Cancer diagnosis is based on visual examination under a microscope of tissue sections from biopsies. But whereas pathologists rely on tissue stains to identify morphological features, automated tissue recognition using color is fraught with problems that stem from image intensity variations due to variations in tissue preparation, variations in spectral signatures of the stained tissue, spectral overlap and spatial aliasing in acquisition, and noise at image acquisition. We present a blind method for color decomposition of histological images. The method decouples intensity from color information and bases the decomposition only on the tissue absorption characteristics of each stain. By modeling the charge-coupled device sensor noise, we improve the method accuracy. We extend current linear decomposition methods to include stained tissues where one spectral signature cannot be separated from all combinations of the other tissues' spectral signatures. We demonstrate both qualitatively and quantitatively that our method results in more accurate decompositions than methods based on non-negative matrix factorization and independent component analysis. The result is one density map for each stained tissue type that classifies portions of pixels into the correct stained tissue allowing accurate identification of morphological features that may be linked to cancer.