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An $\ell^1$-Plug-and-Play Approach for MPI Using a Zero Shot Denoiser with Evaluation on the 3D Open MPI Dataset

Vladyslav Gapyak, Corinna Rentschler, Thomas März, Andreas Weinmann

TL;DR

The paper tackles ill-posed 3D MPI reconstruction by introducing a Plug-and-Play framework that uses a zero-shot denoiser alongside an $\ell^1$-prior within a Half Quadratic Splitting scheme. An adaptive parameter strategy ties the denoiser input to estimated noise levels, enabling automatic updates without MPI-specific training data. The authors validate their ZeroShot-$\ell^1$-PnP and ZeroShot-PnP methods on a hybrid dataset and evaluate on the 3D Open MPI dataset, showing competitive PSNR/SSIM and favorable runtimes compared to Tikhonov, ART, DIP, and PP-MPI. The work demonstrates that a zero-shot denoiser can generalize to MPI tasks, offering a scalable and cost-effective approach with potential for broader MPI applications.

Abstract

Objective: Magnetic particle imaging (MPI) is an emerging medical imaging modality which has gained increasing interest in recent years. Among the benefits of MPI are its high temporal resolution, and that the technique does not expose the specimen to any kind of ionizing radiation. It is based on the non-linear response of magnetic nanoparticles to an applied magnetic field. From the electric signal measured in receive coils, the particle concentration has to be reconstructed. Due to the ill-posedness of the reconstruction problem, various regularization methods have been proposed for reconstruction ranging from early stopping methods, via classical Tikhonov regularization and iterative methods to modern machine learning approaches. In this work, we contribute to the latter class: we propose a plug-and-play approach based on a generic zero-shot denoiser with an $\ell^1$-prior. Approach: We validate the reconstruction parameters of the method on a hybrid dataset and compare it with the baseline Tikhonov, DIP and the previous PP-MPI, which is a plug-and-play method with denoiser trained on MPI-friendly data. Main results: We offer a quantitative and qualitative evaluation of the zero-shot plug-and-play approach on the 3D Open MPI dataset. Moreover, we show the quality of the approach with different levels of preprocessing of the data. Significance: The proposed method employs a zero-shot denoiser which has not been trained for the MPI task and therefore saves the cost for training. Moreover, it offers a method that can be potentially applied in future MPI contexts.

An $\ell^1$-Plug-and-Play Approach for MPI Using a Zero Shot Denoiser with Evaluation on the 3D Open MPI Dataset

TL;DR

The paper tackles ill-posed 3D MPI reconstruction by introducing a Plug-and-Play framework that uses a zero-shot denoiser alongside an -prior within a Half Quadratic Splitting scheme. An adaptive parameter strategy ties the denoiser input to estimated noise levels, enabling automatic updates without MPI-specific training data. The authors validate their ZeroShot--PnP and ZeroShot-PnP methods on a hybrid dataset and evaluate on the 3D Open MPI dataset, showing competitive PSNR/SSIM and favorable runtimes compared to Tikhonov, ART, DIP, and PP-MPI. The work demonstrates that a zero-shot denoiser can generalize to MPI tasks, offering a scalable and cost-effective approach with potential for broader MPI applications.

Abstract

Objective: Magnetic particle imaging (MPI) is an emerging medical imaging modality which has gained increasing interest in recent years. Among the benefits of MPI are its high temporal resolution, and that the technique does not expose the specimen to any kind of ionizing radiation. It is based on the non-linear response of magnetic nanoparticles to an applied magnetic field. From the electric signal measured in receive coils, the particle concentration has to be reconstructed. Due to the ill-posedness of the reconstruction problem, various regularization methods have been proposed for reconstruction ranging from early stopping methods, via classical Tikhonov regularization and iterative methods to modern machine learning approaches. In this work, we contribute to the latter class: we propose a plug-and-play approach based on a generic zero-shot denoiser with an -prior. Approach: We validate the reconstruction parameters of the method on a hybrid dataset and compare it with the baseline Tikhonov, DIP and the previous PP-MPI, which is a plug-and-play method with denoiser trained on MPI-friendly data. Main results: We offer a quantitative and qualitative evaluation of the zero-shot plug-and-play approach on the 3D Open MPI dataset. Moreover, we show the quality of the approach with different levels of preprocessing of the data. Significance: The proposed method employs a zero-shot denoiser which has not been trained for the MPI task and therefore saves the cost for training. Moreover, it offers a method that can be potentially applied in future MPI contexts.
Paper Structure (45 sections, 19 equations, 61 figures, 7 tables, 1 algorithm)

This paper contains 45 sections, 19 equations, 61 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work.
  3. Contribution.
  4. Outline.
  5. Method
  6. The Reconstruction Problem in MPI Using a System Matrix
  7. The Preprocessing of the Data
  8. Bandpass Filtering and Frequency Selection.
  9. Background Correction.
  10. Whitening Estimation and Low Rank Approximation of the System Matrix.
  11. ZeroShot-PnP: The Proposed Plug-and-Play Approach with a Zero-Shot Denoiser.
  12. The Iterative Scheme.
  13. The Denoising Step.
  14. Parameter Selection Strategies
  15. Choice of $\lambda$ and of the $\mu_k$.
  16. ...and 30 more sections

Figures (61)

  • Figure 1: Plot of the PSNR and SSIM distributions on the hybrid validation dataset representing the distribution of PSNR (in green and blue) and SSIM (in ocher and violet) in the ZeroShot-$\ell^1$-PnP (resp. ZeroShot-PnP) and the comparison methods. On the x-axis we display the ranges of the PSNR values (in $[0,40]$) and SSIM values (in $[0,1]$). the distributions have been estimated using Kernel Densities Estimations using Gaussian kernels.
  • Figure 2: Reconstructions of the shape phantom. We display here the 10-th xz-slice.
  • Figure 3: Reconstructions of the resolution phantom. We display the 10-th xy-slice.
  • Figure 4: Reconstructions for the concentration phantom. We display the 13-th xy-slice. We observe that, even though the PSNR value of the DIP reconstruction is high (cf. Table \ref{['tab:exp1:measures']}), it is possible that parts of the phantom are missing.
  • Figure 5: Example of a profile cut for the shape phantom. We consider the 10-th xz-slice and the cut along the 9-th x pixel. We point out that the profiles obtained with the ZeroShot-PnP and the ZeroShot-$\ell^1$-PnP overlap almost perfectly.
  • ...and 56 more figures