This paper aims to study the mathematical properties of the l vmodels that employ measurement matrices with correlated columns.We first show that the l_(1-2)model satisfies the grouping effect which ensures that coeff...This paper aims to study the mathematical properties of the l vmodels 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.展开更多
基金supported by the Zhejiang Provincial Natural Science Foundation of China(LR19A010001)the NSF of China(12022112)Research of Hu Ruifang was supported by the general research project of Jiaxing Nanhu University(62107YL)。
文摘This paper aims to study the mathematical properties of the l vmodels 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.
