Robust Non-Negative Least Squares Using Sparsity

Sparse, non-negative signals occur in many applications. To recover such signals, estimation posed as non-negative least squares problems have proven to be fruitful. Efficient algorithms with high accuracy have been proposed, but many of them assume either perfect knowledge of the dictionary generating the signal, or attempts to explain deviations from this dictionary by attributing them to components that for some reason is missing from the dictionary. In this work, we propose a robust non-negative least squares algorithm that allows the generating dictionary to differ from the assumed dictionary, introducing uncertainty in the setup. The proposed algorithm enables an improved modeling of the measurements, and may be efficiently implemented using a proposed ADMM implementation. Numerical examples illustrate the improved performance as compared to the standard non-negative LASSO estimator.