Algorithm 1 Weights Training of the Denoiser and ResFi

Input: a set of noisy images n, labels l, max iterations of Denoiser maxid, max iterations of ResFi maxir, learning rate α and β

Output: Trained weights w∗ //Weight training of Denoiser

Generate Bernoulli sampled image pairs of a noisy image: ${\left\{{\widehat{\mathit{n}}}_m,{\overline{\mathit{n}}}_m\right\}}_{m=1}^M$

Randomly initialize θ

for iteration = 1: maxid do Update the Denoiser by descending the stochastic gradient:

$${\mathit{\theta }}^{\ast }=\mathit{\theta }-\mathsf{\alpha }\frac{\partial L_D\left(\mathit{\theta }\right)}{\partial \mathit{\theta }}$$

end

Obtain the clean image: ${\mathit{x}}^{\ast }={ℱ}_{\mathit{\theta }}\left({\widehat{\mathit{n}}}_m\right)$

//Weight training of ResFi Randomly initialize w for iteration = 1: maxid do Randomly select a mini-batch of N training samples:

$$\left\{{\mathit{x}}^{\ast }{}_i,l_i\right\}, i=1,\dots ,N$$

Update the ResFi by descending the stochastic gradient:

$${\mathit{w}}^{\ast }=\mathit{w}-\beta \frac{\partial L_R\left(\mathit{w}\right)}{\partial \mathit{w}}$$

End Obtain the optimal weights: w∗