Bandeira Afonso S, Zürich Eth, Chen Yutong, Lederman Roy R, Singer Amit
Department of Mathematics.
Ramistrasse 101, 8092 Zürich, Switzerland.
Inverse Probl. 2020 Jun;36(6). doi: 10.1088/1361-6420/ab7d2c. Epub 2020 Apr 29.
Let be a compact group and let . We define the (NUG) problem as finding to minimize . We introduce a convex relaxation of the NUG problem to a (SDP) by taking the Fourier transform of over . The NUG framework can be seen as a generalization of the problem over the orthogonal group and the problem and includes many practically relevant problems, such as the to registering bandlimited functions over the unit sphere in -dimensions and orientation estimation of noisy cryo-Electron Microscopy (cryo-EM) projection images. We implement a SDP solver for the NUG cryo-EM problem using the alternating direction method of multipliers (ADMM). Numerical study with synthetic datasets indicate that while our ADMM solver is slower than existing methods, it can estimate the rotations more accurately, especially at low (SNR).
设 是一个紧致群，且设 。我们将（NUG）问题定义为找到 以使 最小化。通过在 上对 取傅里叶变换，我们将 NUG 问题松弛为一个凸的半定规划（SDP）问题。NUG 框架可视为正交群上的 问题和 问题的推广，并且包含许多实际相关的问题，例如在 维单位球面上配准带限函数以及对噪声冷冻电子显微镜（cryo - EM）投影图像进行方向估计。我们使用乘子交替方向法（ADMM）为 NUG cryo - EM 问题实现了一个 SDP 求解器。对合成数据集的数值研究表明，虽然我们的 ADMM 求解器比现有方法慢，但它能更准确地估计旋转，尤其是在低信噪比（SNR）情况下。
