Hyperspectral cameras face challenging spatial-spectral resolution trade-offs
and are more affected by shot noise than RGB photos taken over the same total
exposure time. Here, we present a colorization algorithm to reconstruct
hyperspectral images from a grayscale guide image and spatially sparse spectral
clues. We demonstrate that our algorithm generalizes to varying spectral
dimensions for hyperspectral images, and show that colorizing in a low-rank
space reduces compute time and the impact of shot noise. To enhance robustness,
we incorporate guided sampling, edge-aware filtering, and dimensionality
estimation techniques. Our method surpasses previous algorithms in various
performance metrics, including SSIM, PSNR, GFC, and EMD, which we analyze as
metrics for characterizing hyperspectral image quality. Collectively, these
findings provide a promising avenue for overcoming the time-space-wavelength
resolution trade-off by reconstructing a dense hyperspectral image from samples
obtained by whisk or push broom scanners, as well as hybrid spatial-spectral
computational imaging systems.

从灰度引导图像和空间稀疏光谱线索中重构高光谱图像的上色算法，在低秩空间中上色可以减少计算时间和快门噪声的影响，以提高鲁棒性，并超过以往算法在多种性能指标方面，包括 SSIM、PSNR、GFC 和 EMD，这些结果为克服时间 - 空间 - 波长分辨率权衡提供了一种有希望的途径。

超级彩色化：传播稀疏空间噪声光谱线索，重建高光谱图像

HyperColorization: Propagating spatially sparse noisy spectral clues for  reconstructing hyperspectral images

A simple prior free factorization algorithm \cite{dai2014simple} is quite
often cited work in the field of Non-Rigid Structure from Motion (NRSfM). The
benefit of this work lies in its simplicity of implementation, strong
theoretical justification to the motion and structure estimation, and its
invincible originality. Despite this, the prevailing view is, that it performs
exceedingly inferior to other methods on several benchmark datasets
\cite{jensen2018benchmark,akhter2009nonrigid}. However, our subtle
investigation provides some empirical statistics which made us think against
such views. The statistical results we obtained supersedes Dai {\it{et
al.}}\cite{dai2014simple} originally reported results on the benchmark datasets
by a significant margin under some elementary changes in their core algorithmic
idea \cite{dai2014simple}. Now, these results not only exposes some unrevealed
areas for research in NRSfM but also give rise to new mathematical challenges
for NRSfM researchers. We argue that by \textbf{properly} utilizing the
well-established assumptions about a non-rigidly deforming shape i.e, it
deforms smoothly over frames \cite{rabaud2008re} and it spans a low-rank space,
the simple prior-free idea can provide results which is comparable to the best
available algorithms. In this paper, we explore some of the hidden intricacies
missed by Dai {\it{et. al.}} work \cite{dai2014simple} and how some elementary
measures and modifications can enhance its performance, as high as approx. 18\%
on the benchmark dataset. The improved performance is justified and empirically
verified by extensive experiments on several datasets. We believe our work has
both practical and theoretical importance for the development of better NRSfM
algorithms.

通过充分利用非刚性形状针对平稳变形和跨越低秩空间的假设，这篇研究论文摆脱了简单先验算法的约束，对其核心算法进行了一些基本改进措施，从而实现了比先前最优算法还高约 18% 的性能提升，并在多个数据集上进行了验证。