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In this paper, we develop a novel spatial variable selection method forscalar on vector-valued image regression in a multi-group setting. Here,'vector-valued image' refers to the imaging datasets that contain vector-valuedinformation at each pixel/voxel location, such as in RGB color images,multimodal medical images, DTI imaging, etc. The focus of this work is toidentify the spatial locations in the image having an important effect on thescalar outcome measure. Specifically, the overall effect of each voxel is ofinterest. We thus develop a novel shrinkage prior by soft-thresholding the\ell_2 norm of a latent multivariate Gaussian process. It will allow us toestimate sparse and piecewise-smooth spatially varying vector-valued regressioncoefficient functions. For posterior inference, an efficient MCMC algorithm isdeveloped. We establish the posterior contraction rate for parameter estimationand consistency for variable selection of the proposed Bayesian model, assumingthat the true regression coefficients are Holder smooth. Finally, wedemonstrate the advantages of the proposed method in simulation studies andfurther illustrate in an ADNI dataset for modeling MMSE scores based onDTI-based vector-valued imaging markers.

Double soft-thresholded model for multi-group scalar on vector-valued image regression