Abstract

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.

摘要

我们研究了空间域上的稀疏信号检测问题。我们提出了一种新方法来将稀疏和分段平滑的连续信号建模为具有平滑协方差内核的独立高斯 (PING) 过程的乘积。PING过程的平滑性由乘积中高斯分量协方差核的平滑性保证，稀疏性由分量数控制。PING 过程的二元峰态意味着产品中的更多成分导致更粗的尾部和更尖的零峰。我们开发了一种基于光谱方法的高效计算算法。模拟结果表明，对于不同的图像回归，使用 PING 先验优于高斯过程先验的优越估计。我们将我们的方法应用于纵向磁共振成像数据集，以检测该域中受多发性硬化计算影响的区域。本文的补充材料可在线获取。