Abstract:
Deep image prior (DIP) uses a deep convolutional network (ConvNet) structure as an image prior. DIP empirically proves ConvNet structures work for image restoration. Why the DIP works well is unknown. Convolution’s benefit in image reconstruction and enhancement is unclear. This study proposes an interpretable approach that divides convolution into “delay embedding” and “transformation” (encoder–decoder). Our image/tensor modeling method is self-similar and simple. Manifold modeling in embedded space (MMES) uses a denoising autoencoder and a multiway delay-embedding transform. MMES can match DIP on image/tensor completion, super-resolution, deconvolution, and denoising despite its simplicity. In our experiments, MMES competes with DIP. These findings can help interpret DIP from a “low-dimensional patch-manifold prior.”
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