On the optimizing weighting problem in active image processing

以前，我们已经提出了主动(调制)图像处理方法的概念，它是众所周知的调制光谱的扩展，用于二维图像。对于活动图像处理和调制光谱两者，在与活动调制同步的双极加权函数与观测图像/信号相乘之后执行积分操作。为了应用加权函数的乘法，有两种不同的加权实现是可能的。首先是常规的数字加权，然后是停留时间加权。在本研究中，我们定义了一个优化加权问题，以获得这两种加权方法的最优组合，从而得到最大的S/N比。在研究的第一阶段{1994}，针对噪声功率与调制或信号无关的情况进行了理论分析。利用Schwarz不等式，我们得到了精确的解。也就是说，在这个简单的情况下，当只实施停留时间加权时，我们获得了最大的S/N比。在下一阶段，我们应用了两种加权实现的计算机模拟来评估在噪声功率依赖于调制或信号的更复杂情况下的S/N比。同时，我们继续得到了这类优化问题的精确解。从而成功地得到了这类复杂情况的精确解。这是“实施数字加权，因为实施数字加权后的噪声功率与调制无关”，然后“应用停留时间加权以满足整个加权函数”。这一重要结果已经被先前的模拟很好地证实了。

Previously, we have proposed a concept of the active (modulation) image processing method which is an extension of well known modulation spectroscopy, for 2-dimensional images. For both the active image processing and the modulation spectroscopy, integration operation is carried out after multiplication of a bipolar weighting funciton to observed image/signal, synchronized to the active modulation. To apply multiplication of the weighting function, two different weighting implementations are possible. First is a conventional numerical weighting, and next is a time-of-stay weighting. And both weighting implementations can be used together, while such combinaion results in different signal to noise {S/N} ratio for the processed images.In the present study, we have defined an optimizing weighting problem as to obtain optimized combination of these weighting implementations resulting maximum S/N ratio. At the first stage {1994} of the study, theoretical analysis has been aimed to the case in which the noise power is independent on the modulation or the signal. And we have got an exact solution using Schwarz's inequality. Namely, we obtain maximum S/N ratio when only the time-of-stay weighting is implemented in this simple case.In the next stage {1995}, we have applied a computer simulation of both weighting implementations to evaluate the S/N ratio under more complicated cases in which the noise power is dependent on the modulation or the signal. At same time we have continued to get an exact solution of such optimizing problem. And then we have successfully obtain an exact solution for such complicated case. This is `To implement the numerical weighting, as the noise power after the implementation of the numerical weighing is independent on the modulation', and then `To apply the time-of stay weighting to satisfy the whole weighting function'. This important result has been clearly well confirmed by the previous simulation.