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A Diffusion-Based Generative Prior Approach to Sparse-view Computed Tomography

This paper proposes an enhanced Deep Generative Prior (DGP) framework that integrates diffusion-based models with iterative optimization to improve the reconstruction quality of CT images from sparse-view sinograms.

Original authors: Davide Evangelista, Pasquale Cascarano, Elena Loli Piccolomini

Published 2026-02-12

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CC BY 4.0

Original authors: Davide Evangelista, Pasquale Cascarano, Elena Loli Piccolomini

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to solve a massive, complex jigsaw puzzle, but there’s a catch: half of the pieces are missing, and the pieces you do have are slightly blurry and out of focus.

In the world of medicine, this is exactly what happens during a Sparse-View CT Scan. Normally, a CT scanner takes hundreds of X-ray "snapshots" from every angle to build a perfect 3D picture of your insides. But taking too many snapshots means exposing a patient to more radiation. To keep patients safe, doctors want to take fewer snapshots (sparse views). The problem? When you take fewer pictures, the resulting image looks like a ghost—full of streaks, artifacts, and distorted shapes.

This paper introduces a new way to "fill in the blanks" using a method they call RD-DGP. Here is how it works, broken down into simple ideas.

1. The "Artistic Intuition" (The Generative Prior)

Imagine you are an art restorer looking at a damaged painting of a human torso. You don't just guess randomly; you have "artistic intuition." You know what a human ribcage should look like, how muscles curve, and how shadows fall.

The researchers use a Diffusion Model as this "artistic intuition." A diffusion model is an AI that has spent thousands of hours looking at thousands of healthy CT scans. It has learned the "grammar" of human anatomy. Instead of just trying to connect the blurry dots from the X-rays, the AI says, "I see a blurry shape here; based on everything I know about human bodies, that is almost certainly a kidney."

2. The "Smart Starting Point" (Physics-Informed Initialization)

In many AI models, the computer starts guessing from scratch (like starting a puzzle with a blank table). This often leads to "hallucinations"—the AI might accidentally draw a kidney where a lung should be because it got lost in its own imagination.

The researchers added a clever trick: The FBP Head Start.
Before the AI starts its fancy "artistic" reconstruction, they use a standard, old-school math method (Filtered Backprojection) to create a very rough, ugly, but physically accurate sketch. It’s like giving the artist a charcoal outline of the patient before they start painting. This ensures the AI stays "grounded in reality" and doesn't wander off into making up fake anatomy.

3. The "Fine-Tuning" (Cosine Annealing)

Imagine you are trying to park a car in a very tight garage.

At first, you move quickly to get into the general area.
As you get closer to the wall, you slow down to a crawl so you don't crash.

The researchers applied this to the AI's learning process. They use a "Cosine Annealing" schedule. The AI makes big, bold adjustments to the image at the beginning to get the general shape right. As the process continues, the AI "slows down," making tiny, microscopic adjustments to sharpen the edges and clean up the noise. This prevents the image from becoming a blurry mess.

The Result: A Clearer Picture with Less Radiation

By combining Physics (the X-ray data), Artistic Intuition (the Diffusion Model), and Smart Strategy (the starting point and the slowing down), the researchers created a system that can take a very "thin" amount of data and turn it into a high-quality, medically useful image.

In short: They taught the computer how to be a "smart detective"—using the few clues it has (the sparse X-rays) and its deep knowledge of how the human body works to reconstruct a clear, accurate picture without needing to bombard the patient with extra radiation.

Technical Summary: A Diffusion-Based Generative Prior Approach to Sparse-View Computed Tomography

1. Problem Statement

The paper addresses the challenge of sparse-view Computed Tomography (CT) reconstruction. In clinical practice, reducing the number of X-ray projections (sparse-view) is desirable to minimize radiation dose to patients. However, this creates an ill-posed inverse problem: the lack of sufficient data leads to severe reconstruction artifacts, noise, and structural distortions.

Traditional methods like Filtered Backprojection (FBP) or variational regularization (e.g., Total Variation) often struggle to balance data fidelity with image quality in extreme undersampling regimes. While deep learning (CNNs) has improved results, supervised methods require massive paired datasets (which are rare in medical imaging), and CNNs often fail when data is highly noisy or extremely sparse.

2. Methodology

The authors propose the Regularized Diffusion-based Deep Generative Prior (RD-DGP) framework. This approach combines the interpretability of model-based reconstruction with the expressive power of generative models.

Generative Model: The framework uses a Denoising Diffusion Implicit Model (DDIM). Unlike standard diffusion, DDIM allows for a deterministic mapping from a latent noise vector $z$ to a clean image $x_0$ , which enables gradient-based optimization directly in the latent space.
Optimization Objective: The reconstruction is formulated as a regularized latent optimization problem. The goal is to find a latent code $z$ $z$ that minimizes a multi-term objective function $F(z; y_\delta)$ $F (z; y_{δ})$ :
1. Data-Fidelity Term: A least-squares term $\|KG(z) - y_\delta\|^2$ that ensures the generated image is consistent with the measured sinogram $y_\delta$ via the forward operator $K$ .
2. Latent Prior ( $R_1$ ): A Tikhonov penalty ( $\|z\|^2$ ) to ensure the latent variable adheres to the standard Gaussian distribution used during training.
3. Image-Domain Regularizer ( $R_2$ ): A smoothed Total Variation (TV) regularizer applied to the generated image $G(z)$ to promote piecewise smoothness and sharp anatomical boundaries.
Optimization Algorithm: The problem is solved using the Adam optimizer in the latent space, with gradients backpropagated through the pre-trained DDIM generator.

3. Key Contributions

The paper introduces three primary technical advancements to improve the stability and quality of the DGP framework:

Physics-Informed Initialization: To prevent the optimizer from falling into poor local minima (a common issue in non-convex deep learning landscapes), the authors use DDIM Inversion. They first compute a coarse FBP reconstruction and then "invert" it into the diffusion latent space to provide a high-quality starting point $z(0)$ .
Dynamic Learning-Rate Schedule: They implement a cosine annealing schedule for the Adam optimizer. This allows for large steps early in the optimization to explore the latent space and progressively smaller steps to refine fine anatomical details.
Open-Source Contribution: The authors released a diffusion model pre-trained on chest CT images (using an augmented Mayo dataset) and the associated code to facilitate reproducible research in medical imaging.

4. Results and Discussion

The method was evaluated against state-of-the-art diffusion-based methods, including DPS, DiffPIR, and DDRM, across three angular regimes (30, 45, and 60 projection angles).

Quantitative Performance: RD-DGP showed competitive performance, performing slightly better than DDRM in the 40 and 60-angle geometries in terms of MSE, PSNR, and SSIM.
Qualitative Performance: Visual inspections revealed that while DDRM produced high-contrast images, it often suffered from incorrect object shapes and higher noise. RD-DGP maintained better structural integrity and fewer shape distortions.
Ablation Study: The authors proved that the initialization strategy is the most critical component; without it, the model fails to reconstruct the correct patient anatomy. The learning-rate schedule was found to be secondary but helpful for noise reduction and contrast enhancement.

5. Significance

This work represents a significant step toward making generative models clinically viable for CT reconstruction. By decoupling the physical model (the forward operator $K$ ) from the generative prior (the DDIM), the authors maintain the explainability required in medical contexts while leveraging the superior image synthesis capabilities of diffusion models. The approach demonstrates that even in "extreme" undersampling scenarios, high-quality anatomical structures can be recovered, provided the optimization is guided by physics-informed initialization.