# US 10,765,382 B2 · Method for mixed tracers dynamic PET concentration image reconstruction based on stacked autoencoder

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- Number: US 10,765,382 B2
- Document ID: US10765382B2
- Status: Granted
- Kind: B2
- Application number: 15/745,003
- Filed: 2017-07-13
- Published: 2019-01-10
- Granted: 2020-09-08
- Earliest claimed: 2017-07-13
- Assignees: Zhejiang University
- Applicants: Zhejiang University
- Inventors: Huafeng Liu; Dongsheng Ruan
- Web page: https://patentgrep.com/patent/US10765382B2

## CPC

- A61B 6/037: {Emission tomography}
- G01R 33/481: {MR combined with positron emission tomography [PET] or single photon emission computed tomography [SPECT]}
- G01T 1/2985: {In depth localisation, e.g. using positron emitters; Tomographic imaging (longitudinal and transverse section imaging; apparatus for radiation diagnosis sequentially in different planes, steroscopic radiation diagnosis); (using external radiation sources A61B6/02)}
- G06N 3/045: Combinations of networks
- G06N 3/0455: Auto-encoder networks; Encoder-decoder networks
- G06N 3/0499: Feedforward networks
- G06N 3/084: Backpropagation, e.g. using gradient descent
- G06N 3/09: Supervised learning
- G06T 12/00: Tomographic reconstruction from projections
- G06T 12/20: Inverse problem, i.e. transformations from projection space into object space
- G06T 5/70: Denoising; Smoothing
- G06T 7/0012: {Biomedical image inspection}
- G06T 7/20: Analysis of motion (motion estimation for coding, decoding, compressing or decompressing digital video signals H04N19/43, H04N19/51)
- G06T 2207/10104: Positron emission tomography [PET]
- G06T 2210/41: Medical
- G06T 2211/412: Dynamic
- G06T 2211/441: AI-based methods, deep learning or artificial neural networks
- A61B: DIAGNOSIS; SURGERY; IDENTIFICATION (usefulness limited to only animals A61D)
- G01R: MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES (indicating correct tuning of resonant circuits H03J3/12)
- G01T: MEASUREMENT OF NUCLEAR OR X-RADIATION (radiation analysis of materials, mass spectrometry G01N23/00; tubes for determining the presence, intensity, density or energy of radiation or particles H01J47/00)
- G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06T: IMAGE DATA PROCESSING OR GENERATION, IN GENERAL

## Abstract

The present invention discloses a method for reconstructing dynamic PET concentration distribution image of dual-tracer based on stacked autoencoder. The invention introduces deep learning into dynamic tracer PET concentration distribution image reconstruction, and the process is mainly divided into two stages of training and reconstruction. In the training phase, train multiple autoencoders using the concentration distribution images of mixed tracers taken as input, and the concentration distribution images of the two tracers taken as labels to build the stacked autoencoder. In the reconstruction phase, the concentration distribution images of the individual tracer can be reconstructed by inputting the concentration distribution images of the mixed traces to the well trained stacked autoencoder. The present invention realizes the reconstruction of the dynamic PET concentration distribution images of mixed tracers from the data-driven point of view, and effectively solves the problems of poor reconstruction effect and inability of simultaneous injection.

## Claims

### Claim 1

A method for reconstructing mixed tracers dynamic position emission tomography (PET) concentration distribution images based on stacked autoencoder comprising the following steps:
(1) injecting a first tracer and a second tracer into a biological tissue, detecting the biological tissue by using a pair of detectors, and collecting coincidence counting vectors corresponding to different collection time to construct a coincidence counting matrix Y for the first tracer and the second tracer, a coincidence counting matrix Y1 for the first tracer and a coincidence counting matrix Y2 for the second tracer;
(2) according to the coincidence counting matrices Y, Y1 and Y2, obtaining dynamic PET concentration distribution images X for the first tracer and the second tracer, dynamic PET concentration distribution images X1 for the first tracer and dynamic PET concentration distribution images X2 for the second tracer by maximum likelihood-expectation maximization (ML-EM) algorithm using a principle of PET imaging;
then arranging the PET concentration distribution images of different frames in pixel order to obtain a dynamic concentration truth vector set x for the first tracer and the second tracer PET images X, and a dynamic concentration truth vector set o for PET images X1 and X2 after the first tracer and the second tracer are combined, x and o being taken as a training set;
wherein each vector in x is used as an input of a neural network and each vector in o is used as a truth label;
(3) training multiple autoencoders with the training set, cascading trained autoencoders to the stacked autoencoder, and then fine-tuning the stacked autoencoder with the training set to obtain PET concentration distribution image reconstruction model, wherein the stacked autoencoder consists of an input layer, a hidden layer and an output layer, the input layer to the hidden layer is called an encoder, and the hidden layer to the output layer is called a decoder, the hidden layer of a previous autoencoder is the input layer of a latter autoencoder; for any self-encoder, the number of neurons in the hidden layer is less than the number of neurons in the input layer;
(4) repeating the method of the step (1) and using new mixed tracers to acquire a new coincidence counting matrix, then obtaining the dynamic mixed PET concentration distribution images of the new mixed tracers according to the step (2) and arranging the obtained PET concentration distribution images in different frames in pixel order as a test set, inputting the test set into the PET concentration distribution image reconstruction model to reconstruct the dynamic PET concentration distribution images of the first tracer and the second tracer, respectively.

### Claim 2 (depends on 1)

The method for reconstructing dynamic PET concentration distribution images based on stacked autoencoder with mixed tracers according to claim 1 characterized in that: the method for arranging PET concentration distribution images of different frames in pixel order is as follows: first, the pixel data in the dynamic PET concentration distribution images X, X1 and X2 are arranged in the following form:
{
x
=
[
x
1
,
x
2
,
…
⁢
,
x
i
,
…
⁢
,
x
mxm
]
x
1
=
[
x
1
1
,
x
2
1
,
…
⁢
,
x
i
1
,
…
⁢
,
x
mxm
1
]
x
2
=
[
x
1
2
,
x
2
2
,
…
⁢
,
x
i
2
,
…
⁢
,
x
mxm
2
]
wherein x′ is the dynamic concentration truth vector set of pixel points for the first tracer PET concentration distribution image, x2 is the dynamic concentration truth vector set of pixel points for the second tracer PET concentration distribution image, x is the dynamic concentration truth vector of the i-th pixel in the mixed tracers PET concentration distribution images, x, and x, are respectively the dynamic concentration truth vectors of the i-th pixel in the PET concentration distribution images of the first tracer and the second tracer; i is a natural number and 1≤i≤m2, m×m is the resolution of the image, x, x and xj are expressed as follows:
{
x
i
=
[
x
1
⁢
i
,
x
2
⁢
i
,
…
⁢
,
x
ji
,
…
⁢
,
x
ki
]
T
x
i
1
=
[
x
1
⁢
i
1
,
x
2
⁢
i
1
,
…
⁢
,
x
ji
1
,
…
⁢
,
x
ki
1
]
T
x
i
2
=
[
x
1
⁢
i
2
,
x
2
⁢
i
2
,
…
⁢
,
x
ji
2
,
…
⁢
,
x
ki
2
]
T
wherein x, is the concentration value of the i-th pixel in the PET concentration distribution image corresponding to the j-th frame of the mixed tracers and x and x2 are respectively the concentration value of i-th pixel in the PET concentration distribution images of j th frame of the first tracer and the second tracer, j is a natural number and 1≤j≤k, k is the number of PET concentration distribution images for each tracer, T represents transpose;
then x1 and x2 are combined to get o, and the i-th vector in o is
o
i
=
[
x
i
1
x
i
2
]
.

### Claim 3 (depends on 1)

The method for reconstructing dynamic mixed tracers PET concentration distribution images based on stacked autoencoder according to claim 1 characterized in that: the function model of the autoencoder is as follows:
h=f(Wx+b)
p=f(W′h+b′)
wherein x, h, and p are respectively the input, hidden, and output layers of the autoencoder, W and b are respectively the weight and bias of encoder, W′ and b′ are respectively the weight and bias of the decoder, f is the activation function.

### Claim 4 (depends on 3)

The method for reconstructing dynamic mixed tracers PET concentration distribution images based on stacked autoencoder according to claim 3 characterized in that: in step (3), the specific method of training stacked autoencoder is as follows:
(3-1) training the first autoencoder in stacked autoencoder: x in the training set is taken as the input layer of the autoencoder and the minimum of the loss function L between the output layer and the input layer is taken as the target to obtain the model parameters by backpropagation algorithm and gradient descent algorithm;
(3-2) training any autoencoder in stacked autoencoder except for the first and last ones: the hidden layer of previous autoencoder is taken as the input layer of the autoencoder and the minimum of the loss function L between the output layer and the input layer is taken as the target to obtain the model parameters by backpropagation algorithm and gradient descent algorithm;
(3-3) training last autoencoder in stacked autoencoder: the hidden layer of previous autoencoder is taken as the input layer of the autoencoder and the minimum of the loss function L′ between the output layer and o in training set is taken as the target to obtain the model parameters by backpropagation algorithm and gradient descent algorithm;
(3-4) training the stacked autoencoder again using the training set of x and o as input and label of stacked autoencoder to obtain PET concentration distribution image reconstruction model.

### Claim 5 (depends on 4)

The method for reconstructing dynamic mixed tracers PET concentration distribution images based on stacked autoencoder according to claim 4 characterized in that: the loss functions L and L′ of the stack autoencoder is expressed as:
L=∥z−t∥2 L′=∥o−t∥2
wherein o is the truth label of the training sample, z is an input of the stacked autoencoder and t is an output of the stacked autoencoder.

### Claim 6 (depends on 1)

The method for reconstructing dynamic mixed tracers PET concentration distribution images based on stacked autoencoder according to claim 1 characterized in that: in step (4), the test set {circumflex over (x)} is input to the concentration distribution image reconstruction model to reconstruct the dynamic PET concentration distribution images of two tracers, the specific process is as follows:
first, each column in the test set {circumflex over (x)}=[{circumflex over (x)}1, {circumflex over (x)}2, . . . , {circumflex over (x)}m×m] is used as the input of stacked autoencoder to obtain the output:
ô=[ô1,ô2, . . . ,ôm×m]
then ô is decomposed into {circumflex over (x)}1=[{circumflex over (x)}11, {circumflex over (x)}21, . . . , {circumflex over (x)}m×m1] and {circumflex over (x)}2=[{circumflex over (x)}12, {circumflex over (x)}22, . . . , {circumflex over (x)}m×m2] to reconstruct dynamic tracer PET concentration distribution images of two tracers.