Abstract Motivated by the problem of detecting changes in two-dimensional X-ray diffraction data, we propose a Bayesian spatial model for sparse signal detection in image data. Our model places considerable mass near zero and has heavy tails to reflect the prior belief that the image signal is zero for most pixels and large for an important subset. We show that the spatial prior places mass on nearby locations simultaneously being zero, and also allows for nearby locations to simultaneously be large signals. The form of the prior also facilitates efficient computing for large images. We conduct a simulation study to evaluate the properties of the proposed prior and show that it outperforms other spatial models. We apply our method in the analysis of X-ray diffraction data from a two-dimensional area detector to detect changes in the pattern when the material is exposed to an electric field.

中文翻译：

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使用连续收缩先验的空间信号检测

摘要 受检测二维 X 射线衍射数据变化问题的启发，我们提出了一种用于图像数据中稀疏信号检测的贝叶斯空间模型。我们的模型将相当大的质量置于接近零的位置，并具有重尾部，以反映先验信念，即图像信号对于大多数像素而言为零，而对于重要子集而言则较大。我们表明，空间先验将附近位置的质量同时为零，并且还允许附近位置同时为大信号。先验的形式也有利于大图像的高效计算。我们进行了模拟研究来评估所提出的先验的属性，并表明它优于其他空间模型。我们将我们的方法应用于分析二维区域探测器的 X 射线衍射数据，以检测材料暴露于电场时图案的变化。