Joint Sparsity and Order Optimization Based on ADMM With Non-Uniform Group Hard Thresholding
Joint Sparsity and Order Optimization Based on ADMM With Non-Uniform Group Hard Thresholding
复制标题
DOI：
10.1109/tcsi.2017.2763969
复制
发表时间：
2018-05
期刊：
影响因子：
--
通讯作者：
Ryo Matsuoka;Seisuke Kyochi;Shunsuke Ono;M. Okuda
中科院分区：
文献类型：
--
作者：
Ryo Matsuoka;Seisuke Kyochi;Shunsuke Ono;M. Okuda
本文提出了一种用于FIR滤波器设计的稀疏度和滤波器阶数联合优化的新优化框架。由于JOSFO的代价函数涉及$\ well _{0}$和非均匀重叠组$\ well _{0}$范数，它们不是凸的，因此难以获得全局最优解。为了找到非凸问题的近似解，现有的方法重复以下步骤：1)近似成本函数；2)通过最小化成本函数找到零系数的候选者；3)将它们设为零。另一方面，本文采用乘法器的交替方向法，利用$\ell _{0}$和非一致非重叠群$\ell _{0}$范数的伪邻近算子，直接解决了优化问题，而不需要对代价函数进行任何逼近。实验结果表明，该方法设计的滤波器具有更稀疏的系数和更低的阶数，同时满足滤波器的要求，如与期望频率响应的误差。
This paper proposes a new optimization framework for the joint optimization of sparsity and filter order (JOSFO) for FIR filter design. Since the cost function for JOSFO involves $\ell _{0}$ and non-uniform overlapped group $\ell _{0}$ norms, which are not convex, a global optimal solution is difficult to obtain. To find an approximate solution of the non-convex problem, existing approaches repeat the following steps: 1) approximate the cost function; 2) find candidates of zero coefficients by minimizing the cost function; and 3) set them to zero. On the other hand, this paper directly solves the optimization problem, without any approximation to the cost function, by using the alternating direction method of multipliers with the pseudo-proximity operators of $\ell _{0}$ and non-uniform non-overlapped group $\ell _{0}$ norms. Experimental results show that resulting filters designed by the proposed method have sparser coefficients and lower orders, while satisfying filter specifications, such as an error from a desired frequency response.