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Likelihood-Separable Diffusion Inference for Multi-Image MRI Super-Resolution

Samuel W. Remedios, Zhangxing Bian, Shuwen Wei, Aaron Carass, Jerry L. Prince, Blake E. Dewey

TL;DR

The results achieve state-of-the-art super-resolution of anisotropic MRI volumes and, critically, enable reconstruction of near-isotropic anatomy from routine 2D multi-slice acquisitions, which are otherwise highly degraded in orthogonal views.

Abstract

Diffusion models are the current state-of-the-art for solving inverse problems in imaging. Their impressive generative capability allows them to approximate sampling from a prior distribution, which alongside a known likelihood function permits posterior sampling without retraining the model. While recent methods have made strides in advancing the accuracy of posterior sampling, the majority focuses on single-image inverse problems. However, for modalities such as magnetic resonance imaging (MRI), it is common to acquire multiple complementary measurements, each low-resolution along a different axis. In this work, we generalize common diffusion-based inverse single-image problem solvers for multi-image super-resolution (MISR) MRI. We show that the DPS likelihood correction allows an exactly-separable gradient decomposition across independently acquired measurements, enabling MISR without constructing a joint operator, modifying the diffusion model, or increasing network function evaluations. We derive MISR versions of DPS, DMAP, DPPS, and diffusion-based PnP/ADMM, and demonstrate substantial gains over SISR across $4\times/8\times/16\times$ anisotropic degradations. Our results achieve state-of-the-art super-resolution of anisotropic MRI volumes and, critically, enable reconstruction of near-isotropic anatomy from routine 2D multi-slice acquisitions, which are otherwise highly degraded in orthogonal views.

Likelihood-Separable Diffusion Inference for Multi-Image MRI Super-Resolution

TL;DR

The results achieve state-of-the-art super-resolution of anisotropic MRI volumes and, critically, enable reconstruction of near-isotropic anatomy from routine 2D multi-slice acquisitions, which are otherwise highly degraded in orthogonal views.

Abstract

Diffusion models are the current state-of-the-art for solving inverse problems in imaging. Their impressive generative capability allows them to approximate sampling from a prior distribution, which alongside a known likelihood function permits posterior sampling without retraining the model. While recent methods have made strides in advancing the accuracy of posterior sampling, the majority focuses on single-image inverse problems. However, for modalities such as magnetic resonance imaging (MRI), it is common to acquire multiple complementary measurements, each low-resolution along a different axis. In this work, we generalize common diffusion-based inverse single-image problem solvers for multi-image super-resolution (MISR) MRI. We show that the DPS likelihood correction allows an exactly-separable gradient decomposition across independently acquired measurements, enabling MISR without constructing a joint operator, modifying the diffusion model, or increasing network function evaluations. We derive MISR versions of DPS, DMAP, DPPS, and diffusion-based PnP/ADMM, and demonstrate substantial gains over SISR across anisotropic degradations. Our results achieve state-of-the-art super-resolution of anisotropic MRI volumes and, critically, enable reconstruction of near-isotropic anatomy from routine 2D multi-slice acquisitions, which are otherwise highly degraded in orthogonal views.
Paper Structure (13 sections, 1 theorem, 14 equations, 4 figures, 1 table, 4 algorithms)

This paper contains 13 sections, 1 theorem, 14 equations, 4 figures, 1 table, 4 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Diffusion models
  4. 2D Magnetic Resonance Image Acquisition
  5. Diffusion posterior sampling for SISR
  6. Method
  7. MISR Preliminaries
  8. Likelihood separability in DPS
  9. MISR inverse diffusion methods
  10. Experiments and Results
  11. SISR vs MISR
  12. Ablation: noise-weighting
  13. Conclusion

Key Result

Proposition 1

Let $\mu_0(x_t) = \mathbb{E}[x_0\mid x_t]$ be the diffusion model's estimation of the data sample from time $t$. Then, the likelihood gradient to correct $x_t$ towards the data consistent manifold is In particular, each $A_i$ contributes an independent correction direction, and the combined gradient is their sum.

Figures (4)

  • Figure 1: Overview of our proposed MISR generalization to diffusion super-resolution. Our method generalizes existing methods for multi-image super-resolution (MISR). The first column shows low-resolution (LR) anisotropic MRI measurements with 16$\times$ downsampling along orthogonal planes. For super-resolution results, the first row shows the existing methods for single-image super-resolution (SISR), which only use the LR measurement enclosed in the blue dotted box. The second row shows results for our proposed generalization of each method for MISR, which use both LR measurements enclosed in the pink solid box. All methods used the same 3D volumetric diffusion model, and all results are 3D volumetric images. A single sagittal slice is shown for viewing clarity. Volumetric PSNR and SSIM are overlaid in the yellow box, and zoomed inset regions are shown in red. MISR improves performance for all methods and better estimates the anatomy of the reference image, shown on the far right.
  • Figure 2: Qualitative results for a representative subject from the AIBL dataset. Row-wise labels designate LR inputs as "Measurements" and SR estimations named by method. Supercolumns group scale factors together. Within supercolumns, each column corresponds to SISR using only the axial acquisition as input (blue), then MISR using axial and coronal (pink), and MISR using axial, coronal, and sagittal (green). The HR reference is shown at the bottom of the figure. For all methods, the same area highlighting the folia of the cerebellum is zoomed into the inset.
  • Figure 3: Sagittal slices from four representative subjects are shown for $8\times$ scale factor LR inputs. Each displayed image is labeled for its contents. LR: low-resolution; AX: axial acquisition; COR: coronal acquisition; HR: ground-truth high-resolution; SISR: single-image super-resolution, using the axial acquisition as input; MISR: multi-image super-resolution, using the axial and coronal acquisitions as input. Zoomed inset regions are located by the red box, highlighting anatomical differences that are not correctly recovered by SISR.
  • Figure 4: Quantitative results for 100 subjects. For PSNR and SSIM, the mean$\pm$std. are reported. FID is computed as mentioned in Sec. \ref{['sec:experiments']} Best results by scale factor are bolded and second-best results are underlined.

Theorems & Definitions (2)

  • Proposition 1
  • proof