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Intra-scan rigid-body motion is a costly and ubiquitous problem in clinical magnetic resonance imaging (MRI) of the head.State-of-the-art methods for retrospective motion correction in MRI are often computationally expensive or in the case of image-to-image deep learning (DL) based methods can be prone to undesired alterations of the image (hallucinations). In this work we introduce a novel rigid-body motion correction method which combines the advantages of classical model-driven and data-consistency (DC) preserving approaches with a novel DL algorithm, to provide fast and robust retrospective motion correction.The proposed Motion Parameter Estimating Densenet (MoPED) retrospectively estimates subject head motion during MRI acquisitions using a DL network with DenseBlocks and multitask learning. It quantifies the 2D rigid in-plane motion parameters slice-wise for each echo train (ET) of a Cartesian T2-weighted 2D Turbo-Spin-Echo sequence. The network receives a center patch of the motion corrupted k-space as well as an additional motion-free low-resolution reference scan to provide the ground truth orientation. The supervised training utilizes motion simulations based on 28 acquisitions with subject-wise training, validation, and test data splits of 70%, 23%, and 7%. During inference, MoPED is embedded in an iterative DC-driven motion correction algorithm which alternatingly updates estimates of the motion parameters and motion-corrected low-resolution k-space data. The estimated motion parameters are then used to reconstruct the final motion corrected image. The mean absolute/squared error and the Pearson correlation coefficient were used to analyze the motion parameter estimation quality on in-silico data in a quantitative evaluation. Structural similarity (SSIM), DC error and root mean squared error (RMSE) were used as metrics of image quality improvement. Furthermore, the generalization capability of the network was analyzed on 2 in-vivo motion volumes with 28 slices each and on one simulated T1-weighted volume.The motion estimation achieves a Pearson correlation of 0.968 to the simulated ground-truth of the 2,433 test data slices used. In-silico results indicate that MoPED decreases the time for the optimization by a factor of around 27 compared to a conventional method and is able to reduce the RMSE of the reconstructions and average DC error by more than a factor of two compared to uncorrected images. In-vivo experiments show a decrease in computation time by a factor of around 20, a RMSE decrease from 0.055 to 0.033 and an SSIM increase from 0.795 to 0.862. Furthermore, contrast independence is demonstrated as MoPED is also able to correct T1-weighted images in simulations without retraining. Due to the model-based correction, no hallucinations were observed.Incorporating DL in a model-based motion correction algorithm shows great benefit on the optimization and computation time. The k-space-based estimation also allows a data consistent correction and therefore avoids the risk of hallucinations of image-to-image approaches. This article is protected by copyright. All rights reserved.