The imaginary part of the digamma function when its argument is pure imaginary is known as

$$\Im\psi(\mathrm{i}b)=\frac{1}{2}b^{-1}+\frac{1}{2}\pi\coth{\pi b},$$ and its real part is much more involved.

My question is: Can one obtain the real and imaginary parts of $\ln \Gamma (i b)$ in terms of simpler functions, or in terms of $\ln \Gamma (b)$?

($b$ is a positive number.)