Phase transition and higher order analysis of $L_q$ regularization under dependence

Hanwen Huang, Peng Zeng, Qinglong Yang

We study the problem of estimating a $k$-sparse signal ${\mbox{$β$}}_0\in{\bf R}^p$ from a set of noisy observations $\mathbf{y}\in {\mathbf{R}}^n$ under the model ${\bf y}={\bf X}{\mbox{$β…