Efficient Fourier-Domain Inversion for High Dynamic Range Tomography via the Modulo Radon Transform

Core Concepts

A novel Fourier domain algorithm is presented for efficient and stable reconstruction of high dynamic range tomographic images from modulo Radon transform measurements, providing mathematical guarantees and advantages over previous spatial domain approaches.

Abstract

The content discusses a new Fourier domain approach for inverting the modulo Radon transform (MRT) to enable high dynamic range (HDR) tomography. The key highlights are: The authors present a novel, non-sequential algorithm that directly works in the Fourier domain, in contrast to previous spatial domain approaches. This leads to several advantages: Efficient algorithmic implementation with reduced computational complexity. Compatibility with existing Fourier-based Radon transform reconstruction methods. Agnostic to the modulo folding threshold, circumventing the need for ADC calibration. The proposed algorithm is backed by mathematical guarantees, showing that it can achieve exact recovery of the Radon projections from the modulo Radon measurements at sampling rates above the Nyquist rate, which is a factor πe improvement over previous results. Experiments using modulo ADC hardware validate the theoretical claims, demonstrating advantages such as recovery at much lower sampling rates, higher digital resolution or lower quantization noise, and empirical robustness to system noise and outliers. The content provides a comprehensive treatment of the modulo Radon transform inversion problem, bridging the gap between theory and practice for efficient HDR tomographic imaging.

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The content does not provide any explicit numerical data or statistics to support the key claims. The focus is on the theoretical and algorithmic developments.

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Key Insights Distilled From

Fourier-Domain Inversion for the Modulo Radon Transform

by Matthias Bec... at arxiv.org 04-10-2024

https://arxiv.org/pdf/2307.13114.pdf

Deeper Inquiries

How can the proposed Fourier domain approach be extended to handle more practical challenges in HDR tomography, such as limited-angle or sparse-view scenarios

The proposed Fourier domain approach can be extended to handle more practical challenges in HDR tomography, such as limited-angle or sparse-view scenarios, by incorporating advanced reconstruction algorithms. In limited-angle scenarios, where not all angles are available for data acquisition, the Fourier domain recovery algorithm can be modified to incorporate regularization techniques like total variation regularization or compressed sensing methods to improve reconstruction quality. Additionally, iterative reconstruction algorithms like iterative shrinkage-thresholding algorithms (ISTA) or alternating direction method of multipliers (ADMM) can be employed to enhance the reconstruction process in sparse-view scenarios. These algorithms can exploit the sparsity of the data in the Fourier domain to improve image quality and mitigate artifacts caused by limited data.

What are the potential limitations or failure modes of the modulo Radon transform approach compared to alternative HDR imaging techniques, and how can they be addressed

The modulo Radon transform approach, while offering advantages in HDR imaging, has potential limitations and failure modes compared to alternative HDR imaging techniques. One limitation is the sensitivity to noise and artifacts, especially in the presence of high levels of noise or incomplete data. To address this, advanced denoising techniques such as wavelet denoising or deep learning-based denoising can be integrated into the reconstruction process. Another limitation is the dependency on accurate calibration of the modulo threshold λ, which can introduce errors if not calibrated properly. To mitigate this, robust calibration methods or adaptive thresholding techniques can be implemented to improve the accuracy of the reconstruction. Additionally, the modulo Radon transform approach may struggle with complex geometries or heterogeneous materials, requiring further research into adaptive algorithms or hybrid imaging techniques to handle such scenarios effectively.

The content discusses HDR tomography in the context of X-ray imaging. Are there opportunities to apply similar principles to other modalities like MRI or ultrasound to enable HDR imaging capabilities

While the content focuses on HDR tomography in X-ray imaging, similar principles can be applied to other modalities like MRI or ultrasound to enable HDR imaging capabilities. In MRI, for example, where dynamic range limitations can affect image quality, the concept of high dynamic range imaging can be beneficial for capturing details in both low and high signal intensity regions. By adapting the Fourier domain recovery algorithm to MRI data, it is possible to reconstruct HDR images from multiple exposures or different acquisition parameters. Similarly, in ultrasound imaging, where dynamic range challenges can impact image clarity, the modulo Radon transform approach can be utilized to enhance the dynamic range and improve image quality. By exploring the application of HDR principles in MRI and ultrasound, researchers can potentially unlock new possibilities for advanced imaging techniques and improved diagnostic capabilities.