Sparse recovery using an SVD approach to interference removal and parameter estimation

This work focuses on parametric sparse sensing models and looks to improve ℓ1 regularization results when the model dictionary is strongly coherent and/or regularization parameters are unknown. The singular value decomposition (SVD) of the model´s dictionary matrix is used to construct signal and noise subspaces. A method that uses the measurements to automatically optimize the subspace division along with a way to estimate the noise level is introduced. The signal-noise subspace decomposition is then extended to deal with an interfering signal that lies in a known linear subspace by modifying the SVD and performing the sparse recovery in the modified signal subspace. The proposed technique is applied successfully to the Discrete Spectrum of Relaxation Frequencies (DSRF) extraction problem for Electromagnetic Induction (EMI) underground sensing where a strong interference from the soil is a significant concern.