Plug-and-Play Reconstruction for Accelerated Cardiac Perfusion Imaging via Denoising Diffusion Models (RF_FR_328)

Background: Plug-and-play (PnP) is a meta-algorithm designed to balance multiple priors by alternating between data consistency and a denoising steps, which can be integrated into various optimization solvers. Inspired by the Alternating Direction Method of Multipliers (ADMM), PnP replaces the proximal step using a recovered image prior with a Maximum a Posteriori (MAP) estimator, typically implemented via a trained denoiser. However, conventional denoisers are trained to reduce additive Gaussian noise in clean images, effectively approximating a MAP estimator using a Minimum Mean Square Error (MMSE) approach.

Denoising Diffusion Probabilistic Models (DDPMs) have recently emerged as powerful generative methods for sampling from conditional or unconditional posterior distributions, outperforming models like GANs in many scenarios. DDPMs employ a series of MMSE denoisers across different noise levels, similar to the PnP framework, but with greater flexibility in selecting noise levels. This flexibility allows for more accurate image reconstructions.

Our approach combines the PnP framework with the strengths of DDPM to leverage multiple denoiser levels, enhancing reconstruction quality for cardiac MRI, particularly in challenging cardiac perfusion imaging scenarios characterized by low SNR and respiratory motion artifacts. To address the typical long sampling times associated with DDPMs, we initiate sampling from a "warm start," such as parallel imaging reconstruction or zero-filling. This reduces the inference time by a factor of 20 while maintaining comparable reconstruction quality, enabling faster inline reconstruction.

Methods:

We trained a Denoising Diffusion Probabilistic Model (DDPM) on perfusion data from 134 patients who underwent clinically indicated CMR studies on a 3T Siemens Skyra scanner. Each dataset included 3–5 slices with a resolution of 2 × 2 × 8 mm³ and an acceleration rate of R = 2. Perfusion data were reconstructed using HICU, serving as the reference standard.

Five perfusion datasets were retrospectively undersampled at R = 4 using GRO sampling patterns (Figure 1). We compared reconstructions using the PnP-DDPM model with different settings: 1) total time step T=1000 with random noise initialization (DDPM 1000 RN), 2) T=50, with zero-filled initialization (DDPM 50 ZF), 3) T=50 with SENSE initialization (and DDPM 50 SENSE), and 4) SENSE reconstruction alone. The images were evaluated using normalized SNR (nSNR), peak SNR (pSNR), structural similarity index (SSIM), and graded on a 5-point scale by a cardiologist (1 = poor, 5 = excellent).

Results: Figure 2 presents images of three slices from a single subject reconstructed using different techniques. The average nSNR, pSNR, SSIM, and visual grading scores for each method are summarized in Figure 3. The reconstruction quality with the DDPM prior is superior to the traditional SENSE method. There is no statistically significant difference (p > 0.05) between the DDPM 1000 RN, DDPM 50 ZF, and DDPM 50 SENSE methods.

Conclusion:

The PnP framework combined with a DDPM-trained denoiser achieves high-quality cardiac perfusion image reconstruction, both visually and quantitatively. Using effective initialization methods, such as zero-filling or SENSE reconstruction, significantly accelerates the reconstruction process while maintaining comparable quality to the full inference starting from random noise.