Unsupervised parameter selection for denoising with the elastic net
This addresses the challenge of automated parameter tuning in regularization for researchers and practitioners in signal processing and machine learning, offering an incremental improvement over existing methods.
The paper tackles the problem of parameter selection for elastic net regularization in denoising, providing explicit error bounds for a simplified case and a data-driven algorithm for general cases, showing superiority in accuracy and computational time compared to state-of-the-art methods.
Despite recent advances in regularisation theory, the issue of parameter selection still remains a challenge for most applications. In a recent work the framework of statistical learning was used to approximate the optimal Tikhonov regularisation parameter from noisy data. In this work, we improve their results and extend the analysis to the elastic net regularisation, providing explicit error bounds on the accuracy of the approximated parameter and the corresponding regularisation solution in a simplified case. Furthermore, in the general case we design a data-driven, automated algorithm for the computation of an approximate regularisation parameter. Our analysis combines statistical learning theory with insights from regularisation theory. We compare our approach with state-of-the-art parameter selection criteria and illustrate its superiority in terms of accuracy and computational time on simulated and real data sets.