  We address the problem of simultaneously recovering a sequence of point
source signals from observations limited to the low-frequency end of the
spectrum of their summed convolution, where the point spread functions (PSFs)
are unknown. By exploiting the low-dimensional structures of the signals and
PSFs, we formulate this as a low-rank matrix demixing problem. To solve this,
we develop a scaled gradient descent method without balancing regularization.
We establish theoretical guarantees under mild conditions, demonstrating that
our method, with spectral initialization, converges to the ground truth at a
linear rate, independent of the condition number of the underlying data
matrices. Numerical experiments indicate that our approach is competitive with
existing convex methods in terms of both recovery accuracy and computational
efficiency.
