[Paper Review] TRex: A Tomography Reconstruction Proximal Framework for Robust Sparse View X-Ray Applications

Mohamed Aly, Guangming Zang+2 more|arXiv (Cornell University)|Jun 11, 2016

Medical Imaging Techniques and Applications47 references3 citations

TL;DR

TRex is a flexible proximal framework for robust sparse-view X-ray computed tomography reconstruction that uses iterative solvers—particularly SART—directly to compute proximal operators. It outperforms state-of-the-art methods like ADMM-PCG and OS-Mom in reconstruction quality and parameter robustness, especially under low-dose, sparse-view conditions, using Poisson noise modeling and advanced regularizers like SAD.

ABSTRACT

We present TRex, a flexible and robust Tomographic Reconstruction framework using proximal algorithms. We provide an overview and perform an experimental comparison between the famous iterative reconstruction methods in terms of reconstruction quality in sparse view situations. We then derive the proximal operators for the four best methods. We show the flexibility of our framework by deriving solvers for two noise models: Gaussian and Poisson; and by plugging in three powerful regularizers. We compare our framework to state of the art methods, and show superior quality on both synthetic and real datasets.

Motivation & Objective

• To address the challenge of low-dose, sparse-view X-ray CT reconstruction where traditional FBP methods fail due to ill-posedness and noise.
• To develop a flexible, robust reconstruction framework that integrates iterative solvers directly into a proximal algorithmic structure.
• To compare and select the most effective iterative solvers (e.g., SART, ART, BICAV, OS-SQS) for proximal operator computation in sparse-view settings.
• To enable the use of multiple noise models (Gaussian and Poisson) and powerful regularizers (ITV, ATV, SAD) within a unified framework.
• To demonstrate superior reconstruction quality and parameter insensitivity compared to state-of-the-art methods like ADMM-PCG and OS-Mom.

Proposed method

• TRex formulates tomographic reconstruction as a proximal optimization problem, using iterative solvers to compute the proximal operator directly.
• It derives closed-form proximal operators for SART, ART, BICAV, and OS-SQS, enabling their integration into proximal algorithms.
• The framework supports two data fidelity terms: least squares (Gaussian noise) and weighted least squares (Poisson noise approximation).
• It incorporates three advanced regularizers: isotropic total variation (ITV), anisotropic total variation (ATV), and sum of absolute differences (SAD).
• The framework is implemented using the ASTRA toolbox and supports plug-and-play integration of different solvers, data terms, and regularizers.
• Parameter tuning is simplified, with TRex showing high robustness to parameter choices compared to methods like ADMM-PCG.

Experimental results

Research questions

• RQ1 Which iterative reconstruction methods—SART, ART, SIRT, BSSART, BICAV, CG, OS-SQS—perform best in sparse-view tomography under ill-posed conditions?
• RQ2 Can SART be effectively used as a proximal operator in a flexible framework for tomographic reconstruction, despite its lack of guaranteed convergence?
• RQ3 How does the combination of Poisson noise modeling and SAD regularization improve reconstruction quality in low-dose, sparse-view scenarios?
• RQ4 How does TRex compare quantitatively and qualitatively to state-of-the-art methods like ADMM-PCG and OS-Mom in terms of SNR and convergence stability?
• RQ5 To what extent does TRex’s framework reduce parameter sensitivity and improve usability compared to existing proximal solvers?

Key findings

• TRex with SART and SAD regularizer achieves higher SNR than ADMM-PCG and OS-Mom across all datasets, including on 15-projection data.
• For the NCAT and Mouse phantoms, TRex with 15 projections achieves SNR levels comparable to plain SART with 30 projections.
• The OS-Mom method shows inconsistent performance, with SNR decreasing after early iterations in some cases, even with relaxation.
• ADMM-PCG required extensive manual parameter tuning and remained unstable, indicating high sensitivity to parameter settings.
• TRex is significantly easier to tune and more robust than ADMM-PCG and OS-Mom, with consistent high-quality reconstructions across datasets.
• SART is identified as the best-performing solver for sparse-view applications, followed closely by ART and BICAV, despite its lack of convergence guarantees.