应用于双线性问题的无变换正则化

Regularization without transformation for bilinear problems

计算机视觉经常需要解双线性参数估计问题,传统地,这类问题的线性解法是标准的特征值分析算法.通常它使用Hartley变换来实现正则化.通过理论分析和蒙特卡洛实验,证明了所给出的简化特征值分析技术可在无须进行正则化变换的前提下,固有地同时具备噪声预白化功能和数据正则化功能,因此它不但能给出均方误差相当小的无偏估计,而且具有计算快速、实现简单方便的优点.

In computer vision, bilinear parameter estimation problems have been traditionally solved using the standard eigen value decomposition （EVD） algorithm. By means of theoretical analysis and Monte Carlo experiments, a proposed simplified EVD technique was demonstrated to intrinsically have the ability, without transformation, to whiten the data noise and to regularize the condition number of bilinear parameter estimation problems. Therefore, it not only can provide an unbiased estimation with very small mean square error（MSE）, also has the advantage of fast computation and easy realization.