Optic deconvolution in light microscopy (LM) refers to recovering the object details from images, revealing the ground truth of samples. Traditional explicit methods in LM rely on the point spread function (PSF) during image acquisition. Yet, these approaches often fall short due to inaccurate PSF models and noise artifacts, hampering the overall restoration quality. In this paper, we approached the optic deconvolution as an inverse problem. Motivated by the nonstandard-form compression scheme introduced by Beylkin, Coifman, and Rokhlin (BCR), we proposed an innovative physics-informed neural network Multi-Stage Residual-BCR Net (m-rBCR) to approximate the optic deconvolution. We validated the m-rBCR model on four microscopy datasets - two simulated microscopy datasets from ImageNet and BioSR, real dSTORM microscopy images, and real widefield microscopy images. In contrast to the explicit deconvolution methods (e.g. Richardson-Lucy) and other state-of-the-art NN models (U-Net, DDPM, CARE, DnCNN, ESRGAN, RCAN, Noise2Noise, MPRNet, and MIMO-U-Net), the m-rBCR model demonstrates superior performance to other candidates by PSNR and SSIM in two real microscopy datasets and the simulated BioSR dataset. In the simulated ImageNet dataset, m-rBCR ranks the second-best place (right after MIMO-U-Net). With the backbone from the optical physics, m-rBCR exploits the trainable parameters with better performances (from ~30 times fewer than the benchmark MIMO-U-Net to ~210 times than ESRGAN). This enables m-rBCR to achieve a shorter runtime (from ~3 times faster than MIMO-U-Net to ~300 times faster than DDPM). To summarize, by leveraging physics constraints our model reduced potentially redundant parameters significantly in expertise-oriented NN candidates and achieved high efficiency with superior performance.

翻译：光学显微成像中的去卷积旨在从图像中恢复物体细节，揭示样本的真实结构。传统显微成像中的显式方法依赖于图像采集过程中的点扩散函数。然而，由于不准确的PSF模型和噪声伪影，这些方法往往效果有限，制约了整体复原质量。本文将光学去卷积视为逆问题求解。受Beylkin、Coifman和Rokhlin提出的非标准形式压缩方案启发，我们提出了一种创新的物理信息神经网络——多阶段残差BCR网络，用于近似求解光学去卷积问题。我们在四个显微数据集上验证了m-rBCR模型：来自ImageNet和BioSR的两个模拟显微数据集、真实dSTORM显微图像以及真实宽场显微图像。相较于显式去卷积方法和当前主流神经网络模型，m-rBCR在两个真实显微数据集和模拟BioSR数据集上均表现出最优的PSNR与SSIM指标。在模拟ImageNet数据集中，m-rBCR位列第二。基于光学物理原理构建的m-rBCR以更少的可训练参数实现了更优性能，其参数量比基准模型MIMO-U-Net减少约30倍，比ESRGAN减少约210倍。这使得m-rBCR能够获得更短的运行时间。综上所述，通过引入物理约束，我们的模型显著减少了专业神经网络中可能存在的冗余参数，在保证卓越性能的同时实现了高效计算。