论文标题
$α\ ell_ {1}-β\ ell_ {2} $ sparsity正则化的投影梯度方法
A projected gradient method for $α\ell_{1}-β\ell_{2}$ sparsity regularization
论文作者
论文摘要
非convex $α\ | \ cdot \ | _ {\ ell_1}-β\ | \ cdot \ | _ {\ ell_2} $ $（α\geβ\ geq0）$正则化引起了稀疏恢复领域的关注。获得该正则化最小化的一种方法是ST-（$α\ ell_1-β\ ell_2 $）算法，该算法与经典的迭代软阈值算法（ISTA）相似。众所周知，ISTA收敛速度非常缓慢，而ISTA的更快替代品是预测的梯度（PG）方法。但是，常规的PG方法仅限于经典的$ \ ell_1 $ sparsity正则化。在本文中，我们通过将PG方法扩展到非convex $α\ ell_1-β\ ell_2 $ sparsity正则化，提出了ST-（$α\ ell_1-β\ ell_2 $）算法的两个加速替代方案。此外，我们讨论了确定Morozov差异原则的$ \ ell_1 $ -ball约束的半径$ r $。据报道，数值结果说明了所提出的方法的效率。
The non-convex $α\|\cdot\|_{\ell_1}-β\| \cdot\|_{\ell_2}$ $(α\geβ\geq0)$ regularization has attracted attention in the field of sparse recovery. One way to obtain a minimizer of this regularization is the ST-($α\ell_1-β\ell_2$) algorithm which is similar to the classical iterative soft thresholding algorithm (ISTA). It is known that ISTA converges quite slowly, and a faster alternative to ISTA is the projected gradient (PG) method. However, the conventional PG method is limited to the classical $\ell_1$ sparsity regularization. In this paper, we present two accelerated alternatives to the ST-($α\ell_1-β\ell_2$) algorithm by extending the PG method to the non-convex $α\ell_1-β\ell_2$ sparsity regularization. Moreover, we discuss a strategy to determine the radius $R$ of the $\ell_1$-ball constraint by Morozov's discrepancy principle. Numerical results are reported to illustrate the efficiency of the proposed approach.
