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Fast Gradient Methods for Data-Consistent Local Super-Resolution of Medical Images

Junqi Tang, Guixian Xu, Jinglai Li

TL;DR

The paper tackles restoring and refining details in small regions of tomographic medical images without re‑computing a full high‑resolution reconstruction. It introduces data‑consistent local zoom‑in methods (LZFG and its gradient‑restart variant R‑LZFG) that solve ROI‑specific, proximal‑gradient problems using up/down sampling to connect high/low resolutions and measurement data. The approach offers significant computational savings and improved local detail recovery (2–5 dB PSNR gains) over naive global zoom, with convergence acceleration via adaptive restarts. This framework enables real‑time, clinically usable local super‑resolution and can be extended to integrate deep priors in future work.

Abstract

In this work, we propose a new paradigm of iterative model-based reconstruction algorithms for providing real-time solution for zooming-in and refining a region of interest in medical and clinical tomographic images. This algorithmic framework is tailored for a clinical need in medical imaging practice that after a reconstruction of the full tomographic image, the clinician may believe that some critical parts of the image are not clear enough, and may wish to see clearer these regions of interest. A naive approach (which is highly not recommended) would be to perform the global reconstruction of a higher resolution image, which has two major limitations: first, it is computationally inefficient, and second, the image regularization is still applied globally, which may over-smooth some local regions. Furthermore, if one wishes to fine-tune the regularization parameter for local parts, it would be computationally infeasible in practice for the case of using global reconstruction. Our new iterative approaches for such tasks are based on jointly utilizing the measurement information, efficient up-sampling/down-sampling across image spaces, and locally adjusted image prior for efficient and high-quality post-processing. The numerical results in low-dose X-ray CT image local zoom-in demonstrate the effectiveness of our approach.

Fast Gradient Methods for Data-Consistent Local Super-Resolution of Medical Images

TL;DR

The paper tackles restoring and refining details in small regions of tomographic medical images without re‑computing a full high‑resolution reconstruction. It introduces data‑consistent local zoom‑in methods (LZFG and its gradient‑restart variant R‑LZFG) that solve ROI‑specific, proximal‑gradient problems using up/down sampling to connect high/low resolutions and measurement data. The approach offers significant computational savings and improved local detail recovery (2–5 dB PSNR gains) over naive global zoom, with convergence acceleration via adaptive restarts. This framework enables real‑time, clinically usable local super‑resolution and can be extended to integrate deep priors in future work.

Abstract

In this work, we propose a new paradigm of iterative model-based reconstruction algorithms for providing real-time solution for zooming-in and refining a region of interest in medical and clinical tomographic images. This algorithmic framework is tailored for a clinical need in medical imaging practice that after a reconstruction of the full tomographic image, the clinician may believe that some critical parts of the image are not clear enough, and may wish to see clearer these regions of interest. A naive approach (which is highly not recommended) would be to perform the global reconstruction of a higher resolution image, which has two major limitations: first, it is computationally inefficient, and second, the image regularization is still applied globally, which may over-smooth some local regions. Furthermore, if one wishes to fine-tune the regularization parameter for local parts, it would be computationally infeasible in practice for the case of using global reconstruction. Our new iterative approaches for such tasks are based on jointly utilizing the measurement information, efficient up-sampling/down-sampling across image spaces, and locally adjusted image prior for efficient and high-quality post-processing. The numerical results in low-dose X-ray CT image local zoom-in demonstrate the effectiveness of our approach.
Paper Structure (7 sections, 9 equations, 3 figures)

This paper contains 7 sections, 9 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Data-Consistent Local Zoom-in
  3. Optimization Framework
  4. Exploiting local strong-convexity: Gradient-restart for accelerating LZFG
  5. Computational advantages over repeating the full-scale global reconstruction
  6. Numerical Experiments
  7. Conclusion

Figures (3)

  • Figure 1: Quantitative results for the 4 local zoom-in experiments on CT images. The first plot corresponds to the first example presented in Fig.\ref{['e2']}, and the second plot corresponds to the second example presented in Fig.\ref{['e4']}. From the PSNR results we can observe that our proposed data-consistent local zoom-in method LZFG achieves significantly improved reconstruction accuracy compare to the naive approach which directly zoom-in the first-stage reconstruction without utilizing the measurement data.
  • Figure 2: Local zoom-in results for low-dose fan-beam CT image (example 1 with $I_0 = 2 \times 10^{3}$ and $A \in \mathbb{R}^{92160 \times 65536}$)
  • Figure 3: Local zoom-in results for sparse-view fan-beam CT image (example 2 with $I_0 = 2 \times 10^{4}$ and $A \in \mathbb{R}^{13680 \times 65536}$)