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Deep Image Prior for Computed Tomography Reconstruction

Simon Arridge, Riccardo Barbano, Alexander Denker, Zeljko Kereta

TL;DR

The paper surveys the Deep Image Prior (DIP) framework for CT reconstruction, emphasizing its unsupervised, data-efficient nature that relies on a CNN’s architectural bias rather than large paired datasets. It reviews the vanilla DIP formulation and a broad set of extensions to mitigate overfitting and reduce computation, including explicit TV regularisation, learned denoisers (RED), self-guidance, warm-starts, subspace constraints, and stochastic optimization. The authors connect DIP behavior to theoretical analyses (Analytic Deep Prior and neural tangent kernel perspectives) and discuss under-/over-parametrised regimes, highlighting the spectral bias that governs reconstruction quality. They provide a comprehensive experimental comparison on real μCT walnut data, showing that regularised and denoising variants can outperform vanilla DIP and classical TV, with tradeoffs in speed and robustness. The work positions DIP as a data-efficient alternative for inverse CT and outlines future directions such as 3D extensions, diffusion-based priors, and deeper theoretical grounding of architectural priors.

Abstract

We present a comprehensive overview of the Deep Image Prior (DIP) framework and its applications to image reconstruction in computed tomography. Unlike conventional deep learning methods that rely on large, supervised datasets, the DIP exploits the implicit bias of convolutional neural networks and operates in a fully unsupervised setting, requiring only a single measurement, even in the presence of noise. We describe the standard DIP formulation, outline key algorithmic design choices, and review several strategies to mitigate overfitting, including early stopping, explicit regularisation, and self-guided methods that adapt the network input. In addition, we examine computational improvements such as warm-start and stochastic optimisation methods to reduce the reconstruction time. The discussed methods are tested on real $μ$CT measurements, which allows examination of trade-offs among the different modifications and extensions.

Deep Image Prior for Computed Tomography Reconstruction

TL;DR

The paper surveys the Deep Image Prior (DIP) framework for CT reconstruction, emphasizing its unsupervised, data-efficient nature that relies on a CNN’s architectural bias rather than large paired datasets. It reviews the vanilla DIP formulation and a broad set of extensions to mitigate overfitting and reduce computation, including explicit TV regularisation, learned denoisers (RED), self-guidance, warm-starts, subspace constraints, and stochastic optimization. The authors connect DIP behavior to theoretical analyses (Analytic Deep Prior and neural tangent kernel perspectives) and discuss under-/over-parametrised regimes, highlighting the spectral bias that governs reconstruction quality. They provide a comprehensive experimental comparison on real μCT walnut data, showing that regularised and denoising variants can outperform vanilla DIP and classical TV, with tradeoffs in speed and robustness. The work positions DIP as a data-efficient alternative for inverse CT and outlines future directions such as 3D extensions, diffusion-based priors, and deeper theoretical grounding of architectural priors.

Abstract

We present a comprehensive overview of the Deep Image Prior (DIP) framework and its applications to image reconstruction in computed tomography. Unlike conventional deep learning methods that rely on large, supervised datasets, the DIP exploits the implicit bias of convolutional neural networks and operates in a fully unsupervised setting, requiring only a single measurement, even in the presence of noise. We describe the standard DIP formulation, outline key algorithmic design choices, and review several strategies to mitigate overfitting, including early stopping, explicit regularisation, and self-guided methods that adapt the network input. In addition, we examine computational improvements such as warm-start and stochastic optimisation methods to reduce the reconstruction time. The discussed methods are tested on real CT measurements, which allows examination of trade-offs among the different modifications and extensions.
Paper Structure (21 sections, 2 theorems, 36 equations, 9 figures, 2 tables, 8 algorithms)

This paper contains 21 sections, 2 theorems, 36 equations, 9 figures, 2 tables, 8 algorithms.

Table of Contents

  1. Introduction
  2. General Framework
  3. Algorithmic Design Choices
  4. Theoretical Approaches
  5. Analytic Deep Prior
  6. Under-parametrised DIP
  7. Linearised Deep Image Prior
  8. Preventing Overfitting
  9. Early Stopping
  10. Total Variation Regularisation
  11. DIP with Learned Denoisers
  12. Self-Guidance Methods
  13. Computational Considerations
  14. Warm-starting the Optimisation
  15. Subspace DIP
  16. ...and 6 more sections

Key Result

Proposition 1

Consider the one layer deep decoder eq:one_layer_dd with arbitrary upsampling matrix $\mathbf{U}_0 \in {\mathbb R}^{n \times n_0}$ and input ${\mathbf{x}}^{(0)} \in {\mathbb R}^{n_0 \times k}$. Let $\eta \sim \mathcal{N}(0, \sigma^2 \mathbf{I}_n)$. Assume that $k^2 \log(n_0)/n \le 1/32$. Then with

Figures (9)

  • Figure 1: Vanilla DIP on the $\mu$CT walnut with $60$ angles and $128$ detector pixels. We show the DIP reconstruction at different iterations of the optimisation process. Details in Section \ref{['sec:numerical_experiments']}.
  • Figure 2: Vanilla DIP on the $\mu$CT walnut with $60$ angles and $128$ detector pixels. For details see the description in Section \ref{['sec:numerical_experiments']}.
  • Figure 3: The first four images in each row correspond to the first 4 eigenfunctions of ${\mathbf{J}} {\mathbf{J}}^T$. The last image is the initial output of the (untrained) DIP. In (a) the input to the DIP is random noise, in (b) it is the FBP reconstruction of the $\mu$CT walnut image.
  • Figure 4: $\mu$CT walnut reconstructions for the different DIP methods. Left: Best reconstruction. Middle: Early stopping reconstruction. Right: Final reconstruction.
  • Figure 5: Evolution of PSNR during optimisation for all considered DIP variants.
  • ...and 4 more figures

Theorems & Definitions (3)

  • Proposition 1
  • Theorem 1
  • proof