It is well known that a band-limited signal can be reconstructed from its uniformly spaced samples if the sampling rate is sufficiently high. More recently, it has been proved that one can reconstruct a 1D band-limited signal even if the exact sample locations are unknown, but given just the distribution of the sample locations and their ordering in 1D. In this work, we extend the analytical bounds on the reconstruction error in such scenarios for quasi-bandlimited signals. We also prove that the method for such a reconstruction is resilient to a certain proportion of errors in the specification of the sample location ordering. We then express the problem of tomographic reconstruction of 2D images from 1D Radon projections under unknown angles with known angle distribution, as a special case for reconstruction of quasi-bandlimited signals from samples at unknown locations with known distribution. Building upon our theoretical background, we present asymptotic bounds for 2D quasi-bandlimited image reconstruction from 1D Radon projections in the unknown angles setting, which commonly occurs in cryo-electron microscopy (cryo-EM). To the best of our knowledge, this is the first piece of work to perform such an analysis for 2D cryo-EM, even though the associated reconstruction algorithms have been known for a long time.

本文研究了在采样速率足够高时如何通过均匀间隔的样本将带限信号进行重构；同时，研究证明只需要已知一维样本分布和排列顺序即可重构一维带限信号。在此基础上，通过两个理论研究案例分别考虑了二维样本在未知角度情况下的重构问题及其在冷冻电子显微学（cryo-EM）中的应用。

基于未知投影角度分布的二维图像层析重建分析