# Deformable Groupwise Image Registration using Low-Rank and Sparse Decomposition

arXiv: https://arxiv.org/abs/2001.03509 · HTML: https://mlsanity.com/paper/2001.03509/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jan 2020.

## Built on by (most cited first, 1 of 1)

- [Improve Myocardial Strain Estimation based on Deformable Groupwise Registration with a Locally Low-Rank Dissimilarity Metric](https://mlsanity.com/paper/2311.07348/) (2023)

## Abstract (arXiv)

Low-rank and sparse decompositions and robust PCA (RPCA) are highly successful techniques in image processing and have recently found use in groupwise image registration. In this paper, we investigate the drawbacks of the most common RPCA-dissimi-larity metric in image registration and derive an improved version. In particular, this new metric models low-rank requirements through explicit constraints instead of penalties and thus avoids the pitfalls of the established metric. Equipped with total variation regularization, we present a theoretically justified multilevel scheme based on first-order primal-dual optimization to solve the resulting non-parametric registration problem. As confirmed by numerical experiments, our metric especially lends itself to data involving recurring changes in object appearance and potential sparse perturbations. We numerically compare its peformance to a number of related approaches.