  We propose a new algorithm for blind source separation (BSS) using
independent vector analysis (IVA). This is an improvement over the popular
auxiliary function based IVA (AuxIVA) with iterative projection (IP) or
iterative source steering (ISS). We introduce iterative projection with
adjustment (IPA), where we update one demixing filter and jointly adjust all
the other sources along its current direction. Each update involves solving a
non-convex minimization problem that we term log-quadratically penalized
quadratic minimization (LQPQM), that we think is of interest beyond this work.
In the general case, we show that its global minimum corresponds to the largest
root of a univariate function, reminiscent of modified eigenvalue problems. We
propose a simple procedure based on Newton-Raphson to efficiently compute it.
Numerical experiments demonstrate the effectiveness of the proposed method.
First, we show that it efficiently decreases the value of the surrogate
function. In further experiments on synthetic mixtures, we study the
probability of finding the true demixing matrix and convergence speed. We show
that the proposed method combines high success rate and fast convergence.
Finally, we validate the performance on a reverberant blind speech separation
task. We find that all the AuxIVA-based methods perform similarly in terms of
acoustic BSS metrics. However, AuxIVA-IPA converges faster. We measure up to
8.5 times speed-up in terms of runtime compared to the next best AuxIVA-based
method, depending on the number of channels and the signal-to-noise ratio
(SNR).
