Abstract
The spatial resolution of images of living samples obtained by fluorescence microscopes is physically limited due to the diffraction of visible light, which makes the study of entities of size less than the diffraction barrier (around 200 nm in the x-y plane) very challenging. To overcome this limitation, several deconvolution and super-resolution techniques have been proposed. Within the framework of inverse problems, modern approaches in fluorescence microscopy reconstruct a super-resolved image from a temporal stack of frames by carefully designing suitable hand-crafted sparsity-promoting regularisers. Numerically, such approaches are solved by proximal gradient-based iterative schemes. Aiming at obtaining a reconstruction more adapted to sample geometries (e.g. thin filaments), we adopt a plug-and-play denoising approach with convergence guarantees and replace the proximity operator associated with the explicit image regulariser with an image denoiser (i.e. a pre-trained network) which, upon appropriate training, mimics the action of an implicit prior. To account for the independence of the fluctuations between molecules, the model relies on second-order statistics. The denoiser is then trained on covariance images coming from data representing sequences of fluctuating fluorescent molecules with filament structure. The method is evaluated on both simulated and real fluorescence microscopy images, showing its ability to correctly reconstruct filament structures with high values of peak signal-to-noise ratio (PSNR).
Abstract (translated)
荧光显微镜观察的生样本图像的空间分辨率由于可见光的衍射而物理上受到限制,这使得研究尺寸小于衍射屏障(在x-y平面上约为200纳米)的实体非常具有挑战性。为了克服这一限制,已经提出了几种差分和超分辨率技术。在逆问题的框架内,现代荧光显微镜的方法通过精心设计的人工稀疏增强 regulariser 从时间帧序列中重构出一个超分辨率图像。计算上,这些方法通过近邻梯度基迭代算法解决。旨在获得样品几何形状更适应的重构(例如细线状),我们采用了可插拔的去噪方法,并使用图像去噪器(即一个训练过的网络),将其与显式图像 Regulariser 替换为图像去噪器,以便在适当的训练后模拟出隐含先验的行为。为了考虑分子之间的独立性波动,模型依赖于二阶统计。去噪器随后从代表波动荧光分子序列的序列数据中训练出共形图像。方法在模拟和真实的荧光显微镜图像上进行评估,表明它能够以高峰值信号-噪声比(PSNR)的正确重构线状结构。
URL
https://arxiv.org/abs/2303.11212
