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Parameter-free structure-texture image decomposition by unrolling

Laura Girometti, Jean-François Aujol, Antoine Guennec, Yann Traonmilin

TL;DR

The paper tackles structure-texture image decomposition by learning to automate regularization through unrolling. It extends the Low Patch Rank model with a non-convex MCP penalty on gradients and a patch-based nuclear-norm texture prior, solved via an ADMM scheme and then reformulated into an unrolled neural network, LPR-NET, with K blocks and learnable per-block parameters. Key contributions include introducing MCP within LPR, deriving closed-form proximal updates, and exploring architectural variants, while demonstrating competitive performance against variational baselines and a lighter alternative to PnP_joint on synthetic and natural images. The work offers a parameter-free, data-driven approach that generalizes from synthetic training to real-world imagery and provides practical efficiency gains for structure-texture decomposition tasks.

Abstract

In this work, we propose a parameter-free and efficient method to tackle the structure-texture image decomposition problem. In particular, we present a neural network LPR-NET based on the unrolling of the Low Patch Rank model. On the one hand, this allows us to automatically learn parameters from data, and on the other hand to be computationally faster while obtaining qualitatively similar results compared to traditional iterative model-based methods. Moreover, despite being trained on synthetic images, numerical experiments show the ability of our network to generalize well when applied to natural images.

Parameter-free structure-texture image decomposition by unrolling

TL;DR

The paper tackles structure-texture image decomposition by learning to automate regularization through unrolling. It extends the Low Patch Rank model with a non-convex MCP penalty on gradients and a patch-based nuclear-norm texture prior, solved via an ADMM scheme and then reformulated into an unrolled neural network, LPR-NET, with K blocks and learnable per-block parameters. Key contributions include introducing MCP within LPR, deriving closed-form proximal updates, and exploring architectural variants, while demonstrating competitive performance against variational baselines and a lighter alternative to PnP_joint on synthetic and natural images. The work offers a parameter-free, data-driven approach that generalizes from synthetic training to real-world imagery and provides practical efficiency gains for structure-texture decomposition tasks.

Abstract

In this work, we propose a parameter-free and efficient method to tackle the structure-texture image decomposition problem. In particular, we present a neural network LPR-NET based on the unrolling of the Low Patch Rank model. On the one hand, this allows us to automatically learn parameters from data, and on the other hand to be computationally faster while obtaining qualitatively similar results compared to traditional iterative model-based methods. Moreover, despite being trained on synthetic images, numerical experiments show the ability of our network to generalize well when applied to natural images.

Paper Structure

This paper contains 7 sections, 1 theorem, 16 equations, 6 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Proposed structure-texture decomposition model
  3. Low Patch Rank model for structure-texture decomposition
  4. ADMM-based algorithm for LPR
  5. LPR-NET architecture
  6. Numerical Experiments
  7. Conclusion

Key Result

proposition thmcounterproposition

Given $v \in \mathbb{R}^2$, $a \geq 0$, $\mu, \rho_t > 0$, the function $\frac{\mu}{\rho_t}\phi(\cdot;a) + \frac{1}{2}||t_i - v||^2$ is strongly convex if $a \leq \frac{\rho_t}{\mu}$. Morever, it has a unique global minimizer that has the following closed-form expression:

Figures (6)

  • Figure 1: Graphical action of the patch operator $\mathcal{P}$.
  • Figure 2: Flow of the $k$-th block of the network. Each operation performed in a block corresponds to a step of the ADMM algorithm described in \ref{['t_subpb']}-\ref{['eq:y_subpb']}.
  • Figure 3: Unrolling of the Projected Gradient Descent algorithm.
  • Figure 4: Decomposition results of a synthetic image obtained with our LPR-NET with $(\mathrm{K}, n)=(20,5)$ and with the joint structure-texture model proposed in PnP_joint(PSNR($u_{\mathrm{LPR-NET}},u^{GT}$) = 41.93, PSNR($u_{R_{x}(u,v)},u^{GT}$) = 40.53, PSNR($v_{\mathrm{LPR-NET}},v^{GT}$) = 41.80, PSNR($v_{R_{x}(u,v)},v^{GT}$) = 40.25).
  • Figure 5: Decomposition results on natural images obtained with our LPR-NET with $(\mathrm{K},n)= (20,5)$ (left) and with the model proposed in PnP_joint (right).
  • ...and 1 more figures

Theorems & Definitions (1)

  • proposition thmcounterproposition