Robust dictionary learning: Application to signal disaggregation

It is well known that the Euclidean norm is sensitive to outliers; yet it is widely used for minimizing it is easy. Dictionary learning is no exception - the l
₂
-norm allows for easy update of the basis/dictionary atoms. In this work, we propose a robust dictionary learning method that is based on minimizing the robust l
₁
-norm. The ensuing optimization is solved using the Split Bregman approach. We apply the proposed technique to signal (energy and water) disaggregation and show that it excels over existing dictionary learning techniques (based on l
₂
-norm).