Multiplex immunohistochemistry (IHC) staining is a new, emerging technique for the detection of multiple biomarkers within a single tissue section. The initial key step in multiplex IHC image analysis in digital pathology is of tremendous clinical importance due to its ability to accurately unmix the IHC image and differentiate each of the stains. The technique has become popular due to its significant efficiency and the rich diagnostic information it contains. The intriguing task of unmixing a three-channel CCD color camera acquired RGB image into more than three colors is very challenging, and to the best of our knowledge, hardly studied in academic literature. This paper presents a novel stain unmixing algorithm for brightfield multiplex IHC images based on a group sparsity model. The proposed framework achieves robust unmixing for more than three chromogenic dyes while preserving the biological constraints of the biomarkers. Typically, a number of biomarkers co-localize in the same cell parts named priori. With this biological information in mind, the number of stains at one pixel therefore has a fixed up-bound, i.e. equivalent to the number of co-localized biomarkers. By leveraging the group sparsity model, the fractions of stain contributions from the co-localized biomarkers are explicitly modeled into one group to yield the least square solution within the group. A sparse solution is obtained among the groups since ideally only one group of biomarkers is present at each pixel. The algorithm is evaluated on both synthetic and clinical data sets, and demonstrates better unmixing results than the existing strategies. 
Group sparsity model for stain unmixing in brightfield multiplex immunohistochemistry images