Low-resolution image representation is a special form of sparse representation that retains only low-frequency information while discarding high-frequency components. This property reduces storage and transmission costs and benefits various image processing tasks. However, a key challenge is to preserve essential visual content while maintaining the ability to accurately reconstruct the original images. This work proposes LR2Flow, a nonlinear framework that learns low-resolution image representations by integrating wavelet tight frame blocks with normalizing flows. We conduct a reconstruction error analysis of the proposed network, which demonstrates the necessity of designing invertible neural networks in the wavelet tight frame domain. Experimental results on various tasks, including image rescaling, compression, and denoising, demonstrate the effectiveness of the learned representations and the robustness of the proposed framework.

翻译：低分辨率图像表示是一种特殊的稀疏表示形式，仅保留低频信息而舍弃高频分量。这一特性降低了存储与传输成本，并有益于多种图像处理任务。然而，其核心挑战在于如何在保持准确重建原始图像能力的同时，保留必要的视觉内容。本研究提出LR2Flow，一种通过将小波紧框架块与归一化流相结合来学习低分辨率图像表示的非线性框架。我们对所提网络进行了重建误差分析，论证了在小波紧框架域中设计可逆神经网络的必要性。在图像重缩放、压缩与去噪等多种任务上的实验结果表明，所学表示具有有效性且所提框架具备鲁棒性。