In this work, we investigate the different sensing schemes for the detection of four targets as observed through a vector Poisson and Gaussian channels when the sensing time resource is limited and the source signals can be observed through a variety of sum combinations during that fixed time. For this purpose, we can maximize the mutual information or the detection probability with respect to the time allocated to different sum combinations, for a given total fixed time. It is observed that for both Poisson and Gaussian channels; mutual information and Bayes risk with $0-1$ cost are not necessarily consistent with each other. Concavity of mutual information between input and output, for certain sensing schemes, in Poisson channel and Gaussian channel is shown to be concave w.r.t given times as linear time constraint is imposed. No optimal sensing scheme for any of the two channels is investigated in this work.

翻译：在这项工作中,当感测时间资源有限,而且源信号可在固定时间内通过各种总和组合观测时,我们调查通过矢量 Poisson 和Gaussian 频道观测到的检测四个目标的不同感测计划,为此,我们可以在一定的完全固定时间内最大限度地扩大对不同总和组合所分配时间的相互信息或探测概率,发现Poisson 和Gaussian 频道的相互信息和Bayes 风险,费用为0-1美元,不一定彼此一致。 Poisson 频道和Gaussian 频道的某些感测计划,对输入和输出的相互信息,在规定线性时间限制时,显示在某些感测计划中,对输入和输出的相互信息的准确性是相同的。在这项工作中,没有调查这两个频道中任何一条的最佳感测方法。