4,197 research outputs found
Robust Cardiac Motion Estimation using Ultrafast Ultrasound Data: A Low-Rank-Topology-Preserving Approach
Cardiac motion estimation is an important diagnostic tool to detect heart
diseases and it has been explored with modalities such as MRI and conventional
ultrasound (US) sequences. US cardiac motion estimation still presents
challenges because of the complex motion patterns and the presence of noise. In
this work, we propose a novel approach to estimate the cardiac motion using
ultrafast ultrasound data. -- Our solution is based on a variational
formulation characterized by the L2-regularized class. The displacement is
represented by a lattice of b-splines and we ensure robustness by applying a
maximum likelihood type estimator. While this is an important part of our
solution, the main highlight of this paper is to combine a low-rank data
representation with topology preservation. Low-rank data representation
(achieved by finding the k-dominant singular values of a Casorati Matrix
arranged from the data sequence) speeds up the global solution and achieves
noise reduction. On the other hand, topology preservation (achieved by
monitoring the Jacobian determinant) allows to radically rule out distortions
while carefully controlling the size of allowed expansions and contractions.
Our variational approach is carried out on a realistic dataset as well as on a
simulated one. We demonstrate how our proposed variational solution deals with
complex deformations through careful numerical experiments. While maintaining
the accuracy of the solution, the low-rank preprocessing is shown to speed up
the convergence of the variational problem. Beyond cardiac motion estimation,
our approach is promising for the analysis of other organs that experience
motion.Comment: 15 pages, 10 figures, Physics in Medicine and Biology, 201
Robust Rotation Synchronization via Low-rank and Sparse Matrix Decomposition
This paper deals with the rotation synchronization problem, which arises in
global registration of 3D point-sets and in structure from motion. The problem
is formulated in an unprecedented way as a "low-rank and sparse" matrix
decomposition that handles both outliers and missing data. A minimization
strategy, dubbed R-GoDec, is also proposed and evaluated experimentally against
state-of-the-art algorithms on simulated and real data. The results show that
R-GoDec is the fastest among the robust algorithms.Comment: The material contained in this paper is part of a manuscript
submitted to CVI
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