Information Theoretic Approach to L-Estimators
Alex Dytso, Martina Cardone, Cynthia Rush · 2021 55th Asilomar Conference on Signals, Systems, and Computers · 2021
We propose a novel way of choosing the coefficients of a class of robust estimators, known as L-estimators. Towards this end, we leverage information theoretic measures, such as the entropy and mutual information, to rigorously characterize the amount of information contained in any subset of the complete collection of order statistics. As an application, we show how the developed framework can be used for image denoising. In particular, we demonstrate that the proposed method is competitive with off-the-shelf filters, as well as with wavelet-based denoising methods, for both discrete (e.g., salt and pepper) and continuous (e.g., mixed Gaussian) noise distributions.