Abstract: We consider the problem of transforming a signal to a representation in which the components are statistically independent. When the signal is generated as a linear transformation of independent Gaussian or non-Gaussian sources, the solution may be computed using a linear transformation (PCA, or ICA, respectively). Here, we examine a complementary case, in which the source is non-Gaussian but elliptically symmetric. In this situation, the source cannot be decomposed into independent components using a linear transform, but we show that a simple nonlinear transformation, which we call radial Gaussianization (RG), is able to remove all dependencies. We apply this methodology to natural signals, demonstrating that the joint distributions of bandpass ﬁlter responses, for both sound and images, are better described as elliptical as linearly transformed independent sources. Consistent with this, we demonstrate that the reduction in dependency achieved by applying RG to either pairs or blocks of bandpass ﬁlter responses is signiﬁcantly greater than that achieved by PCA or ICA.