  Independent Component Analysis (ICA) is a popular model for blind signal
separation. The ICA model assumes that a number of independent source signals
are linearly mixed to form the observed signals. We propose a new algorithm,
PEGI (for pseudo-Euclidean Gradient Iteration), for provable model recovery for
ICA with Gaussian noise. The main technical innovation of the algorithm is to
use a fixed point iteration in a pseudo-Euclidean (indefinite "inner product")
space. The use of this indefinite "inner product" resolves technical issues
common to several existing algorithms for noisy ICA. This leads to an algorithm
which is conceptually simple, efficient and accurate in testing.
  Our second contribution is combining PEGI with the analysis of objectives for
optimal recovery in the noisy ICA model. It has been observed that the direct
approach of demixing with the inverse of the mixing matrix is suboptimal for
signal recovery in terms of the natural Signal to Interference plus Noise Ratio
(SINR) criterion. There have been several partial solutions proposed in the ICA
literature. It turns out that any solution to the mixing matrix reconstruction
problem can be used to construct an SINR-optimal ICA demixing, despite the fact
that SINR itself cannot be computed from data. That allows us to obtain a
practical and provably SINR-optimal recovery method for ICA with arbitrary
Gaussian noise.
