Using density invariant graph Laplacian to resolve unobservable parameters for three-dimensional optical bio-imaging

We explore the graph Laplacian eigenmap for the application of three-dimensional (3D) optical bioimaging. By using the density invariant graph Laplacian, each high-dimensional sampling (e.g. an image) could be represented by a low-dimensional description. These descriptions not only preserve key features of raw images but also estimate unobservable parameters for 3D imaging. In this paper, we apply this method for two 3D optical microscopies under following scenarios: (i) 3D optical tomography with projections of unknown orientation. (ii) 3D deconvolution microscopy with a disordered focal stack. To prove the robustness of the method, we use images from real biological systems and experimental measurements. In both cases, our results show that the density invariant graph Laplacian is able to overcome practical issues such as limited number of measurement, unstable environment, misalignment and experimental noise.