In the present paper, we are concerned with introducing a simple method for signal detection problem in one realization of a two-dimensional random field based on the one-dimensional random projection technique. Formally, we provide a Bayesian projection-based approach for signal detection in the two-dimensional Gaussian scale space random field, though it is applicable for higher dimensions. It will be shown by a series of simulation studies that our purposed method, controls the error rate in nominal level and has the high performance for signal detection, and this procedure completely distinguishes between the two hypotheses of “no signal” and the alternative. Also, we provide two applications of the proposed procedure, one from a real dataset of a two-dimensional random field of R-fMRI data of an autistic individual and the other with a two-dimensional random field of fMRI data.

在本文中，我们关注的是在基于一维随机投影技术的二维随机场的一种实现中引入一种用于信号检测问题的简单方法。形式上，我们提供了一种基于贝叶斯投影的方法，用于二维高斯尺度空间随机场中的信号检测，尽管它适用于更高维度。一系列仿真研究表明，我们的目的方法将错误率控制在标称级别，并且具有高性能的信号检测，并且该过程完全区分了“无信号”和替代两种假设。此外，我们提供了所提出程序的两种应用，一种来自R-fMRI二维随机场的真实数据集一个自闭症个体的数据和另一个具有二维随机场的fMRI数据。