Spatial Shrinkage Via the Product Independent Gaussian Process Prior
提出一种乘积独立高斯过程先验，用于建模空间域上稀疏且分段光滑的连续信号，通过控制成分数量实现稀疏性，并开发了基于谱方法的计算算法，在图像回归和纵向MRI数据中表现优于传统高斯过程。
We study the problem of sparse signal detection on a spatial domain. We propose a novel approach to model continuous signals that are sparse and piecewise-smooth as the product of independent Gaussian (PING) processes with a smooth covariance kernel. The smoothness of the PING process is ensured by the smoothness of the covariance kernels of the Gaussian components in the product, and sparsity is controlled by the number of components. The bivariate kurtosis of the PING process implies that more components in the product results in the thicker tail and sharper peak at zero. We develop an efficient computation algorithm based on spectral methods. The simulation results demonstrate superior estimation using the PING prior over Gaussian process prior for different image regressions. We apply our method to a longitudinal magnetic resonance imaging dataset to detect the regions that are affected by multiple sclerosis computation in this domain. Supplementary materials for this article are available online.