Manifold Modeling in Embedded Space: An Interpretable Alternative to Deep Image Prior.

Area of Science:

• Computer Vision
• Machine Learning
• Image Processing

Background:

• Deep Image Prior (DIP) leverages deep convolutional networks (ConvNets) as an image prior, demonstrating effectiveness in image restoration.
• The underlying mechanisms of DIP's success and the role of convolution in image reconstruction remain unclear.

Purpose of the Study:

• To provide an interpretable explanation for the effectiveness of ConvNets in Deep Image Prior (DIP).
• To propose a novel, interpretable image/tensor modeling method related to self-similarity.

Main Methods:

• Developed Manifold Modeling in Embedded Space (MMES), an interpretable approach.
• MMES decomposes convolution into "delay embedding" and "transformation" (encoder-decoder).
• Implemented MMES using a denoising autoencoder and a multiway delay-embedding transform.

Main Results:

• MMES achieves results comparable to DIP in image/tensor completion, super-resolution, deconvolution, and denoising.
• MMES demonstrates competitive performance against DIP in experimental evaluations.
• The proposed method offers insights into DIP as a "low-dimensional patch-manifold prior."

Conclusions:

• MMES provides a clear, interpretable framework for understanding ConvNet-based image priors.
• The study clarifies the role of convolution in image enhancement and reconstruction.
• MMES offers a viable and competitive alternative to DIP for various image restoration tasks.