Computational deconvolution is a time and cost-efficient approach to obtain cell type-specific information from bulk gene expression of heterogeneous tissues like blood. Deconvolution can aim to either estimate cell type proportions or abundances in samples, or estimate how strongly each present cell type expresses different genes, or both tasks simultaneously. Among the two separate goals, the estimation of cell type proportions/abundances is widely studied, but less attention has been paid on defining the cell type-specific expression profiles. Here, we address this gap by introducing a novel method Rodeo and empirically evaluating it and the other available tools from multiple perspectives utilizing diverse datasets.