Filtering Pixel Latent Variables for Unmixing Volumetric Images

Measurements of different overlapping components require robust unmixing algorithms to convert the raw multi-dimensional measurements to useful unmixed images. Such algorithms perform reliable separation of the components when the raw signal is fully resolved and contains enough information to fit curves on the raw distributions. In experimental physics, measurements are often noisy, undersampled, or unresolved spatially or spectrally. We propose a novel method where bandpass filters are applied to the latent space of a multi-dimensional convolutional neural network to separate the overlapping signal components and extract each of their relative contributions. Simultaneously processing all dimensions with multi-dimensional convolution kernels empowers the network to combine the information from adjacent pixels and time- or spectral-bins, facilitating component separation in instances where individual pixels lack well-resolved information. We demonstrate the applicability of the method to real experimental physics problems using fluorescence lifetime microscopy and mode decomposition in optical fibers as test cases. The successful application of our approach to these two distinct experimental cases, characterized by different measured distributions, highlights the versatility of our approach in addressing a wide array of imaging tasks.