Inverse problems generally require a regularizer or prior for a good solution. A recent trend is to train a convolutional net to denoise images, and use this net as a prior when solving the inverse problem. Several proposals depend on a singular value decomposition of the forward operator, and several others backpropagate through the denoising net at runtime. Here we propose a simpler approach that combines the traditional gradient-based minimization of reconstruction error with denoising. Noise is also added at each step, so the iterative dynamics resembles a Langevin or diffusion process. Both the level of added noise and the size of the denoising step decay exponentially with time. We apply our method to the problem of tomographic reconstruction from electron micrographs acquired at multiple tilt angles. With empirical studies using simulated tilt views, we find parameter settings for our method that produce good results. We show that high accuracy can be achieved with as few as 50 denoising steps. We also compare with DDRM and DPS, more complex diffusion methods of the kinds mentioned above. These methods are less accurate (as measured by MSE and SSIM) for our tomography problem, even after the generation hyperparameters are optimized. Finally we extend our method to reconstruction of arbitrary-sized images and show results on 128 $\times$ 1568 pixel images

翻译：逆问题通常需要正则化器或先验知识才能获得良好解。近期趋势是训练卷积网络进行图像去噪，并在求解逆问题时将该网络用作先验。已有多种方法依赖前向算子的奇异值分解，另有若干方法在运行时通过去噪网络进行反向传播。本文提出一种更简便的方法，将传统基于梯度的重建误差最小化与去噪相结合。由于每一步均添加噪声，迭代动力学类似于朗之万或扩散过程。添加噪声的强度与去噪步长均随时间呈指数衰减。我们将该方法应用于多倾角电子显微图像断层重建问题。通过模拟倾斜视图的实证研究，确定了使方法产生良好效果的参数设置。结果表明，仅需50步去噪即可实现高精度重建。我们还与DDRM及DPS（上述类型的更复杂扩散方法）进行了比较。针对本研究的断层重建问题，即使优化了生成超参数，这些方法的精度（以MSE和SSIM衡量）仍较低。最后，我们将方法扩展至任意尺寸图像重建，并展示了128×1568像素图像的重建结果。