Feature Adaptive Filtering: Exploiting Hidden Sparsity

We have been witnessed a growing research activity to advance new strategies to detect and exploit underlying sparsity in the parameters of physical models. In many cases, the sparsity is not explicit in the relations among the parameter coefficients requiring some suitable tools to reveal the potential sparsity. This work proposes a family of adaptive filtering algorithms, aimed at exposing some hidden features of the unknown parameters. Although the basic idea applies to any algorithm, we will concentrate the work in the LMS-type algorithms, giving rise to a family collectively named as Feature LMS (F-LMS) algorithms. These algorithms increase the convergence speed and reduce the steady-state mean-squared error, in comparison with the classical LMS solution. The main idea is to apply linear transformations, through the so-called feature matrices, to reveal the sparsity hidden in the coefficient vector, followed by a sparsity-promoting penalty function to exploit the exposed sparsity. For illustration, a few F-LMS algorithms for lowpass, bandpass, and highpass systems are introduced by using simple feature matrices that require either only simple operations or can learn the features. Simulations and real-life experiments demonstrate that the F-LMS algorithms bring about several performance improvements whenever the unknown sparsity of parameters is exposed.