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Indirect image registration is a promising technique to improve imagereconstruction quality by providing a shape prior for the reconstruction task.In this paper, we propose a novel hybrid method that seeks to reconstruct highquality images from few measurements whilst requiring low computational cost.With this purpose, our framework intertwines indirect registration andreconstruction tasks is a single functional. It is based on two majornovelties. Firstly, we introduce a model based on deep nets to solve theindirect registration problem, in which the inversion and registration mappingsare recurrently connected through a fixed-point interaction based sparseoptimisation. Secondly, we introduce specific inversion blocks, that use theexplicit physical forward operator, to map the acquired measurements to theimage reconstruction. We also introduce registration blocks based deep nets topredict the registration parameters and warp transformation accurately andefficiently. We demonstrate, through extensive numerical and visualexperiments, that our framework outperforms significantly classicreconstruction schemes and other bi-task method; this in terms of both imagequality and computational time. Finally, we show generalisation capabilities ofour approach by demonstrating their performance on fast Magnetic ResonanceImaging (MRI), sparse view computed tomography (CT) and low dose CT withmeasurements much below the Nyquist limit.

Rethinking Medical Image Reconstruction via Shape Prior, Going Deeper and Faster: Deep Joint Indirect Registration and Reconstruction