A method to infer and synthetically extrapolate roughness fields from
electron microscope scans of additively manufactured surfaces using an
adaptation of Rogallo's synthetic turbulence method [R. S. Rogallo, NASA
Technical Memorandum 81315, 1981] based on Fourier modes is presented. The
resulting synthetic roughness fields are smooth and are compatible with grid
generators in computational fluid dynamics or other numerical simulations.
Unlike machine learning methods, which can require over twenty scans of surface
roughness for training, the Fourier mode based method can extrapolate
homogeneous synthetic roughness fields using a single physical roughness scan
to any desired size and range. Five types of synthetic roughness fields are
generated using an electron microscope roughness image from literature. A
comparison of their spectral energy and two-point correlation spectra show that
the synthetic fields closely approximate the roughness structures and spectral
energy of the scan.

采用傅里叶模式的方法从电子显微镜扫描的添加制造表面中推断和合成粗糙度场，使得合成的粗糙度场光滑并且与计算流体动力学中的网格生成器或其他数值模拟相兼容。与机器学习方法不同，傅里叶模式的方法只需要一次物理粗糙度扫描即可将均匀的合成粗糙度场外推到任意所需大小和范围。从文献中使用电子显微镜粗糙度图像生成了五种类型的合成粗糙度场，它们的频谱能量和双点相关谱的比较表明合成场与扫描的粗糙度结构和频谱能量非常接近。

从图像中合成增材制造粗糙度表面的模态生成

A Synthetic Modal Generation of Additive Manufacturing Roughness  Surfaces from Images

Various alignment problems arising in cryo-electron microscopy, community
detection, time synchronization, computer vision, and other fields fall into a
common framework of synchronization problems over compact groups such as Z/L,
U(1), or SO(3). The goal of such problems is to estimate an unknown vector of
group elements given noisy relative observations. We present an efficient
iterative algorithm to solve a large class of these problems, allowing for any
compact group, with measurements on multiple 'frequency channels' (Fourier
modes, or more generally, irreducible representations of the group). Our
algorithm is a highly efficient iterative method following the blueprint of
approximate message passing (AMP), which has recently arisen as a central
technique for inference problems such as structured low-rank estimation and
compressed sensing. We augment the standard ideas of AMP with ideas from
representation theory so that the algorithm can work with distributions over
compact groups. Using standard but non-rigorous methods from statistical
physics we analyze the behavior of our algorithm on a Gaussian noise model,
identifying phases where the problem is easy, (computationally) hard, and
(statistically) impossible. In particular, such evidence predicts that our
algorithm is information-theoretically optimal in many cases, and that the
remaining cases show evidence of statistical-to-computational gaps.

通过采用来自表示理论的思想并结合于统计物理中标准但非严谨的方法，我们提出了一种高效的迭代算法，用于解决利用多个 “频道”（傅里叶模式或更一般的群表示）对紧致群上的同步问题进行测量的大类问题。