Filtering Pixel Latent Variables for Unmixing Noisy and Undersampled Volumetric Images

The development of robust 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, significantly affecting the efficacy of signal unmixing algorithms. We propose applying band-pass filters to the latent space of a multi-dimensional convolutional neural network to disentangle overlapping signal components, enabling the isolation and quantification of their individual contributions. Using multi-dimensional convolution kernels to process all dimensions simultaneously enhances the network's ability to extract information from adjacent pixels, 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. Application of latent unmixing to real FLIM experiments will increase the number of distinguishable fluorescent markers. It will also open new possibilities in optics and photonics for multichannel separations at increased sampling rate.