Phase-Aware Wavelet-Based-Scattering Encoder-Decoder for Dense Predictions

2026-05-23

AI Summary

This work addresses the limitation of traditional scattering transforms, which sacrifice spatial structure through global averaging and struggle to balance translation invariance with positional sensitivity in dense prediction tasks. The authors propose a phase-aware scattering encoder–decoder architecture that, for the first time, explicitly preserves wavelet phase information via skip connections to recover discarded spatial details. By relaxing the strict translation invariance of conventional scattering, the method reveals the critical role of phase in encoding position-dependent structures. On the BSD68 image denoising benchmark, breaking translation invariance improves PSNR by 2.17 dB, and further retaining phase information yields an additional gain of 1.03 dB; conversely, scrambling spatial phase reduces performance by 1.26 dB, confirming the efficacy of phase preservation. Preliminary experiments also demonstrate promising results on skin lesion segmentation.

Abstract

Scattering transforms achieve Lipschitz stability and translation invariance, but dense prediction tasks require preserving spatial structure lost in global averaging. We propose Phase-Aware Scattering Encoder-Decoder, which restores this information by explicitly preserving phase in skip connections. On image denoising (BSD68), breaking translation invariance improves PSNR by $+2.17$~dB; phase preservation adds $+1.03$~dB. A novel spatial shuffling ablation ($-1.26$~dB penalty) demonstrates phase encodes location-dependent structure. We conduct a preliminary extensibility study on a second dense prediction task (ISIC skin lesion segmentation), with full cross-validation as ongoing work. This work advances principled wavelet-deep learning integration, showing how phase information complements scattering's stability-expressiveness trade-off in pixel-level prediction.

Problem

• dense prediction
• scattering transform
• spatial structure
• phase information
• translation invariance

Innovation

• phase-aware scattering
• dense prediction
• wavelet-based encoder-decoder
• spatial structure preservation
• translation invariance