Deep learning tomographic reconstruction through hierarchical decomposition of domain transforms

Deep learning (DL) has shown unprecedented performance for many image analysis and image enhancement tasks. Yet, solving large-scale inverse problems like tomographic reconstruction remains challenging for DL. These problems involve non-local and space-variant integral transforms between the input and output domains, for which no efficient neural network models are readily available. A prior attempt to solve tomographic reconstruction problems with supervised learning relied on a brute-force fully connected network and only allowed reconstruction with a 128(4) system matrix size. This cannot practically scale to realistic data sizes such as 512(4) and 512(6) for three-dimensional datasets. Here we present a novel framework to solve such problems with DL by casting the original problem as a continuum of intermediate representations between the input and output domains. The original problem is broken down into a sequence of simpler transformations that can be well mapped onto an efficient hierarchical network architecture, with exponentially fewer parameters than a fully connected network would need. We applied the approach to computed tomography (CT) image reconstruction for a 512(4) system matrix size. This work introduces a new kind of data-driven DL solver for full-size CT reconstruction without relying on the structure of direct (analytical) or iterative (numerical) inversion techniques. This work presents a feasibility demonstration of full-scale learnt reconstruction, whereas more developments will be needed to demonstrate superiority relative to traditional reconstruction approaches. The proposed approach is also extendable to other imaging problems such as emission and magnetic resonance reconstruction. More broadly, hierarchical DL opens the door to a new class of solvers for general inverse problems, which could potentially lead to improved signal-to-noise ratio, spatial resolution and computational efficiency in various areas.