Enhancing Low-resolution Image Representation Through Normalizing Flows

TL;DR

LR2Flow tackles the challenge of learning low-resolution image representations that enable accurate high-resolution reconstruction by fusing wavelet tight-frame analysis with invertible neural mappings. The method defines downscaling and upscaling through a nonlinear, invertible transform applied to wavelet coefficients, and models remaining high-frequency content with a latent prior for sampling. The authors provide a reconstruction-error analysis showing benefits of nonlinear, data-adaptive transforms and redundancy over orthonormal bases, and validate the approach across image rescaling, compression, and denoising, achieving state-of-the-art or strong performance with good stability and scalability. The work advances practical LR representations with theoretical guarantees and demonstrates broad applicability to real-world image processing tasks.

Abstract

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.

Figures (5)

• Figure 1: Qualitative comparison of $\times 4$ image rescaling results. Representative examples are selected from the Set14, BSD100, and Urban100 datasets.
• Figure 2: Qualitative comparison of compression results on the DIV2K validation set with a rescaling factor $s=2$ and JPEG QF=30.
• Figure 3: Quantitative comparison of compression performance with $\times 2$ rescaling across various JPEG QFs on the Set5, Set14, BSD100, and Urban100 benchmarks.
• Figure 4: Quantitative evaluation of the R-D trade-off. We report the curves of bpp versus PSNR, SSIM, and LPIPS for the compared compression methods.
• Figure 5: Qualitative comparison of denoising results on the CBSD68 benchmark at noise level $\sigma_{{\mathbf{n}}}=50$.

Theorems & Definitions (16)

• Proposition 1
• Proposition 2
• Remark 1
• Proposition 3
• proof : Proof of Proposition \ref{['prop:single_affine_coupling_case']}
• proof : Proof of Proposition \ref{['prop:case2_reconstruction_error']}
• proof : Proof of \ref{['eqn:bound']}
• Lemma 1
• proof : Proof of Lemma \ref{['lemma:general_inn_reconstruction']}
• proof : Proof of Proposition \ref{['prop:iresnet_optiom_reconstruction_error']}