On the grouping effect of the l 1−2 models

This paper aims to study the mathematical properties of the l 1−2 models that employ measurement matrices with correlated columns. We first show that the l 1−2 model satisfies the grouping effect which ensures that coefficients corresponding to highly correlated columns in a measurement matrix have small differences. Then we provide the stability analysis based on the sparse approximation property. When the entries of the vectors have different signs, we show that the grouping effect also holds for the constraint l 1+2 minimization model which is implicated by the linearized Bregman iteration.