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).

翻译：荧光显微镜获取活体样本图像的空间分辨率受可见光衍射的物理限制，这使得研究尺寸小于衍射极限（在xy平面约为200纳米）的实体极具挑战。为克服这一限制，研究者提出了多种解卷积与超分辨率技术。在逆问题框架下，现代荧光显微镜方法通过精心设计合适的显式稀疏性正则化项，从时间序列图像堆栈中重建超分辨率图像。数值求解这类方法通常采用基于近端梯度的迭代算法。为获得更适应样本几何结构（如细丝结构）的重建结果，我们采用具有收敛保证的即插即用去噪方法，将显式图像正则化项对应的近端算子替换为图像去噪器（即预训练网络），该网络通过适当训练可模拟隐式先验的作用。为描述分子间波动的独立性，模型基于二阶统计量构建。去噪器使用来自具有细丝结构的波动荧光分子序列数据的协方差图像进行训练。该方法在模拟与真实荧光显微镜图像上均进行了评估，结果表明其能正确重建细丝结构，并具有高峰值信噪比。