稀疏重构算法

Sparse Reconstruction Algorithm

在图像处理和统计中,对于一个大的欠定线性方程,找到一个稀疏的近似解,是一种常见问题。标准方法是对一个目标函数求极小值,其中目标函数由一个二次的误差项l2加一个正则项l1组成。针对一般性问题,目标函数有一个光滑的凸函数加上一个非光滑的正则项,提出了一种算法结构。该算法通过求解最优子问题,从而求出稀疏的近似解。仿真结果表明,该算法能够更快的求出近似解,在正则项是凸的情况下,可以证明目标函数的极小解是收敛的。

In image processing and statistics, to find a sparse approximate solution for a large underdetermined linear equation is a common problem. The standard method is to look for the minimum value of an objective function, which includes a quadratic l2 error term added to a regularizer l2. For the more general problem, we propose an algo-rithm, where the objective function is made up of a smooth convex function and a nonsmooth regularizer. The algo- rithm obtains the sparse approximate solution by solving the optimal sub-problems. The simulation result shows that the algorithm can find the approximate solution quickly and the minima solution of the function is convergent under the conditions namely convexity of the regularizer.