In this paper, we derive a novel optimal image transport algorithm over
sparse dictionaries by taking advantage of Sparse Representation (SR) and
Optimal Transport (OT). Concisely, we design a unified optimization framework
in which the individual image features (color, textures, styles, etc.) are
encoded using sparse representation compactly, and an optimal transport plan is
then inferred between two learned dictionaries in accordance with the encoding
process. This paradigm gives rise to a simple but effective way for
simultaneous image representation and transformation, which is also empirically
solvable because of the moderate size of sparse coding and optimal transport
sub-problems. We demonstrate its versatility and many benefits to different
image-to-image translation tasks, in particular image color transform and
artistic style transfer, and show the plausible results for photo-realistic
transferred effects.

本论文通过利用稀疏表示和最优传输，推导出一种新颖的针对稀疏字典的最优图像传输算法。通过将图像特征编码为稀疏表示并根据编码过程在两个学习字典之间推测最优传输计划，得到了一种简单而有效的同时图像表示和转换方法，可广泛应用于图像转换任务。

稀疏字典上的最优图像传输

Optimal Image Transport on Sparse Dictionaries

We consider the problem of learning sparsely used dictionaries with an
arbitrary square dictionary and a random, sparse coefficient matrix. We prove
that $O (n \log n)$ samples are sufficient to uniquely determine the
coefficient matrix. Based on this proof, we design a polynomial-time algorithm,
called Exact Recovery of Sparsely-Used Dictionaries (ER-SpUD), and prove that
it probably recovers the dictionary and coefficient matrix when the coefficient
matrix is sufficiently sparse. Simulation results show that ER-SpUD reveals the
true dictionary as well as the coefficients with probability higher than many
state-of-the-art algorithms.

本文介绍了一个多项式时间算法 ER-SpUD 来恢复使用稀疏矩阵的稀疏字典，证明了只需 O（nlog n）个样本即足以唯一确定系数矩阵，模拟结果表明 ER-SpUD 的恢复率优于当前众多算法