Spatial Shrinkage Via the Product Independent Gaussian Process Prior
Spatial Shrinkage Via the Product Independent Gaussian Process Prior
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DOI：
10.1080/10618600.2021.1923512
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发表时间：
2018-05
影响因子：
2.4
通讯作者：
Arkaprava Roy;B. Reich;J. Guinness;R. Shinohara;A. Staicu
中科院分区：
文献类型：
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作者：
Arkaprava Roy;B. Reich;J. Guinness;R. Shinohara;A. Staicu
摘要研究了空域上的稀疏信号检测问题。我们提出了一种新的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核的独立高斯(PING)过程的乘积。PING过程的光滑性由乘积中高斯分量的协方差核的光滑性保证，稀疏性由分量的数量控制。Ping过程的双变量峰度意味着产品中的成分越多，尾部越厚，零点处的峰越尖锐。提出了一种基于谱方法的高效计算算法。仿真结果表明，对于不同的图像回归，PING先验优于高斯过程先验。我们将我们的方法应用于纵向磁共振成像数据集，以检测在该域中受多发性硬化症计算影响的区域。这篇文章的补充材料可以在网上找到。
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.