Flesh-dect (media 2021) -- a viewpoint of material decomposition

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reference

Estimating dual-energy CT imaging from single-energy CT data with material decomposition convolutional neural network

Just made a about this paper PPT, So a lot of content in this blog is copied directly PPT Screenshot .

One 、 Introduction to concept and model functions

First of all, a brief introduction to dual energy CT Basic concepts of ：

As for using dual energy CT I won't introduce more about your motivation , This article mainly explains this paper Thought ——material decomposition, The idea that CT Each image pixel All by different basis material Composed of .

Introduce the function of the model ：

For example, now I have one in my hand 100kV Low energy of CT chart , I want to get a 140kV High energy CT chart , Then I just need to get 140kV Projection data of the next angle （sinogram）, And low energy CT Input the model together with the figure , You can get one 140kV High energy CT chart .

Of course, this model may be a little too idealistic in practical application , But it doesn't hinder its material decomposition My thought is very interesting , Next, let's focus on this idea .

Two 、material decomposition Thought

I just put what I did PPT The screenshots ：

First of all, the author believes that ,CT Each of the graphs pixel Can be seen as made up of many basis material Composed of , Each of these material Each has its own attenuation coefficient , So the attenuation coefficient at this point can be regarded as different material Linear combination of attenuation coefficients . Then according to the attenuation coefficient and CT The relationship between values , We can conclude that ：

That is, the of a point CT Values are different basis material Of CT Linear combination of values , Suppose there is m in basis material, Then it corresponds to m individual α To control the coefficient of linear combination . Of course, the above line of formula is just a pixel The situation of , Suppose a CT The picture has $n_{pix}$ individual pixel, Then the number of coefficients needs $n_{pix}\times m$ individual , Store these coefficients in a matrix A in , We can rewrite the above formula into the form of matrix ：

In short, each pixel Of CT Values are treated as several basis material Of CT Linear combination of values , The combination coefficient is stored in the matrix A in （ You can also see A For each basis material The proportion of ）.

Notice the formula in the above figure , Except matrix A Outside , There is also a vector b, This vector stores each basis material Of CT value . How to calculate this b Is very important , And before , We say one of this model input Namely a single-view high energy projection data, We remember it as $P_{high}$; similarly , Because of another input It's low energy CT chart , We can get a single-view low energy projection data, Write it down as $P_{low}$. We make $P_{dif}=P_{high}-P_{low}$, Note in this article , all $xx{x}_{dif}$ Such symbols , All represent the corresponding $xx{x}_{high}-xx{x}_{low}$, That is, the case of high energy minus the corresponding case of low energy . We said , How to work out b It's important , In fact, it is necessary to calculate $b_{dif}$, because $P_{dif}$ It is known. , So we can analyze P and b The relationship between , This is the next part .

3、 ... and 、P and b The relationship between

Again ,P yes single-view projection data, That is, single angle sinogram;b Is stored differently basis material Of CT A vector of values .

First , According to the above conclusion , We have ：


According to the above formula , We have ：

This is the author in paper The formula given in , If you understand the formula before , Then the above picture should be ok . Then define the matrix M=R·A：

We got it P and b Relational expression for , Be careful M There is an unknown quantity in A, So strictly speaking , If known A and $P_{dif}$, Then we can solve $b_{dif}$. The solution is as follows ：

P Data from the input model ,A How to solve it , With this question , Next, we can introduce the paper Methods ——FLESH-DECT 了 .

Four 、FLESH-DECT framework

The above figure is the method logic of the architecture , We mentioned before when talking about the input and output of architecture , The input of this architecture is low energy CT chart 、 Single angle high-energy projection data . We can get through the input of the architecture $P_{dif}$, And then through $P_{dif}$ and A, It can be calculated $b_{dif}$, And then through A and $b_{dif}$, You can get $I_{dif}$. You will now $I_{dif}$ Add to low energy CT On the drawing , You can get high energy CT Graph .

After knowing the method logic , Let's look directly at the architecture diagram ：

I have marked out the more important formulas in the figure . Note that low-energy images should be denoised by neural network first , also $P_{dif}$ We also need to preprocess the neural network first . In the above architecture MD-CNN It's generation A Of .

There's one in the picture above loss, But that's just loss1, One more loss2. Yes loss Is described as follows ：

Notice the loss2 Contains material decomposition An important thought of , That is because you can A and b The multiplication of is regarded as basis material The combination of , So this multiplication process should have the effect of denoising , therefore A and b The multiplication result of can be used as a reference for low energy in the architecture CT Figure of denoising results label. Of course, the above formula needs to be calculated $b_{low}$, The calculation method is similar to $b_{dif}$, I won't go into that .

5、 ... and 、 Network details

Simply look at the network structure ：

This is a network for denoising low-energy pictures .

This is a network for preprocessing single angle projection data .

This is the generation A Of MD-CNN.

6、 ... and 、 experimental result

First of all, yes m Parameter of value ：

m It represents the number of assumptions basis material, It can be seen that m by 10 When , It is better to .

Finally, let's have a brief look at the experimental results , On the left is low energy CT chart , In the middle is high energy CT chart （ground-truth）, On the right is the high energy predicted by the model CT chart ：