Noguchi's finiteness conjecture for hyperbolic complex spaces

Let $X$ be a Zariski open subset of an irreducible compact complex space. A compact irreducible complex space $Y$ is hyperbolic in the sense used by Noguchi, and $f:X\rightarrow Y$ is a dominant meromorphic map. Noguchi's conjecture. The set of compact irreducible hyperbolic complex spaces $Y$ which admit a dominant meromorphic map $f:X\rightarrow Y$ is finite. This is presented as a complex-space analogue of the Iitaka–Severi finiteness statement and is attributed to Noguchi; the supplied text does not state a resolution of it.