论文标题
在线性最小二乘中添加约束的成本是多少？
What is the cost of adding a constraint in linear least squares?
论文作者
论文摘要
尽管众所周知，受约束最小二乘（CLS）的估计理论通常是不可避免地应用的。但是，在某些情况下，约束是可选的。例如，在相机颜色校准中，如果对所需的颜色校正矩阵的行总和对行的约束进行约束，则获得了几种可能的颜色加工系统之一；在此示例中，尚不清楚先验是否施加约束是否会导致更好的系统性能。在本文中，我们得出了一个确切的表达式，该表达式将约束与从施加拟合误差的增加相连。作为另一个贡献，我们展示了如何确定将测量数据分为两个组件的投影矩阵：第一个组件由于施加约束而导致拟合误差驱动误差，第二个组件不受约束的影响。我们在颜色校准问题中证明了这些结果的使用。
Although the theory of constrained least squares (CLS) estimation is well known, it is usually applied with the view that the constraints to be imposed are unavoidable. However, there are cases in which constraints are optional. For example, in camera color calibration, one of several possible color processing systems is obtained if a constraint on the row sums of a desired color correction matrix is imposed; in this example, it is not clear a priori whether imposing the constraint leads to better system performance. In this paper, we derive an exact expression connecting the constraint to the increase in fitting error obtained from imposing it. As another contribution, we show how to determine projection matrices that separate the measured data into two components: the first component drives up the fitting error due to imposing a constraint, and the second component is unaffected by the constraint. We demonstrate the use of these results in the color calibration problem.
