We study the nonconvex optimization landscape for maximum likelihood estimation in the discrete orbit recovery model with Gaussian noise. This is a statistical model motivated by applications in molecular microscopy and image processing, where each measurement of an unknown object is subject to an independent random rotation from a known rotational group. Equivalently, it is a Gaussian mixture model where the mixture centers belong to a group orbit.

中文翻译：

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离散轨道恢复模型的似然景观和最大似然估计

我们研究了具有高斯噪声的离散轨道恢复模型中最大似然估计的非凸优化景观。这是一个受分子显微镜和图像处理应用推动的统计模型，其中未知物体的每次测量都受到来自已知旋转组的独立随机旋转的影响。等价地，它是一个高斯混合模型，其中混合中心属于一个群轨道。