Bioimaging using endogenous cell fluorescence, without any external biomarkers makes it possible to explore cells and tissues in their original native state, also in vivo. In order to be informative, this label-free method requires careful multispectral or hyperspectral recording of autofluorescence images followed by unsupervised extraction (unmixing) of biochemical signatures. The unmixing is difficult due to the scarcity of biochemically pure regions in cells and also because autofluorescence is weak compared with signals from labelled cells, typically leading to low signal to noise ratio. Here, we solve the problem of unsupervised hyperspectral unmixing of cellular autofluorescence by introducing the Robust Dependent Component Analysis (RoDECA). This approach provides sophisticated and statistically robust quantitative biochemical analysis of cellular autofluorescence images. We validate our method on artificial images, where the addition of varying known level of noise has allowed us to quantify the accuracy of our RoDECA analysis in a way that can be applied to real biological datasets. The same unsupervised statistical minimisation is then applied to imaging of mouse retinal photoreceptor cells where we establish the identity of key endogenous fluorophores (free NADH, FAD and lipofuscin) and derive the corresponding molecular abundance maps. The pre-processing methodology of image datasets is also presented, which is essential for the spectral unmixing analysis, but mostly overlooked in the previous studies.