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LIP-CAR: contrast agent reduction by a deep learned inverse problem

Davide Bianchi, Sonia Colombo Serra, Davide Evangelista, Pengpeng Luo, Elena Morotti, Giovanni Valbusa

TL;DR

This work reframes contrast-agent reduction as a learned inverse problem (LIP-CAR) by first training a neural network to map high-dose to low-dose images, forming a forward operator $oldsymbol{ extPsi}_{ extnormal{H2L}}$, and then solving a regularized inverse problem to recover high-dose-like images from noisy low-dose data. By integrating classic regularization (TV and GenTV) with a learned forward model, the method achieves improved robustness and stability compared to end-to-end approaches, with theoretical convergence and practical validation on a pre-clinical MRI dataset. Key findings show that LIP-CAR can match or surpass end-to-end performance while offering greater resilience to out-of-domain noise, particularly when pre-dose information is used and GenTV priors are employed. The approach provides a principled, explainable framework for CAR that blends deep learning with variational optimization, with potential to enhance safety, reliability, and efficiency in imaging workflows.

Abstract

The adoption of contrast agents in medical imaging protocols is crucial for accurate and timely diagnosis. While highly effective and characterized by an excellent safety profile, the use of contrast agents has its limitation, including rare risk of allergic reactions, potential environmental impact and economic burdens on patients and healthcare systems. In this work, we address the contrast agent reduction (CAR) problem, which involves reducing the administered dosage of contrast agent while preserving the visual enhancement. The current literature on the CAR task is based on deep learning techniques within a fully image processing framework. These techniques digitally simulate high-dose images from images acquired with a low dose of contrast agent. We investigate the feasibility of a ``learned inverse problem'' (LIP) approach, as opposed to the end-to-end paradigm in the state-of-the-art literature. Specifically, we learn the image-to-image operator that maps high-dose images to their corresponding low-dose counterparts, and we frame the CAR task as an inverse problem. We then solve this problem through a regularized optimization reformulation. Regularization methods are well-established mathematical techniques that offer robustness and explainability. Our approach combines these rigorous techniques with cutting-edge deep learning tools. Numerical experiments performed on pre-clinical medical images confirm the effectiveness of this strategy, showing improved stability and accuracy in the simulated high-dose images.

LIP-CAR: contrast agent reduction by a deep learned inverse problem

TL;DR

This work reframes contrast-agent reduction as a learned inverse problem (LIP-CAR) by first training a neural network to map high-dose to low-dose images, forming a forward operator , and then solving a regularized inverse problem to recover high-dose-like images from noisy low-dose data. By integrating classic regularization (TV and GenTV) with a learned forward model, the method achieves improved robustness and stability compared to end-to-end approaches, with theoretical convergence and practical validation on a pre-clinical MRI dataset. Key findings show that LIP-CAR can match or surpass end-to-end performance while offering greater resilience to out-of-domain noise, particularly when pre-dose information is used and GenTV priors are employed. The approach provides a principled, explainable framework for CAR that blends deep learning with variational optimization, with potential to enhance safety, reliability, and efficiency in imaging workflows.

Abstract

The adoption of contrast agents in medical imaging protocols is crucial for accurate and timely diagnosis. While highly effective and characterized by an excellent safety profile, the use of contrast agents has its limitation, including rare risk of allergic reactions, potential environmental impact and economic burdens on patients and healthcare systems. In this work, we address the contrast agent reduction (CAR) problem, which involves reducing the administered dosage of contrast agent while preserving the visual enhancement. The current literature on the CAR task is based on deep learning techniques within a fully image processing framework. These techniques digitally simulate high-dose images from images acquired with a low dose of contrast agent. We investigate the feasibility of a ``learned inverse problem'' (LIP) approach, as opposed to the end-to-end paradigm in the state-of-the-art literature. Specifically, we learn the image-to-image operator that maps high-dose images to their corresponding low-dose counterparts, and we frame the CAR task as an inverse problem. We then solve this problem through a regularized optimization reformulation. Regularization methods are well-established mathematical techniques that offer robustness and explainability. Our approach combines these rigorous techniques with cutting-edge deep learning tools. Numerical experiments performed on pre-clinical medical images confirm the effectiveness of this strategy, showing improved stability and accuracy in the simulated high-dose images.
Paper Structure (18 sections, 3 theorems, 29 equations, 8 figures, 3 tables)

This paper contains 18 sections, 3 theorems, 29 equations, 8 figures, 3 tables.

Table of Contents

  1. Introduction
  2. State of the art
  3. The proposed method
  4. NN operators for learning an inverse problem
  5. The regularized LIP-CAR model
  6. Convergence analysis of LIP-CAR
  7. Robustness and stability of LIP-CAR
  8. Experimental setup
  9. Data set
  10. Approaches and notations
  11. Metrics for quality assessment
  12. Network architecture and training
  13. Specifications about the regularized model
  14. Numerical experiments
  15. Ablation study of image-to-image approaches
  16. ...and 3 more sections

Key Result

Lemma 2

For every $k\in \mathbb{N}$ there exists an $\mathcal{R}$-minimizing solution ${\boldsymbol{x}}_k^\dagger$, and the sets $\underset{{\boldsymbol{x}} \in \mathcal{X}}{\operatorname{argmin}}\{\Gamma_{k,i}({\boldsymbol{x}})\}$ and $\underset{{\boldsymbol{x}} \in \mathcal{X}}{\operatorname{argmin}}\{\Ga

Figures (8)

  • Figure 1: MRI images of a human brainvassantachart2023segmentation, acquired without CA (on the left) and with a high dosage of CA (on the right).
  • Figure 2: Visual representation of the paradigm change for the CAR task: from an end-to-end NN-based approach to a Learned Inverse Problem framework.
  • Figure 3: Values of relative errors computed on each image of the test set (left) and train set (right), in case of in-domain input images and in case of out-of-domain noisy input images.
  • Figure 4: Results on test images number 39, 141 and 226, achieved from the low-dose ${\boldsymbol{x}}_L$ images (first column) having the high-dose ${\boldsymbol{x}}_H$ images (second column) as references: the NN-L2H framework based on the end-to-end $\Phi_{L2H}$ operator (third column), the LIP-H2L-TV proposed method based on the forward $\Phi_{PH2L}$ operator and the TV prior \ref{['eq:TV']} (last column).
  • Figure 5: Results on test images number 39, 141 and 226, achieved when the pre-dose ${\boldsymbol{x}}_P$ images (first column) are available: the NN-PL2H framework based on the end-to-end $\Phi_{PL2H}$ operator (second column), the LIP-PH2L-TV proposed method based on the forward $\Phi_{PH2L}$ operator and the TV prior \ref{['eq:TV']} (third column), and the LIP-PH2L-GenTV proposed method based on the $\Phi_{PH2L}$ operator and the GenTV prior \ref{['eq:GenTV']} (last column).
  • ...and 3 more figures

Theorems & Definitions (8)

  • Definition 1: Solutions
  • Lemma 2: Well-posedness
  • proof
  • Theorem 3: Stability
  • proof
  • Theorem 4: Convergence
  • proof
  • Remark 5