题 目：Sparse Recovery via Non-convex Minimization

汇报人：Prof.Cun-Hui Zhang, Rutgers University

时 间：2008年6月19日（周四）下午3：00

地 点：拉斯维加斯9888116室

提要：We consider recovery of the sparsest linear representation of data with an over complete dictionary. We propose a new family of concave penalty functions which includes the $\ell_1$ as a special case. We propose a fast algorithm which tracks a piecewise linear continuous path of critical points of the penalized squared loss. We prove that under mild conditions on sparse eigenvalues of the dictionary, the new algorithm finds the sparsest solution of the highly ill-posed linear system by solving a finite sequence of low-dimensional convex minimization problems, even though the penalized loss is globally non-convex. Our simulation experiments demonstrate that the new method is more accurate and computationally more efficient compared with the $\ell_1$ penalized optimization