Minimum noiseless description length (MNDL) based regularization parameter selection

The l_p-norm regularized least square technique has been effectively exploited for sparse reconstruction problems. However, the choice of an optimum regularization parameter in the optimization routine still remains a challenge. In this paper we propose a new criterion which is based on MNDL, a new method for optimum subspace selection in data representation, to select the optimum regularization parameter utilizing l_p-regularized least-squares. Simulations are done for combined model order selection and parameter estimation for the ubiquitous sinusoids-in-noise model. The results show that the MNDL based regularization parameter selection outperforms the state of the art methods that use MDL for the correct estimation of number of components in the signal.