# Blind source separation with one source rotated

I have two images:

$$I_1 = w_{11}A + w_{12}B, \\ I_2 = w_{21}A + w_{22} \bar{B}.$$

$$A$$ and $$B$$ are unknown. $$\bar{B}$$ is $${B}$$ rotated by 180 degree. For both images, $$A$$ has higher signal-to-noise ratio. What would be an effective way to extract $$A$$ out of these two images?