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


The use of a deep convolutional network (ConvNet) structure as an image prior has garnered a lot of attention in the fields of computer vision and Machine Learning. The deep image prior (DIP) technique is responsible for this. Empirical evidence demonstrates that ConvNet structures are effective for a variety of image restoration applications, and DIP provides this evidence. However, it is still not clear what causes the DIP to be so successful. Additionally, it is not entirely clear why the convolution operation is helpful in image reconstruction or image enhancement. This is another area where there is a lack of clarity. This ambiguity of ConvNet/DIP is addressed in this study by the proposal of an approach that can be interpreted, and it does so by separating the convolution into "delay embedding" and "transformation" (i.e., encoder–decoder). Our approach is a straightforward yet fundamental method for modeling images and tensors that is closely connected to the concept of self-similarity. Since it is implemented using a denoising autoencoder in combination with a multiway delay-embedding transform, the method that was proposed was given the name manifold modeling in embedded space (MMES). MMES, despite its simplicity, is capable of achieving results that are quite comparable to those obtained by DIP when it comes to image/tensor completion, super-resolution, deconvolution, and denoising. In addition, the results of our research have demonstrated that MMES is capable of competing favorably with DIP. The interpretation and characterization of DIP can also be made easier by these results when viewed from the perspective of a "low-dimensional patch-manifold prior."

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