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Bi-level Guided Diffusion Models for Zero-Shot Medical Imaging Inverse Problems

Hossein Askari, Fred Roosta, Hongfu Sun

TL;DR

The experimental findings reveal that BGDM is more effective and efficient compared to the baselines, faithfully generating high-fidelity medical images and substantially reducing hallucinatory artifacts in cases of severe degradation.

Abstract

In the realm of medical imaging, inverse problems aim to infer high-quality images from incomplete, noisy measurements, with the objective of minimizing expenses and risks to patients in clinical settings. The Diffusion Models have recently emerged as a promising approach to such practical challenges, proving particularly useful for the zero-shot inference of images from partially acquired measurements in Magnetic Resonance Imaging (MRI) and Computed Tomography (CT). A central challenge in this approach, however, is how to guide an unconditional prediction to conform to the measurement information. Existing methods rely on deficient projection or inefficient posterior score approximation guidance, which often leads to suboptimal performance. In this paper, we propose \underline{\textbf{B}}i-level \underline{G}uided \underline{D}iffusion \underline{M}odels ({BGDM}), a zero-shot imaging framework that efficiently steers the initial unconditional prediction through a \emph{bi-level} guidance strategy. Specifically, BGDM first approximates an \emph{inner-level} conditional posterior mean as an initial measurement-consistent reference point and then solves an \emph{outer-level} proximal optimization objective to reinforce the measurement consistency. Our experimental findings, using publicly available MRI and CT medical datasets, reveal that BGDM is more effective and efficient compared to the baselines, faithfully generating high-fidelity medical images and substantially reducing hallucinatory artifacts in cases of severe degradation.

Bi-level Guided Diffusion Models for Zero-Shot Medical Imaging Inverse Problems

TL;DR

The experimental findings reveal that BGDM is more effective and efficient compared to the baselines, faithfully generating high-fidelity medical images and substantially reducing hallucinatory artifacts in cases of severe degradation.

Abstract

In the realm of medical imaging, inverse problems aim to infer high-quality images from incomplete, noisy measurements, with the objective of minimizing expenses and risks to patients in clinical settings. The Diffusion Models have recently emerged as a promising approach to such practical challenges, proving particularly useful for the zero-shot inference of images from partially acquired measurements in Magnetic Resonance Imaging (MRI) and Computed Tomography (CT). A central challenge in this approach, however, is how to guide an unconditional prediction to conform to the measurement information. Existing methods rely on deficient projection or inefficient posterior score approximation guidance, which often leads to suboptimal performance. In this paper, we propose \underline{\textbf{B}}i-level \underline{G}uided \underline{D}iffusion \underline{M}odels ({BGDM}), a zero-shot imaging framework that efficiently steers the initial unconditional prediction through a \emph{bi-level} guidance strategy. Specifically, BGDM first approximates an \emph{inner-level} conditional posterior mean as an initial measurement-consistent reference point and then solves an \emph{outer-level} proximal optimization objective to reinforce the measurement consistency. Our experimental findings, using publicly available MRI and CT medical datasets, reveal that BGDM is more effective and efficient compared to the baselines, faithfully generating high-fidelity medical images and substantially reducing hallucinatory artifacts in cases of severe degradation.
Paper Structure (24 sections, 1 theorem, 43 equations, 15 figures, 5 tables, 1 algorithm)

This paper contains 24 sections, 1 theorem, 43 equations, 15 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Diffusion Models
  4. Diffusion Models for Linear Inverse Problems
  5. Proposed Method
  6. Bi-level Guided Diffusion Model (BGDM)
  7. Refined Version: R-BGDM
  8. Experiments
  9. Setup
  10. Data Sets
  11. Baselines
  12. Implementation
  13. Architecture
  14. Sampling Settings and Hyper-parameters.
  15. Results
  16. ...and 9 more sections

Key Result

Proposition 3.1

Consider the least squares problem $\min_{\mathbf{x} \in \mathbb{R}^{n}} \Vert \mathbf{y} -\mathcal{A}\mathbf{x} \Vert_2^2$ where $\mathcal{A} \in \mathbb{R}^{m \times n}$ is any matrix and $\mathbf{y} \in \mathbb{R}^m$. Gradient descent, initialized at ${\bar{\mathbf{x}}} \in \mathbb{R}^{n}$ and w

Figures (15)

  • Figure 1: A high-level illustration of BGDM that leverages pre-trained diffusion models to solve inverse problems via a bi-level guidance (BG) strategy. BG encourages consistency at two levels by utilizing information from observed measurements $\mathbf{y}$ and the forward model $\mathcal{A}$. The inner level ① establishes the reference point $\bar{\mathbf{x}}$ by approximating the conditional posterior mean $\mathbb{E}[\mathbf{x}_0|\mathbf{x}_t, \mathbf{y}]$, employing gradient guidance for this purpose. Subsequently, the outer level ② tackles a proximal optimization objective to enforce measurement consistency further.
  • Figure 2: An illustration of the geometric principles underpinning diffusion samplers and various guidance schemes. (a) DDIM is an unconditional diffusion sampler devoid of guidance. (b) DPS employs gradient guidance with possible deviation from the accurate manifold. (c) DDNM projects denoised samples into a measurement-consistent subspace. (d) our proposed method employs a bi-level guidance strategy; the inner level approximates the initial prediction with a conditional posterior mean through gradient guidance, while the outer level tackles an optimization problem to impose measurement consistency further. Note that ACPM stands for Approximated Conditional Posterior Mean derived in \ref{['eqnew2']}.
  • Figure 3: In the horizontal array of graphs from left to right, the first two graphs illustrate the BraTs undersampled MRI reconstruction results for 200 timesteps at various acceleration rates, and the last two graphs display the results over a span of 350 timesteps at a fixed ACR of 4.
  • Figure 4: The qualitative results of undersampled MRI reconstruction on the BraTS dataset, depicted for ACR 4, 8, and 24.
  • Figure 5: The visual representation of results from the fastMRI knee dataset, obtained using 100 steps for Gaussian1D and Uniform1D masks at an ACR of 8.
  • ...and 10 more figures

Theorems & Definitions (2)

  • Proposition 3.1
  • proof