It is essential but challenging to share medical image datasets due to
privacy issues, which prohibit building foundation models and knowledge
transfer. In this paper, we propose a novel dataset distillation method to
condense the original medical image datasets into a synthetic one that
preserves useful information for building an analysis model without accessing
the original datasets. Existing methods tackle only natural images by randomly
matching parts of the training trajectories of the model parameters trained by
the whole real datasets. However, through extensive experiments on medical
image datasets, the training process is extremely unstable and achieves
inferior distillation results. To solve these barriers, we propose to design a
novel progressive trajectory matching strategy to improve the training
stability for medical image dataset distillation. Additionally, it is observed
that improved stability prevents the synthetic dataset diversity and final
performance improvements. Therefore, we propose a dynamic overlap mitigation
module that improves the synthetic dataset diversity by dynamically eliminating
the overlap across different images and retraining parts of the synthetic
images for better convergence. Finally, we propose a new medical image dataset
distillation benchmark of various modalities and configurations to promote fair
evaluations. It is validated that our proposed method achieves 8.33%
improvement over previous state-of-the-art methods on average, and 11.7%
improvement when ipc=2 (i.e., image per class is 2). Codes and benchmarks will
be released.

我们提出了一种新的医学图像数据集精华方法，通过设计新的渐进轨迹匹配策略提高了医学图像数据集精华的训练稳定性，并通过动态消除不同图像之间的重叠来改善合成数据集的多样性和最终性能，进而在各种模态和配置上建立了一个新的医学图像数据集精华基准，实验证明我们提出的方法相比之前的最先进方法平均提高了 8.33%，当 ipc=2 时，提高了 11.7%。

医疗数据集提炼的渐进式轨迹匹配

Progressive trajectory matching for medical dataset distillation

Exploiting a priori known structural information lies at the core of many
image reconstruction methods that can be stated as inverse problems. The
synthesis model, which assumes that images can be decomposed into a linear
combination of very few atoms of some dictionary, is now a well established
tool for the design of image reconstruction algorithms. An interesting
alternative is the analysis model, where the signal is multiplied by an
analysis operator and the outcome is assumed to be the sparse. This approach
has only recently gained increasing interest. The quality of reconstruction
methods based on an analysis model severely depends on the right choice of the
suitable operator.
In this work, we present an algorithm for learning an analysis operator from
training images. Our method is based on an $\ell_p$-norm minimization on the
set of full rank matrices with normalized columns. We carefully introduce the
employed conjugate gradient method on manifolds, and explain the underlying
geometry of the constraints. Moreover, we compare our approach to
state-of-the-art methods for image denoising, inpainting, and single image
super-resolution. Our numerical results show competitive performance of our
general approach in all presented applications compared to the specialized
state-of-the-art techniques.

本文介绍了从训练图像中学习分析算子的算法，并将其应用于图像去噪、修补和超分辨率的领域，相对于专业技术上的最新方法具有竞争性的综合性能。

分析算子学习及其在图像重建中的应用

Analysis Operator Learning and Its Application to Image Reconstruction

After a decade of extensive study of the sparse representation synthesis
model, we can safely say that this is a mature and stable field, with clear
theoretical foundations, and appealing applications. Alongside this approach,
there is an analysis counterpart model, which, despite its similarity to the
synthesis alternative, is markedly different. Surprisingly, the analysis model
did not get a similar attention, and its understanding today is shallow and
partial. In this paper we take a closer look at the analysis approach, better
define it as a generative model for signals, and contrast it with the synthesis
one. This work proposes effective pursuit methods that aim to solve inverse
problems regularized with the analysis-model prior, accompanied by a
preliminary theoretical study of their performance. We demonstrate the
effectiveness of the analysis model in several experiments.

本文研究信号的分析模型作为一种生成模型并与综合模型进行对比，提出了有效的寻求方法以解决逆问题并在多个实验中证明了分析模型的有效性。