I have the measured signal $y(t)$ that can be modeled in the frequency domain as $Y(f)$:
$$Y(f) = X(f)\cdot A(f) - [X(f)\cdot B(f)] \ast C(f)$$
where $\ast$ is the convolution. I know $A(f)$, $B(f)$, and $C(f)$. I measure $Y(f)$. Is there a way to retrieve $X(f)$? I know that if $C(f)$ is constant and $1$, then I can easily retrieve $X(f)$ except for frequencies with $A(f)=B(f)$. But how do I go about this for an arbitrary but known $C(f)$?