Algorithm 1.

Progressive Back-Projection Network for COVID-CT super-resolution.

Require: Learning ratel, batch sizem, and iteration epochE

Input: The training set${\left\{I_{LR}^i,I_{HR}^i\right\}}_{i=1}^N$

Output: super-resolution reconstruction imageISR

Ensure: Parameterθ

Initialization: θis initialized randomly

fore=1,…,Edo

n=1

whilen ≤ N − mdo

${\left\{L_{initial}^i\right\}}_{i=n}^{n+m}=C_{initial}*{\left\{I_{LR}^i\right\}}_{i=n}^{n+m}$

The first stage

${\left\{L_{bp}^i\right\}}_{i=n}^{n+m}=f_{bp}\left({\left\{L_{initial}^i\right\}}_{i=n}^{n+m}\right)$

${\left\{L_{deep}^i\right\}}_{i=n}^{n+m}=f_{deep}\left({\left\{L_{bp}^i\right\}}_{i=n}^{n+m}\right)$

${\left\{L_{up}^i\right\}}_{i=n}^{n+m}=f_{up}({\left\{L_{initial}^i\right\}}_{i=n}^{n+m}+C_{middle}*{\left\{L_{deep}^i\right\}}_{i=n}^{n+m})$

The second stage

${\left\{L_{bp}^i\right\}}_{i=n}^{n+m}=f_{bp}\left({\left\{L_{up}^i\right\}}_{i=n}^{n+m}\right)$

${\left\{L_{deep}^i\right\}}_{i=n}^{n+m}=f_{deep}\left({\left\{L_{bp}^i\right\}}_{i=n}^{n+m}\right)$

${\left\{L_{up}^i\right\}}_{i=n}^{n+m}=f_{up}({\left\{L_{up}^i\right\}}_{i=n}^{n+m}+C_{middle}*{\left\{L_{deep}^i\right\}}_{i=n}^{n+m})$

${\left\{I_{SR}^i\right\}}_{i=n}^{n+m}=C_{res}*{\left\{L_{up}^i\right\}}_{i=n}^{n+m}$

$L\left(\mathit{\theta }\right)=\frac{1}{m}\sum _{i=n}^{n+m}{\parallel I_{SR}^i-I_{HR}^i\parallel }_1$

θ = optimizer(L(θ),l), update parameter with Adam optimizer

n = n + m

end while

end for