Stabilizing Deep Tomographic Reconstruction Networks

Tomographic image reconstruction with deep learning (DL) is an emerging field of applied artificial intelligence, but a recent landmark study reveals that several deep reconstruction networks are unstable for computed tomography (CT) and magnetic resonance imaging (MRI). Since deep reconstruction is now a mainstream approach to achieve better tomographic image quality, stabilizing deep networks is an urgent challenge. Here we propose an Analytic Compressive Iterative Deep (ACID) framework to address this challenge. Instead of only using DL or compressed sensing, ACID consists of four modules: deep learning, compressed sensing-inspired sparsity promotion, analytic mapping, and iterative refinement. This paper shows the convergence and stability of ACID under a bounded error norm condition (a special case of the Lipschitz continuity), improves deep reconstruction quality by stabilizing an unstable deep reconstruction network in the ACID framework, and demonstrates the power of ACID in both stabilizing an unstable network and being resilient against adversarial attacks to the whole ACID workflow. In our experiments, ACID eliminated all three kinds of instabilities and significantly improved image quality in the context of the aforementioned study on the instabilities, demonstrating that data-driven reconstruction can be stabilized to outperform reconstruction using sparsity-regularized reconstruction alone. The mechanism of ACID is to synergize a deep reconstruction network trained on big data, compressed sensing-based improvement with kernel awareness, and iterative refinement to eliminate any data residual inconsistent with real data. We anticipate that this integrative closed-loop data-driven approach helps advance deep tomographic image reconstruction methods into clinical applications.