  In this paper we derive a new framework for independent component analysis
(ICA), called measure-transformed ICA (MTICA), that is based on applying a
structured transform to the probability distribution of the observation vector,
i.e., transformation of the probability measure defined on its observation
space. By judicious choice of the transform we show that the separation matrix
can be uniquely determined via diagonalization of several measure-transformed
covariance matrices. In MTICA the separation matrix is estimated via
approximate joint diagonalization of several empirical measure-transformed
covariance matrices. Unlike kernel based ICA techniques where the
transformation is applied repetitively to some affine mappings of the
observation vector, in MTICA the transformation is applied only once to the
probability distribution of the observations. This results in performance
advantages and reduced implementation complexity. Simulations demonstrate the
advantages of the proposed approach as compared to other existing
state-of-the-art methods for ICA.
