⚡ electrical engineering

FCDM: A Physics-Guided Bidirectional Frequency Aware Convolution and Diffusion-Based Model for Sinogram Inpainting

FCDM is a physics-guided diffusion framework for sinogram inpainting that utilizes bidirectional frequency reasoning and angular-aware masking to overcome the limitations of conventional RGB-oriented methods in preserving the global structure and physical consistency of sparse-view CT data.

Original authors: Jiaze E, Srutarshi Banerjee, Tekin Bicer, Guannan Wang, Yanfu Zhang, Bin Ren

Published 2026-02-10

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Jiaze E, Srutarshi Banerjee, Tekin Bicer, Guannan Wang, Yanfu Zhang, Bin Ren

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 the pieces are missing, and the pieces you do have are strangely shaped and follow very specific, invisible rules about where they must fit.

This is the problem scientists face in Computed Tomography (CT) scanning. To get a perfect 3D image of a battery, a bone, or a biological sample, a CT scanner needs to take hundreds of "photos" (called projections) from every single angle. But taking all those photos takes a long time and exposes the sample to a lot of radiation, which can actually damage what you're trying to study.

To save time and protect the sample, scientists use "Sparse-View CT"—they take only a few photos. The problem? The resulting data (called a sinogram) has huge gaps in it. If you try to turn those gaps into a 3D image using standard computer methods, the result looks blurry, streaky, and "fake."

FCDM is the new "Super-Puzzle Solver" designed to fix this. Here is how it works, broken down into three simple ideas:

1. The "Two-Way Street" Vision (Bidirectional Frequency Awareness)

Most AI models look at images like a standard photograph—they look at local shapes and colors. But a sinogram isn't a photo; it’s a mathematical map. It has two very different "directions": the detector axis (the sensor's view) and the angle axis (the rotation of the scanner).

Think of it like listening to a song. A standard AI might just listen to the volume. FCDM, however, listens to the melody (the structure) and the rhythm (the pattern) separately. By looking at the "frequency" (the patterns) in both directions at once, it understands the "music" of the sinogram much better than a standard AI could.

2. The "Physics Teacher" (Physics-Guided Regularization)

Standard AI is like an artist who is great at making things look pretty, even if they aren't real. If you ask a standard AI to fill in a gap, it might draw something that looks right but violates the laws of science.

FCDM has a "Physics Teacher" built into its brain. This teacher enforces a rule called Total Absorption Conservation. Imagine you are measuring how much light passes through a glass of water. If you measure the top and the bottom, the math must add up. FCDM won't allow itself to "cheat" by filling in a gap with data that doesn't obey these mathematical laws of light and matter. This ensures the final 3D image isn't just pretty—it's scientifically accurate.

3. The "Smart Eraser" (Diffusion with a Twist)

The model uses a technique called Diffusion. Imagine starting with a blurry, noisy mess and slowly "cleaning" it until a clear image emerges.

However, most "cleaning" methods treat all noise the same. FCDM uses a Frequency-Adaptive Noise Schedule. Think of this like restoring an old, damaged painting. Instead of scrubbing the whole canvas with the same brush, FCDM uses a large, soft brush first to fix the big, blurry shapes (the global structure), and then switches to a tiny, fine-tipped brush to fix the tiny details (the high-frequency textures). It also uses "Smart Masks" that tell the AI, "Hey, this gap isn't just a hole; it's a hole at a 45-degree angle," helping it understand the geometry of the missing pieces.

The Result

Because FCDM understands the math, the physics, and the patterns of the data, it can fill in those massive gaps with incredible precision. In tests, it achieved much higher accuracy (SSIM and PSNR scores) than previous methods, meaning scientists can get crystal-clear 3D images while using much less radiation and much less time.

Technical Summary: FCDM (Physics-Guided Bidirectional Frequency Aware Convolution and Diffusion-Based Model)

1. Problem Statement

In Computed Tomography (CT), acquiring full-view sinograms is time-consuming and exposes samples to high radiation doses. While sparse-view CT mitigates these issues by reducing the number of projections, it results in incomplete sinograms. This leads to "structured signal loss," which causes nonlinear distortions and artifacts during the reconstruction process.

The authors identify a critical modality gap: conventional inpainting methods (designed for RGB images) fail on sinograms because:

Global Coupling: Unlike RGB pixels, sinogram pixels are globally coupled via the Radon transform.
Anisotropic Frequency Patterns: Sinograms exhibit highly directional and asymmetric spectral distributions (detector vs. angle axes).
Physical Constraints: Sinograms must obey physical laws, such as total X-ray absorption conservation, which standard generative models ignore.

2. Methodology

The proposed FCDM is a two-stage framework that combines an encoder-decoder architecture with a latent-space diffusion process.

Stage 1: Representation Learning (Encoder-Decoder)
The goal is to learn a physically consistent latent representation.

Bidirectional Frequency-Domain Convolution (BFDC): To capture the anisotropic nature of sinograms, the model applies convolutions independently along the detector ( $H$ ) and angular ( $W$ ) axes in the Fourier domain. This disentangles the spectral features that are otherwise entangled in spatial convolutions.
Physics-Guided Loss Functions:
- Total Projection Consistency Loss ( $L_{absorp}$ ): Enforces that the sum of projections at each angle matches the total attenuation of the object, ensuring physical realism.
- Frequency Domain Consistency Loss ( $L_{freq}$ ): Minimizes the difference between the Fourier transforms of the inpainted and ground-truth sinograms to prevent spectral artifacts.

Stage 2: Guided Denoising (Diffusion Model)
The diffusion process operates within the learned latent space to refine the inpainting.

Fourier-Enhanced Mask Embedding (FEME): Instead of using simple binary masks, FEME encodes the projection-angle information using a Fourier basis. This provides the model with "angular context," allowing it to understand the periodic and geometric relationships between missing views.
Frequency-Adaptive Noise Scheduling (FANS): Standard diffusion uses uniform Gaussian noise. FANS modulates noise based on frequency sensitivity—preserving low-frequency components early in the process to stabilize global structure, then progressively introducing high-frequency noise to refine fine textures. It also includes a "soft absorption constraint" to maintain row-wise intensity consistency.

3. Key Contributions

Domain-Specific Architecture: Introduced BFDC to handle the unique bidirectional spectral characteristics of sinograms.
Geometric Awareness: Developed FEME to bridge the gap between spatial masking and angular projection geometry.
Physics Integration: Integrated total absorption conservation and frequency-domain regularization directly into the training objective.
Adaptive Diffusion: Proposed FANS to align the noise injection process with the structural requirements of tomographic data.

4. Results

The model was evaluated on two large-scale real-world datasets: TomoBank and LoDoPaB.

Quantitative Performance: FCDM consistently outperformed ten state-of-the-art baselines (including diffusion-based models like RePaint and task-specific models like SinoTx). It achieved high fidelity with SSIM > 0.93 and PSNR > 31 dB across various sparse-view settings (random and periodic masking).
Qualitative Performance: Visual comparisons showed that FCDM produces smoother, more consistent sinograms and significantly reduces the angular streaking artifacts common in other methods.
Ablation Studies: Experiments confirmed that every component (BFDC, physics losses, FEME, and FANS) is essential for achieving optimal reconstruction quality.

5. Significance

FCDM represents a significant advancement in medical and scientific imaging. By moving away from "RGB-centric" deep learning and toward physics-guided generative modeling, the authors provide a robust solution for high-resolution CT imaging. This approach enables high-quality 3D reconstructions from minimal data, potentially reducing radiation exposure in clinical settings and increasing throughput in industrial and synchrotron-based material characterization.