Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networks (1810.03982v2)

Abstract: Deep neural networks, in particular convolutional neural networks, have become highly effective tools for compressing images and solving inverse problems including denoising, inpainting, and reconstruction from few and noisy measurements. This success can be attributed in part to their ability to represent and generate natural images well. Contrary to classical tools such as wavelets, image-generating deep neural networks have a large number of parameters---typically a multiple of their output dimension---and need to be trained on large datasets. In this paper, we propose an untrained simple image model, called the deep decoder, which is a deep neural network that can generate natural images from very few weight parameters. The deep decoder has a simple architecture with no convolutions and fewer weight parameters than the output dimensionality. This underparameterization enables the deep decoder to compress images into a concise set of network weights, which we show is on par with wavelet-based thresholding. Further, underparameterization provides a barrier to overfitting, allowing the deep decoder to have state-of-the-art performance for denoising. The deep decoder is simple in the sense that each layer has an identical structure that consists of only one upsampling unit, pixel-wise linear combination of channels, ReLU activation, and channelwise normalization. This simplicity makes the network amenable to theoretical analysis, and it sheds light on the aspects of neural networks that enable them to form effective signal representations.

• The paper demonstrates that Deep Decoder, an untrained non-convolutional network, achieves competitive image compression and denoising using an underparameterized design.
• The architecture employs pixel-wise linear operations, upsampling, ReLU activations, and normalization to construct concise image representations without overfitting noise.
• Empirical results show that Deep Decoder rivals traditional methods like wavelet thresholding and BM3D, paving the way for efficient untrained models in imaging tasks.

An Evaluation of the Deep Decoder: Concise Image Representations from Untrained Non-Convolutional Networks

The paper by Reinhard Heckel and Paul Hand, titled "Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networks," presents an innovative approach to image modeling and solving inverse problems using a novel architecture characterized by its simplicity and effectiveness without the need for training. This research contributes to the ongoing exploration of deep neural network applications, particularly in the fields of image compression and restoration.

Summary of Key Contributions

The paper introduces the deep decoder, an untrained image model built from a deep neural network architecture devoid of convolutions. This model requires fewer parameters than the conventional convolutional neural networks (CNNs), with the number of parameters being less than the output dimensionality. This underparameterized approach prevents overfitting, which is a significant advantage in tasks like denoising where training data might not be available or appropriate for all test scenarios.

The deep decoder is structurally simple, consisting of layers that include upsampling, pixel-wise linear operations on channels, ReLU activation functions, and channel-wise normalization. Such a structure not only facilitates theoretical analysis but also underscores the effectiveness of neural networks in forming robust signal representations without convolutional layers or extensive training data.

Numerical Results and Claims

The paper asserts that the deep decoder achieves image compression performance on par with wavelet-based methods like thresholding, which are widely used in formats such as JPEG-2000. Further, it shows competitive denoising performance compared to untrained approaches like BM3D and even trained networks specifically designed for denoising tasks. Notably, the deep decoder achieves these results while operating without training, highlighting its practicality across diverse image processing applications.

Theoretical Insights

A theoretical analysis underpins the empirical findings, explaining why the deep decoder constructs effective representations and avoids overfitting noise. The underparameterization acts as a natural barrier against fitting noise by limiting the number of parameters used, which is directly related to the network’s representation power. The paper also engages in a discussion about the significance of non-convolutional upsampling operations and the robustness of its parameterization.

Implications and Future Directions

Practically, the deep decoder's approach proposes an adaptable image processing tool requiring no pre-training, making it suitable for applications where traditional methods may fail, especially in environments where computational resources for training are limited. Theoretically, this model opens pathways for further exploration into the capabilities of non-convolutional architectures, especially in understanding the minimum structural complexity required for effective image representation.

In the broader context of AI developments, deep decoder models suggest a shift in designing flexible architectures that excel in naturally structuring data, even in the absence of large, representative datasets. Future research could extend this work by exploring deep decoder models in varied domains, such as video processing or three-dimensional data, and by improving theoretical understanding of its underlying mechanisms, potentially enriching the landscape of deep learning methodologies.

This work, framed as a challenge to conventional narrator norms in neural networks, underscores a foundational shift towards appreciating structure and parameter efficiency in designing future AI systems. Such advancements in untrained approaches may redefine strategies across numerous image reconstruction and generation tasks.