Refractive Index Tomography is an inverse problem in which we seek to
reconstruct a scene's 3D refractive field from 2D projected image measurements.
The refractive field is not visible itself, but instead affects how the path of
a light ray is continuously curved as it travels through space. Refractive
fields appear across a wide variety of scientific applications, from
translucent cell samples in microscopy to fields of dark matter bending light
from faraway galaxies. This problem poses a unique challenge because the
refractive field directly affects the path that light takes, making its
recovery a non-linear problem. In addition, in contrast with traditional
tomography, we seek to recover the refractive field using a projected image
from only a single viewpoint by leveraging knowledge of light sources scattered
throughout the medium. In this work, we introduce a method that uses a
coordinate-based neural network to model the underlying continuous refractive
field in a scene. We then use explicit modeling of rays' 3D spatial curvature
to optimize the parameters of this network, reconstructing refractive fields
with an analysis-by-synthesis approach. The efficacy of our approach is
demonstrated by recovering refractive fields in simulation, and analyzing how
recovery is affected by the light source distribution. We then test our method
on a simulated dark matter mapping problem, where we recover the refractive
field underlying a realistic simulated dark matter distribution.

逆问题中，我们试图从二维投影图像测量中重构场景的三维折射场，为此我们引入了一种使用基于坐标的神经网络对场景中的连续折射场进行建模的方法，并通过分析合成方法优化该网络的参数，以实现对折射场的重建。

基于神经场的单视角折射率层析成像

Single View Refractive Index Tomography with Neural Fields

Neural Radiance Field (NeRF) has gained considerable attention recently for
3D scene reconstruction and novel view synthesis due to its remarkable
synthesis quality. However, image blurriness caused by defocus or motion, which
often occurs when capturing scenes in the wild, significantly degrades its
reconstruction quality. To address this problem, We propose Deblur-NeRF, the
first method that can recover a sharp NeRF from blurry input. We adopt an
analysis-by-synthesis approach that reconstructs blurry views by simulating the
blurring process, thus making NeRF robust to blurry inputs. The core of this
simulation is a novel Deformable Sparse Kernel (DSK) module that models
spatially-varying blur kernels by deforming a canonical sparse kernel at each
spatial location. The ray origin of each kernel point is jointly optimized,
inspired by the physical blurring process. This module is parameterized as an
MLP that has the ability to be generalized to various blur types. Jointly
optimizing the NeRF and the DSK module allows us to restore a sharp NeRF. We
demonstrate that our method can be used on both camera motion blur and defocus
blur: the two most common types of blur in real scenes. Evaluation results on
both synthetic and real-world data show that our method outperforms several
baselines. The synthetic and real datasets along with the source code is
publicly available at this https URL

提出了 Deblur-NeRF 方法，采用分析合成方法重建模糊视图，通过 Deformable Sparse Kernel 模块对空间可变模糊核进行建模，共同优化 NeRF 和 DSK 模块，从而恢复锐利的 NeRF。