  Music source separation in the time-frequency domain is commonly achieved by
applying a soft or binary mask to the magnitude component of (complex)
spectrograms. The phase component is usually not estimated, but instead copied
from the mixture and applied to the magnitudes of the estimated isolated
sources. While this method has several practical advantages, it imposes an
upper bound on the performance of the system, where the estimated isolated
sources inherently exhibit audible "phase artifacts". In this paper we address
these shortcomings by directly estimating masks in the complex domain,
extending recent work from the speech enhancement literature. The method is
particularly well suited for multi-instrument musical source separation since
residual phase artifacts are more pronounced for spectrally overlapping
instrument sources, a common scenario in music. We show that complex masks
result in better separation than masks that operate solely on the magnitude
component.
