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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<jats:sup>4<\/jats:sup> system matrix size. This cannot practically scale to realistic data sizes such as 512<jats:sup>4<\/jats:sup> and 512<jats:sup>6<\/jats:sup> 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<jats:sup>4<\/jats:sup> 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 <jats:italic>feasibility<\/jats:italic> demonstration of full-scale learnt reconstruction, whereas more developments will be needed to demonstrate <jats:italic>superiority<\/jats:italic> 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.<\/jats:p>","DOI":"10.1186\/s42492-022-00127-y","type":"journal-article","created":{"date-parts":[[2022,12,9]],"date-time":"2022-12-09T08:02:42Z","timestamp":1670572962000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Deep learning tomographic reconstruction through hierarchical decomposition of domain transforms"],"prefix":"10.1186","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9368-8881","authenticated-orcid":false,"given":"Lin","family":"Fu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bruno","family":"De Man","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2022,12,9]]},"reference":[{"key":"127_CR1","doi-asserted-by":"publisher","unstructured":"Wang G, Ye JC, De Man B (2020) Deep learning for tomographic image reconstruction. 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