Continuous Filtered Backprojection by Learnable Interpolation Network

TL;DR

The paper tackles interpolation errors in the backprojection step of CT reconstruction by introducing LInFBP, a learnable continuous representation-based backprojection. It formulates a local continuous sinogram representation as a weighted sum of basis functions, with weights predicted by a lightweight network, enabling end-to-end optimization while preserving FBP structure. Two basis-function families are proposed: Fourier-based (F-LInFBP) and linear-kernel-based (L-LInFBP), trading representation capacity against computation. Extensive experiments across full, quarter-dose, and sparse-view CT scenarios, as well as cross-domain and model-combination settings, show that LInFBP improves reconstruction quality and generalization, with L-LInFBP offering substantial efficiency gains and robust performance.

Abstract

Accurate reconstruction of computed tomography (CT) images is crucial in medical imaging field. However, there are unavoidable interpolation errors in the backprojection step of the conventional reconstruction methods, i.e., filtered-back-projection based methods, which are detrimental to the accurate reconstruction. In this study, to address this issue, we propose a novel deep learning model, named Leanable-Interpolation-based FBP or LInFBP shortly, to enhance the reconstructed CT image quality, which achieves learnable interpolation in the backprojection step of filtered backprojection (FBP) and alleviates the interpolation errors. Specifically, in the proposed LInFBP, we formulate every local piece of the latent continuous function of discrete sinogram data as a linear combination of selected basis functions, and learn this continuous function by exploiting a deep network to predict the linear combination coefficients. Then, the learned latent continuous function is exploited for interpolation in backprojection step, which first time takes the advantage of deep learning for the interpolation in FBP. Extensive experiments, which encompass diverse CT scenarios, demonstrate the effectiveness of the proposed LInFBP in terms of enhanced reconstructed image quality, plug-and-play ability and generalization capability.

Figures (11)

• Figure 1: An overview of the FBP process (taking the parallel-beam imaging geometry as instance). The interpolation issue arises when sampling the value of a FBP slice from the filtered sinogram.
• Figure 2: The total framework of our model. Utilizing a trained deep learning model to predict composition weights, we achieve a continuous representation of the sinogram by combining a series of basis functions. When sampling sinogram values from positions not covered by existing detectors, we can directly obtain these transformed values from this continuous representation using relative coordinates as queries. This approach effectively mitigates interpolation errors.
• Figure 3: Illustrations of the Fourier and linear basis function set.
• Figure 4: Visual comparison of the representative images at only quarter-view case. Zoomed-in ROIs and error images indicated by the cyan boxes and and the quantitative assessments are illustrated on the corresponding images. The display window is [-160,240] HU and the zoom-in window is [60,200] HU.
• Figure 5: Visual comparison of the representative images at quarter-view with quarter-dose case. Zoomed-in ROIs and error images are indicated by the green boxes and and the quantitative assessments are illustrated on the corresponding images. The display window is [-160,240] HU and the zoom-in window is [-100,200] HU.