Unmixing Optical Signals from Undersampled Volumetric Measurements by Filtering the Pixel Latent Variables

The development of signal unmixing algorithms is essential for leveraging multimodal datasets acquired through a wide array of scientific imaging technologies, including hyperspectral or time-resolved acquisitions. In experimental physics, enhancing the spatio-temporal resolution or expanding the number of detection channels often leads to diminished sampling rate and signal-to-noise ratio (SNR), significantly affecting the efficacy of signal unmixing algorithms. We propose Latent Unmixing, a new approach which applies band-pass filters to the latent space of a multi-dimensional convolutional neural network to disentangle overlapping signal components. It enables better isolation and quantification of individual signal contributions, especially in the context of undersampled distributions. Using multi-dimensional convolution kernels to process all dimensions simultaneously enhances the network's ability to extract information from adjacent pixels, and time- or spectral-bins. This approach enables more effective separation of components in cases where individual pixels do not provide clear, well-resolved information. We showcase the method's practical use in experimental physics through two test cases that highlight the versatility of our approach: fluorescence lifetime microscopy and mode decomposition in optical fibers. The latent unmixing method extracts valuable information from complex signals that cannot be resolved by standard methods. It opens new possibilities in optics and photonics for multichannel separations at an increased sampling rate.