This paper describes a new, physically interpretable, fully automatic algorithm for removal of tissue autofluorescence (AF) from fluorescence microscopy images, by non-negative matrix factorization. Measurement of signal intensities from the concentration of certain fluorescent reporter molecules at each location within a sample of biological tissue is confounded by fluorescence produced by the tissue itself (autofluorescence). Spectral mixing models use mixing coefficients to specify how much fluorescence from each source is present and unmixing algorithms separate the two fluorescent sources. Current spectral unmixing methods for AF removal often require a priori knowledge of mixing coefficients. Those which do not, such as principal component analysis, generate negative mixing coefficients that are not physically meaningful. Non-negative matrix factorization constrains mixing coefficients to be non-negative, and has been used for spectral unmixing, but not AF removal. This paper describes a novel non-negative matrix factorization algorithm which separates fluorescent images into true signal and AF components utilizing an estimate of the dark current. We also present a test-bed, based on fluorescent beads, to compare the performance of different AF removal algorithms. Our algorithm out-performed previous state of the art on validation images.