# Deformation corrected compressed sensing (DC-CS): a novel framework for accelerated dynamic MRI

arXiv: https://arxiv.org/abs/1405.7718 · HTML: https://mlsanity.com/paper/1405.7718/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2014.

## Built on by (most cited first, 6 of 6)

- [Accelerated Motion Correction with Deep Generative Diffusion Models](https://mlsanity.com/paper/2211.00199/) (2022)
- [LAPNet: Non-rigid Registration derived in k-space for Magnetic Resonance Imaging](https://mlsanity.com/paper/2107.09060/) (2021)
- [X-Metric: An N-Dimensional Information-Theoretic Framework for Groupwise Registration and Deep Combined Computing](https://mlsanity.com/paper/2211.01631/) (2022)
- [RED-PSM: Regularization by Denoising of Factorized Low Rank Models for Dynamic Imaging](https://mlsanity.com/paper/2304.03483/) (2023)
- [RSR-NF: Neural Field Regularization by Static Restoration Priors for Dynamic Imaging](https://mlsanity.com/paper/2503.10015/) (2025)
- [Latent-space disentanglement with untrained generator networks for the isolation of different motion types in video data](https://mlsanity.com/paper/2205.10367/) (2022)

## Abstract (arXiv)

We propose a novel deformation corrected compressed sensing (DC-CS) framework to recover dynamic magnetic resonance images from undersampled measurements. We introduce a generalized formulation that is capable of handling a wide class of sparsity/compactness priors on the deformation corrected dynamic signal. In this work, we consider example compactness priors such as sparsity in temporal Fourier domain, sparsity in temporal finite difference domain, and nuclear norm penalty to exploit low rank structure. Using variable splitting, we decouple the complex optimization problem to simpler and well understood sub problems; the resulting algorithm alternates between simple steps of shrinkage based denoising, deformable registration, and a quadratic optimization step. Additionally, we employ efficient continuation strategies to minimize the risk of convergence to local minima. The proposed formulation contrasts with existing DC-CS schemes that are customized for free breathing cardiac cine applications, and other schemes that rely on fully sampled reference frames or navigator signals to estimate the deformation parameters. The efficient decoupling enabled by the proposed scheme allows its application to a wide range of applications including contrast enhanced dynamic MRI. Through experiments on numerical phantom and in vivo myocardial perfusion MRI datasets, we demonstrate the utility of the proposed DC-CS scheme in providing robust reconstructions with reduced motion artifacts over classical compressed sensing schemes that utilize the compact priors on the original deformation un-corrected signal.