[Paper Review] Tomographic X-ray data of a walnut

K. Hämäläinen, Lauri Harhanen+4 more|arXiv (Cornell University)|Feb 11, 2015

Nuclear Physics and ApplicationsPhysics and Astronomy19 citations

TL;DR

This paper presents a publicly available tomographic X-ray data set of a walnut, including high-resolution sinograms, measurement matrices, and a ground truth FBP reconstruction, enabling benchmarking of sparse-data and regularization-based CT reconstruction algorithms. The data supports testing of wavelet-based sparsity methods, total variation regularization, and S-curve parameter selection in low-projection scenarios.

ABSTRACT

This is the documentation of the tomographic X-ray data of a walnut made available at http://www.fips.fi/dataset.php . The data can be freely used for scientific purposes with appropriate references to the data and to this document in arXiv. The data set consists of (1) the X-ray sinogram of a single 2D slice of the walnut with three different resolutions and (2) the corresponding measurement matrices modeling the linear operation of the X-ray transform. Each of these sinograms was obtained from a measured 120-projection fan-beam sinogram by down-sampling and taking logarithms. The original (measured) sinogram is also provided in its original form and resolution. In addition, a larger set of 1200 projections of the same walnut was measured and a high-resolution filtered back-projection reconstruction was computed from this data; both the sinogram and the FBP reconstruction are included in the data set, the latter serving as a ground truth reconstruction.

Motivation & Objective

• To provide real-world CT data for testing sparse-data reconstruction algorithms in medical and industrial imaging.
• To address the challenge of limited projection data in tomography by offering a realistic, complex biological sample with high contrast and structural non-convexity.
• To support the development and validation of regularization techniques such as Tikhonov and total variation in low-signal regimes.
• To offer a ground truth reconstruction from 1200 projections to enable quantitative evaluation of reconstruction accuracy.
• To facilitate methodological research in inverse problems by providing a standardized, reproducible data set with known measurement geometry and resolution levels.

Proposed method

• Acquired 120-projection fan-beam CT data of a walnut using a custom-built µCT system with 80 kV, 200 µA, and 50 µm pixel resolution.
• Extracted central rows from 2D projection images to form a 2296×120 fan-beam sinogram, representing the central 2D cross-section.
• Down-sampled the original sinogram via binning and applied logarithmic transformation to generate three resolution levels: 82×82, 164×164, and 328×328.
• Constructed sparse measurement matrices A of size N²×M, where M is the number of projections and N is the reconstruction pixel count, modeling the linear X-ray transform.
• Acquired a second, high-resolution 1200-projection data set with 0.3° angular step for improved accuracy and used filtered back-projection (FBP) to compute a high-resolution ground truth reconstruction.
• Provided MATLAB-compatible data files including sinograms, measurement matrices, and the FBP reconstruction for direct use in algorithm testing and validation.

Experimental results

Research questions

• RQ1 How well can sparsity-promoting reconstruction methods perform on real, complex biological data with limited projections?
• RQ2 What is the impact of regularization parameter selection on reconstruction quality in low-data regimes?
• RQ3 How does the choice of measurement matrix resolution affect the accuracy and stability of iterative reconstruction algorithms?
• RQ4 To what extent does the ground truth reconstruction from 1200 projections serve as a reliable benchmark for evaluating sparse-data methods?
• RQ5 Can the walnut’s structural complexity—featuring layered shells and non-convex internal features—effectively simulate clinical or industrial CT challenges?

Key findings

• The data set includes three down-sampled sinograms at resolutions 82×82, 164×164, and 328×328, with corresponding measurement matrices and sinogram data.
• The original 120-projection sinogram has dimensions 2296×120, with pixel size 0.513 mm, 0.257 mm, and 0.128 mm for the three resolution levels.
• A high-resolution FBP reconstruction was computed from 1200 projections (0.3° angular step), resulting in a 2296×2296 ground truth image.
• The measurement matrices A are sparse and represent the linear system A*x = m(:), enabling use in Tikhonov and total variation regularization frameworks.
• The data set has been successfully used to test wavelet-based sparsity methods and the S-curve method for regularization parameter selection.
• The data is freely available for scientific use with proper citation, supporting reproducibility and benchmarking in inverse problems research.