We present two computational methods for solving the non-convex maximum a posteriori estimation problem. Following a Bayesian approach, we derive a posterior density. The problem has similar structure to blind deconvolution, except binary constraints are present in the formulation and enforced in our approach. We formulate strain identification as an inverse problem that aims at simultaneously estimating a binary matrix (encoding presence or absence of mutations) and a real-valued vector (representing the mixture of strains) such that their product is approximately equal to the measured data vector. Our method is applicable in public health domains where efficient identification of pathogens is paramount, such as the monitoring of disease outbreaks. We provide a mathematical formulation and develop a computational framework for identifying multiple strains of microorganisms from mixed samples of DNA.
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