Spatial shrinkage via the product independent Gaussian process prior

TL;DR

This paper introduces the PING prior, a novel Gaussian process product model for sparse, piecewise smooth signals, demonstrating improved estimation and detection in high-dimensional imaging data, especially for multiple sclerosis analysis.

Contribution

The paper proposes the PING prior, a new Gaussian process product model that enhances sparse signal detection and estimation in high-dimensional spatial data.

Findings

PING prior outperforms Gaussian process prior in simulations.

Application to MRI data identifies MS-affected regions more effectively.

Spectral domain computation enables handling of large image datasets.

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 product of independent Gaussian processes (PING) with a smooth covariance kernel. The smoothness of the PING process is ensured by the smoothness of the covariance kernels of Gaussian components in the product, and sparsity is controlled by the number of components. The bivariate kurtosis of the PING process shows more components in the product results in thicker tail and sharper peak at zero. The simulation results demonstrate the improvement in estimation using the PING prior over Gaussian process (GP) prior for different image regressions. We apply our method to a longitudinal MRI dataset to detect the regions that are affected by multiple sclerosis (MS) in the greatest magnitude through an image-on-scalar regression model. Due to huge dimensionality of these images, we transform the data into the spectral domain and develop methods to conduct computation in this domain. In our MS imaging study, the estimates from the PING model are more informative than those from the GP model.