BGRem: A background noise remover for astronomical images based on a diffusion model

Open Access

Table 1

Training and inference steps in BGRem.

Training	Inference
Sample a clean source image y	Start from observed noisy image x_T
Sample a noise level t ~ U(0,1); σ(t) = sin(θ_t)	Set diffusion steps t = T, . . ., 1
Sample background noise x	At each step condition on t
Construct noisy image x_t = y + σ_t · x	Predict noise ${\hat{x}}_{θ}$ $Mathematical equation: $\[\hat{x}_{\theta}\]$$
Condition Attn. U-Net on noise level t	Estimate clean image $\hat{y}$ $Mathematical equation: $\[\hat{y}\]$$
Predict noise ${\hat{x}}_{θ} (x_{t}, t)$ $Mathematical equation: $\[\hat{x}_{\theta}\left(x_{t}, t\right)\]$$	Compute next state x_t–1
Minimize L1 loss (Eq. (5))	Repeat until t = 0
Learn denoising for all noise levels	Output final denoised image

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