Question about the denoising calibration in Stage 3

[Calvin-Pang]

Hi,
Thanks for sharing the excellent work! I am reading the paper and have a question about the calibration mentioned in Equation (4). Since the approximated residual noise from Stage 1 is the $\bar{\epsilon}$ in Equation 1, then after calibration, why it should be adding $\frac{\lambda_2 \mu}{\lambda_1}$? I tried to derive the equation 4, and get the following equation:

$x = \lambda_1 y + (\bar{\epsilon}_{zeromean} + \mu)$

$y = \frac{x}{\lambda_1} - \frac{\bar{\epsilon}_{zeromean}}{\lambda_1} - \frac{\mu}{\lambda_1}$

I am wondering why the calibration is not adding $\frac{\mu}{\lambda_1}$ instead of $\frac{\lambda_2 \mu}{\lambda_1}$.

Could you please help me figure out if there is anything wrong with my derivation? Thanks so much!