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Design Choices in Splitting-Based Self-Supervised Sparse-View CT Reconstruction

This paper introduces a unified framework to analyze design choices in splitting-based self-supervised sparse-view CT reconstruction, demonstrating that optimal partitioning strategies depend on noise structure and that multi-partition splitting with complementary metrics yields superior performance across simulated and real-world datasets.

Original authors: Nadja Gruber, Lukas Neumann, Ander Biguri, Gyeongha Hwang, Markus Haltmeier, Johannes Schwab

Published 2026-07-14

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Nadja Gruber, Lukas Neumann, Ander Biguri, Gyeongha Hwang, Markus Haltmeier, Johannes Schwab

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 giant, 3D jigsaw puzzle, but someone has stolen half the pieces. In the world of medical CT scans, this is a real problem: doctors need clear pictures of the inside of your body, but taking too many X-rays can be dangerous or just take too long. So, they only take a few "snapshots" (measurements) and try to guess the rest.

Usually, computers need a "perfect" picture to learn how to fill in the gaps. But in the real world, we don't have those perfect pictures to compare against. That's where this paper steps in with a clever trick called Self-Supervised Learning.

The Big Idea: The "Blind Spot" Game

Think of the computer as a student trying to learn how to draw a perfect landscape. Instead of showing it the finished painting, the teacher covers up random parts of the student's drawing and says, "You can't look at these spots, but you must guess what's underneath them based on the rest of the picture."

The computer tries to fill in the blanks. Then, it checks its own work against the parts of the original photo it wasn't allowed to see during the guess. If it gets it right, it learns. If it gets it wrong, it tries again. This is the "splitting" method: splitting the data into "what I see" and "what I guess."

The Plot Twist: Noise is a Sneaky Villain

The paper's main discovery is that not all noise is created equal, and the strategy you use to play this guessing game depends entirely on how the "noise" (static or fuzziness) behaves.

In a perfect, simulated world where the noise is totally random and independent (like static on an old TV where every pixel flickers on its own), the best strategy is Lattice Splitting.

The Analogy: Imagine a checkerboard. You cover up every other square in a strict grid pattern. The computer learns to fill in the gaps by looking at the surrounding squares. In this "clean" noise world, this grid pattern works like a charm.

But, in the real world, noise is often "correlated." This happens because of the physical detectors in the machine (scintillators) that blur together, making neighboring pixels act like a team rather than individuals.

The Analogy: Imagine the noise isn't random static, but a thick fog that rolls across the whole picture at once. If you try to use the strict checkerboard (Lattice) strategy here, the fog messes up the whole grid, and the computer gets confused.
The Solution: In this "foggy" real-world scenario, the paper found that Angular Splitting is the hero. Instead of a grid, you hide entire rows of the picture (whole angles of the X-ray beam). Because the fog moves across the detector, hiding whole rows breaks the connection between the noisy neighbors, allowing the computer to learn much better.

The Paper's "Don't Do This" List

The authors are very clear about what doesn't work well in certain situations:

Don't use the Grid (Lattice) strategy if your data has real-world, correlated noise. The paper shows that in these conditions, the grid method leaves the image looking "contaminated" with noise.
Don't just leave the missing pieces as black holes (Zero-filling). When the computer sees a missing piece, it shouldn't just assume it's empty space. The paper suggests Linear Interpolation is better.
- The Analogy: If you are missing a piece of a puzzle, don't just leave a black hole. Look at the pieces next to it and guess the color that fits in between. The paper found that "guessing" the missing values before the computer starts working makes the final picture much clearer.

The "Super-Team" Strategy

The paper also introduces a new, fancy move called Multi-Partition Splitting.

The Analogy: Imagine you are playing the guessing game, but instead of just hiding a grid or just hiding rows, you hide both at the same time. You create a "super-mask" that forces the computer to learn from multiple different angles at once.
The Result: The paper suggests this "super-team" approach consistently improves the results, acting like a powerful safety net that helps the computer handle both random noise and foggy noise better than using just one strategy alone.

How Sure Are They?

The authors are very careful with their claims. They didn't just guess; they ran thousands of computer simulations using a dataset called LoDoPaB-CT and tested their ideas on a real-world dataset called 2DeteCT.

What they proved: They showed that the "best" strategy changes depending on the noise. They proved that Angular Splitting is more robust for real, noisy data, while Lattice Splitting is better for clean, simulated data.
What they measured: They didn't just look at the pictures; they used special math tools (like PSNR, SSIM, LPIPS, and HaarPSI) to measure how close the computer's guess was to the truth. They found that some strategies look good on simple math scores but fail to capture the "feel" of the image, which is why they used those extra perceptual tools.

The Takeaway for a Curious Teen

If you are building a robot to fix broken CT scans, don't just pick one "magic" trick.

If your robot is working in a perfect, clean lab, use the Grid (Lattice) strategy.
If your robot is working in a real, messy hospital with fuzzy detectors, switch to the Row (Angular) strategy.
And if you want to be extra safe, use the Super-Team (Multi-Partition) strategy to cover your bases.

The paper concludes that there is no single "best" way to split the data; the secret sauce is matching your strategy to the specific type of noise your machine is dealing with.

Technical Summary: Design Choices in Splitting-Based Self-Supervised Sparse-View CT Reconstruction

Problem Statement
In X-ray computed tomography (CT), reconstruction from sparse-view measurements is an ill-posed inverse problem, often exacerbated by noise and limited data due to radiation dose or time constraints. While deep learning has achieved state-of-the-art results, most methods rely on supervised training with paired ground-truth images, which are frequently unavailable in clinical or industrial settings. Self-supervised learning, specifically measurement splitting (e.g., Noise2Self variants), offers a solution by training on incomplete measurements without ground truth. However, the influence of critical design choices—specifically data partitioning strategies, preprocessing of masked measurements, and inference mechanisms—remains poorly understood. Furthermore, many splitting methods assume measurement independence, an assumption often violated in real CT systems where scintillator blur induces spatially correlated noise between detector elements. This paper investigates how these design choices interact with different noise structures (independent vs. correlated) to determine optimal reconstruction strategies.

Methodology
The authors propose a unified framework that decomposes splitting-based self-supervised reconstruction into three core components: partitioning, preprocessing, and inference.

Partitioning Strategies: The study evaluates various geometric splitting strategies applied to the sinogram (projection data):
- Lattice Splitting ( $P_{lat}$ ): Divides the sinogram into regular or irregular grids of $d \times d$ patches, masking pixels based on their relative position within the patch.
- Angular Splitting ( $P_{ang}$ ): Masks entire projection angles (rows in the sinogram) in blocks.
- Multi-Partition Splitting ( $P_{mult}$ ): A novel extension that simultaneously enforces invariance along both angular and detector dimensions, aggregating losses from two independent partition systems.
Preprocessing: The authors compare two methods for handling masked entries before reconstruction via Filtered Backprojection (FBP):
- Zero-filling: Leaving masked entries as zero.
- Linear Interpolation: Estimating masked entries from available neighbors.
Inference Strategies: Three strategies are evaluated for generating the final image $\hat{x}$ $\overset{x}{^}$ :
- Direct Inference (D-inf): Applying the trained network directly to the full data.
- Average Inference (A-inf): Averaging reconstructions from complementary data splits.
- P-invariant Inference (P-inf): A novel strategy that aggregates sub-reconstructions in the sinogram space (using refined angular sampling) to ensure the output is invariant to the specific masking partition, thereby reducing null-space ambiguities.

The framework is evaluated on the LoDoPaB-CT dataset (simulated) under both uncorrelated Poisson noise and correlated noise (simulated via Gaussian noise and convolution to mimic scintillator blur). Validation is also performed on the real-world 2DeteCT dataset. Evaluation metrics include standard error-based measures (PSNR, SSIM) and perceptual/structural metrics (LPIPS, HaarPSI).

Key Contributions

Unified Framework: The work introduces a modular framework that isolates partitioning, preprocessing, and inference, enabling controlled comparison of existing methods and new extensions.
Systematic Benchmarking: A comprehensive evaluation across independent and correlated noise regimes reveals that the optimal strategy is highly dependent on the noise structure.
Novel Extensions: The introduction of Multi-Partition Splitting and P-invariant Inference provides new tools for leveraging complementary measurement partitions and enforcing invariance during inference.
Noise-Dependent Guidelines: The study demonstrates that lattice-based splitting is superior under independent noise, whereas angular masking is more robust under correlated noise and real-world data. Multi-partition splitting consistently improves upon pure projection-wise splitting in several settings.
Metric Analysis: The inclusion of perceptual metrics (LPIPS, HaarPSI) reveals structural differences between masking strategies that are not captured by PSNR or SSIM alone.

Results

Preprocessing: Linear interpolation of masked measurements prior to FBP consistently improves reconstruction quality (SSIM and HaarPSI) compared to zero-filling, particularly for direct inference.
Noise Regimes:
- Uncorrelated Noise: Lattice-based splitting outperforms angular splitting. Multi-partition splitting shows a systematic improvement over pure angular masking.
- Correlated Noise: Angular splitting significantly outperforms lattice splitting, as it avoids the horizontal correlations induced by scintillator blur. Multi-partition splitting further enhances performance, sometimes surpassing angular splitting alone under invariant inference.
Inference: Both Average and P-invariant inference strategies consistently outperform Direct Inference. The improvement is more pronounced in correlated noise regimes, where P-invariant inference yields the best results by effectively aggregating information while respecting the masking structure.
Splitting Density: The number of splits ( $s \in \{4, 9, 16\}$ ) has a minor impact on performance in uncorrelated noise but shows distinct trends in correlated noise, where fewer splits (coarser masking) can slightly benefit lattice and multi-partition strategies, while angular splitting remains robust to parameter variations.

Significance
The paper provides practical design guidelines for developing self-supervised sparse-view CT reconstruction methods. It highlights that the assumption of measurement independence, common in many splitting-based approaches, is a critical limitation in realistic imaging environments where detector physics introduce structured noise. By demonstrating that angular masking is more robust to correlated noise and that multi-partition strategies can leverage additional redundancies, the work offers a path toward more reliable self-supervised reconstruction in clinical and industrial settings where ground truth is unavailable and noise structures are complex. The findings underscore the necessity of selecting partitioning and inference strategies that align with the specific noise characteristics of the imaging system.