Learning Image-Adaptive Gabor Frames for Self-supervised Image Restoration

Learning image representations that adapt to local structures while retaining explicit reconstruction guarantees offers a principled foundation for image restoration. We propose GaborCanvas, a framework for learning image-adaptive Gabor frames. A neural network predicts the scales, orientations, and frequencies of Gabor atoms, aligning them with edges and textures so that relatively few significant coefficients can capture most image structures. We construct corresponding dual frames that ensure perfect reconstruction under suitable conditions. Together, structural adaptation and an explicit reconstruction formula provide an efficient and interpretable image representation that supports coefficient-based processing. We exploit the resulting coefficient sparsity through self-supervised formulations of three tasks: image denoising, inpainting, and super-resolution. The restoration models are trained without accessing truth images. GaborCanvas achieves competitive performance across all three tasks.