[Paper Review] Radon Inversion via Deep Learning

Ji He, Jianhua Ma|arXiv (Cornell University)|Aug 9, 2018

Medical Imaging Techniques and Applications2 references3 citations

TL;DR

This paper proposes iRadonMap, a deep learning framework for end-to-end Radon inversion in X-ray CT that replaces traditional multi-stage reconstruction with a unified neural network. The method uses a learnable filtering and sinusoidal back-projection layer followed by a residual CNN, achieving superior artifact suppression and edge preservation compared to FBP, especially in low-dose, sparse-view scenarios.

ABSTRACT

Radon transform is widely used in physical and life sciences and one of its major applications is the X-ray computed tomography (X-ray CT), which is significant in modern health examination. The Radon inversion or image reconstruction is challenging due to the potentially defective radon projections. Conventionally, the reconstruction process contains several ad hoc stages to approximate the corresponding Radon inversion. Each of the stages is highly dependent on the results of the previous stage. In this paper, we propose a novel unified framework for Radon inversion via deep learning (DL). The Radon inversion can be approximated by the proposed framework with an end-to-end fashion instead of processing step-by-step with multiple stages. For simplicity, the proposed framework is short as iRadonMap (inverse Radon transform approximation). Specifically, we implement the iRadonMap as an appropriative neural network, of which the architecture can be divided into two segments. In the first segment, a learnable fully-connected filtering layer is used to filter the radon projections along the view-angle direction, which is followed by a learnable sinusoidal back-projection layer to transfer the filtered radon projections into an image. The second segment is a common neural network architecture to further improve the reconstruction performance in the image domain. The iRadonMap is overall optimized by training a large number of generic images from ImageNet database. To evaluate the performance of the iRadonMap, clinical patient data is used. Qualitative results show promising reconstruction performance of the iRadonMap.

Motivation & Objective

• To address the limitations of conventional multi-stage X-ray CT reconstruction pipelines that are sensitive to errors in sequential stages.
• To develop a unified, end-to-end deep learning framework for Radon inversion that bypasses ad hoc, sequential processing steps.
• To improve image reconstruction quality in low-dose and sparse-view CT by learning optimal filtering and back-projection operations directly from data.
• To evaluate the generalization capability of the model on real clinical patient data without using such data during training.
• To reduce streak artifacts and preserve fine structural details compared to conventional FBP and iterative methods.

Proposed method

• The iRadonMap framework consists of two main segments: a learnable fully-connected filtering layer along the view-angle direction and a learnable sinusoidal back-projection layer.
• The first segment processes raw Radon projections using a parameterized filtering operation followed by a parameterized back-projection using sinusoidal basis functions.
• The second segment employs a fully convolutional residual CNN (inspired by ResNet) to refine the reconstructed image, enhancing texture and structural fidelity.
• The entire network is trained end-to-end using mean square error (MSE) loss between predicted and reference images on a large-scale dataset of ImageNet-derived images.
• Training uses the RMSProp optimizer with a learning rate of 0.00002, batch size of 2, and no batch normalization in the residual network.
• Radon projections are generated using the ASTRA Toolbox with parallel geometry, and the network is trained on 62,899 central 512×512 cropped greyscale images.

Experimental results

Research questions

• RQ1 Can a deep learning framework achieve superior Radon inversion performance compared to conventional filtered back-projection (FBP) in low-dose and sparse-view CT?
• RQ2 To what extent can an end-to-end deep learning model reduce streak artifacts and preserve edge details in CT reconstruction?
• RQ3 How well does a model pre-trained on generic ImageNet images generalize to clinical patient data without fine-tuning on real CT scans?
• RQ4 Can learnable filtering and sinusoidal back-projection layers effectively replace traditional, fixed projection operators in Radon inversion?
• RQ5 Does the proposed two-stage network architecture (projection processing + image refinement) outperform standard FBP and iterative methods in qualitative image quality?

Key findings

• The iRadonMap achieves reconstruction quality comparable to FBP in full-view scenarios (1160 views), indicating robustness in standard imaging conditions.
• In sparse-view scenarios (e.g., 145 and 72 views), the iRadonMap significantly reduces streak artifacts compared to FBP, which exhibits severe noise and streaking.
• The difference images between the reference and iRadonMap reconstructions show less error and better preservation of fine details than those between reference and FBP.
• The iRadonMap preserves more edge details than FBP, as evidenced by qualitative comparisons in the difference images and visual reconstruction quality.
• The model generalizes well to real clinical patient data, with no clinical data used during training, demonstrating strong transferability from generic ImageNet data.
• The use of a learnable sinusoidal back-projection layer enables effective reconstruction with fewer parameters than fully connected layers, improving efficiency and learnability.