Fluorescence microscopy is an extremely powerful technique that allows to distinguish multiple labels based on their emission color or other properties, such as their photobleaching and fluorescence recovery kinetics. These kinetics are ideally assumed to be mono-exponential in nature, where the time constants intrinsic to each fluorophore can be used to quantify their presence in the sample. However, these time constants also depend on the specifics of the illumination and sample conditions, meaning that identifying the different contributions in a mixture using a single-channel detection may not be straightforward. In this work, we propose a factor analysis approach called Slicing to identify the different contributions in a multiplexed fluorescence microscopy image exploiting a single measurement channel. With Slicing, a two-way dataset is rearranged into a three-way dataset, which allows the application of a trilinear decomposition model to derive individual profiles for all the model components. We demonstrate this method on bleaching - recovery fluorescence microscopy imaging data of U2OS cells, allowing us to determine the spatial distribution of the dyes and their associated characteristic relaxation traces, without relying on a parametric fitting. By requiring little a priori knowledge and efficiently handling perturbation factors, our method represents a general approach for the recovery of multiple mono-exponential profiles from single-channel microscopy data.