  The noise produced by the inspiral of millions of white dwarf binaries in the
Milky Way may pose a threat to one of the main goals of the space-based LISA
mission: the detection of massive black hole binary mergers. We present a novel
study for reconstruction of merger waveforms in the presence of Galactic
confusion noise using dictionary learning. We discuss the limitations of
untangling signals from binaries with total mass from $10^2 M_{\odot}$ to $10^4
M_{\odot}$. Our method proves extremely successful for binaries with total mass
greater than $\sim 3\times 10^3$ $ M_{\odot}$ up to redshift 3 in conservative
scenarios, and up to redshift 7.5 in optimistic scenarios. In addition,
consistently good waveform reconstruction of merger events is found if the
signal-to-noise ratio is approximately 5 or greater.
