Recover Cell Tensor: Diffusion-Equivalent Tensor Completion for Fluorescence Microscopy Imaging

Fluorescence microscopy (FM) imaging is a fundamental technique for observing live cell division, one of the most essential processes in the cycle of life and death. Observing 3D live cells requires scanning through the cell volume while minimizing lethal phototoxicity. That limits acquisition time and results in sparsely sampled volumes with anisotropic resolution and high noise. Existing image restoration methods, primarily based on inverse problem modeling, assume known and stable degradation processes and struggle under such conditions, especially in the absence of high-quality reference volumes. In this paper, from a new perspective, we propose a novel tensor completion framework tailored to the nature of FM imaging, which inherently involves nonlinear signal degradation and incomplete observations. Specifically, FM imaging with equidistant Z-axis sampling is essentially a tensor completion task under a uniformly random sampling condition. On one hand, we derive the theoretical lower bound for exact cell tensor completion, validating the feasibility of accurately recovering 3D cell tensor. On the other hand, we reformulate the tensor completion problem as a mathematically equivalent score-based generative model. By incorporating structural consistency priors, the generative trajectory is effectively guided toward denoised and geometrically coherent reconstructions. Our method demonstrates state-of-the-art performance on SR-CACO-2 and three real \textit{in vivo} cellular datasets, showing substantial improvements in both signal-to-noise ratio and structural fidelity.

Volume Tells: Dual Cycle-Consistent Diffusion for 3D Fluorescence Microscopy De-noising and Super-Resolution

3D fluorescence microscopy is essential for understanding fundamental life processes through long-term live-cell imaging. However, due to inherent issues in imaging principles, it faces significant challenges including spatially varying noise and anisotropic resolution, where the axial resolution lags behind the lateral resolution up to 4.5 times. Meanwhile, laser power is kept low to maintain cell viability, leading to inaccessible low-noise and high-resolution paired ground truth (GT). To tackle these limitations, a dual Cycle-consistent Diffusion is proposed to effectively mine intra-volume imaging priors within 3D cell volumes in an unsupervised manner, i.e., Volume Tells (VTCD), achieving de-noising and super-resolution (SR) simultaneously. Specifically, a spatially iso-distributed denoiser is designed to exploit the noise distribution consistency between adjacent low-noise and high-noise regions within the 3D cell volume, suppressing the spatially varying noise. Then, in light of the structural consistency of the cell volume, a cross-plane global-propagation SR module propagates high-resolution details from the XY plane into adjacent regions in the XZ and YZ planes, progressively enhancing resolution across the entire 3D cell volume. Experimental results on 10 in vivo cellular dataset demonstrate high improvements in both denoising and super-resolution, with axial resolution enhanced from ~ 430 nm to ~ 90 nm.