Quantification of gene expression in tissues or cells can inform on etiology of disease. Nowadays there have been rich bulk expression data collected from hundreds of subjects at the tissue level. More recently, to generate cell type information, single-cell RNA-sequencing data have been emerging. While there are many strengths to single-cell expression, the data tend to be noisy. Hence we propose a method to glean more insight from bulk gene expression. Our objective is to borrow information across multiple measurements of the same tissue per subject, such as multiple regions of the brain, using an empirical Bayes approach to estimate subject-level cell-type-specific gene expression. Through simulations, we demonstrate the advantages of the proposed method as compared to the existing method designed for deconvolving a single measure of bulk expression. To illustrate, we estimate gene co-expression networks in specific brain cell types, which are then interpreted in light of genetic findings in autism spectrum disorder.