Detecting, counting, and classifying various cell types in images of human blood is important in many biomedical applications. However, these tasks can be very difficult due to the wide range of biological variability and the resolution limitations of many imaging modalities. This paper proposes a new approach to detecting, counting and classifying white blood cell populations in holographic images, which capitalizes on the fact that the variability in a mixture of blood cells is constrained by physiology. The proposed approach is based on a probabilistic generative model that describes an image of a population of cells as the sum of atoms from a convolutional dictionary of cell templates. The class of each template is drawn from a prior distribution that captures statistical information about blood cell mixtures. The parameters of the prior distribution are learned from a database of complete blood count results obtained from patients, and the cell templates are learned from images of purified cells from a single cell class using an extension of convolutional dictionary learning. Cell detection, counting and classification is then done using an extension of convolutional sparse coding that accounts for class proportion priors. This method has been successfully used to detect, count and classify white blood cell populations in holographic images of lysed blood obtained from 20 normal blood donors and 12 abnormal clinical blood discard samples. The error from our method is under 6.8% for all class populations, compared to errors of over 28.6% for all other methods tested.