Manifold Modeling in Embedded Space: A Perspective for Interpreting "Deep Image Prior"

Tatsuya Yokota, Hidekata Hontani, Qibin Zhao, Andrzej Cichocki

Keywords: Deep image prior, Manifold model, Auto-encoder, Convolutional neural network, Delay-embedding, Hankelization, Tensor completion, Image inpainting, Supperresolution

TL;DR: We propose a new auto-encoder incorporated with multiway delay-embedding transform toward interpreting deep image prior.

Abstract: Deep image prior (DIP), which utilizes a deep convolutional network (ConvNet) structure itself as an image prior, has attracted huge attentions in computer vision community. It empirically shows the effectiveness of ConvNet structure for various image restoration applications. However, why the DIP works so well is still unknown, and why convolution operation is essential for image reconstruction or enhancement is not very clear. In this study, we tackle these questions. The proposed approach is dividing the convolution into ``delay-embedding'' and ``transformation (\ie encoder-decoder)'', and proposing a simple, but essential, image/tensor modeling method which is closely related to dynamical systems and self-similarity. The proposed method named as manifold modeling in embedded space (MMES) is implemented by using a novel denoising-auto-encoder in combination with multi-way delay-embedding transform. In spite of its simplicity, the image/tensor completion and super-resolution results of MMES are quite similar even competitive to DIP in our extensive experiments, and these results would help us for reinterpreting/characterizing the DIP from a perspective of ``low-dimensional patch-manifold prior''.