 2D convolutional layers and one normalization layer; each convolutional layer comprises 64 3×3 filters, and first seven convolutional layers use an activation function ReLU and batch normalization (BN); the eight 2D convolutional layers learn a residual error between the reconstructed image containing noise and a clean reconstructed image; an output of an eighth convolutional layer is subtracted from an input of the improved denoising convolutional neural network, and a result is then processed by the one normalization layer to obtain a clean reconstructed image.

6. The method of claim 1 , wherein in 5), both the original projection data and the tag are subjected to single-frame normalization:

X

n

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o

⁢

r

⁢

m

=

X

-

X

min

X

max

-

X

min

;

(

3

)

wherein X min and X max are a minimum value and a maximum value of single-frame data, respectively.

7. The method of claim 1 , wherein in 6), the projection data to be reconstructed is normalized before being input into the trained FBP-Net.

8. The method of claim 1 , wherein data input to the FBP-Net is 2D PET scanning data.