A Practical Formulation for Computation of Complex Gradients and its Application to Maximum Likelihood ICA

We introduce a framework for complex-valued signal processing such that all computations can be directly carried out in the complex domain. The framework, based on an elegant result due to Brandwood, allows for easy derivation of many complex-valued algorithms and their efficient analyses. We demonstrate its application to derivation of relative gradient updates for independent component analysis using maximum likelihood and discuss the selection of score functions within this framework.