Coordinate networks like Multiplicative Filter Networks (MFNs) and BACON
offer some control over the frequency spectrum used to represent continuous
signals such as images or 3D volumes. Yet, they are not readily applicable to
problems for which coarse-to-fine estimation is required, including various
inverse problems in which coarse-to-fine optimization plays a key role in
avoiding poor local minima. We introduce a new coordinate network architecture
and training scheme that enables coarse-to-fine optimization with fine-grained
control over the frequency support of learned reconstructions. This is achieved
with two key innovations. First, we incorporate skip connections so that
structure at one scale is preserved when fitting finer-scale structure. Second,
we propose a novel initialization scheme to provide control over the model
frequency spectrum at each stage of optimization. We demonstrate how these
modifications enable multiscale optimization for coarse-to-fine fitting to
natural images. We then evaluate our model on synthetically generated datasets
for the the problem of single-particle cryo-EM reconstruction. We learn high
resolution multiscale structures, on par with the state-of-the art.

通过引入跳连接和新的初始化方案，我们提出了一种新的坐标网络架构和训练方案，实现了对学习重建的频率支持的细粒度控制，并在多尺度优化的背景下解决了粗到中等估计的问题，该方法在单粒子冷冻电镜重建的实验中，取得了与最先进技术相媲美的高分辨率多尺度结构。