20 research outputs found
Divergence-free Wavelets and High Order Regularization
International audienceExpanding on a wavelet basis the solution of an inverse problem provides several advantages. Wavelet bases yield a natural and efficient multiresolution analysis. The continuous representation of the solution with wavelets enables analytical calculation of regularization integrals over the spatial domain. By choosing differentiable wavelets, high-order derivative regularizers can be designed, either taking advantage of the wavelet differentiation properties or via the basis's mass and stiffness matrices. Moreover, differential constraints on vector solutions, such as the divergence-free constraint in physics, can be handled with biorthogonal wavelet bases. This paper illustrates these advantages in the particular case of fluid flows motion estimation. Numerical results on synthetic and real images of incompressible turbulence show that divergence-free wavelets and high-order regularizers are particularly relevant in this context
Regional flux analysis for discovering and quantifying anatomical changes: An application to the brain morphometry in Alzheimer's disease
International audienceIn this study we introduce the regional flux analysis, a novel approach to deformation based morphometry based on the Helmholtz decomposition of deformations parameterized by stationary velocity fields. We use the scalar pressure map associated to the irrotational component of the deformation to discover the critical regions of volume change. These regions are used to consistently quantify the associated measure of volume change by the probabilistic integration of the flux of the longitudinal deformations across the boundaries. The presented framework unifies voxel-based and regional approaches, and robustly describes the volume changes at both group-wise and subject-specific level as a spatial process governed by consistently defined regions. Our experiments on the large cohorts of the ADNI dataset show that the regional flux analysis is a powerful and flexible instrument for the study of Alzheimer's disease in a wide range of scenarios: cross-sectional deformation based morphometry, longitudinal discovery and quantification of group-wise volume changes, and statistically powered and robust quantification of hippocampal and ventricular atrophy
Image Guided Respiratory Motion Analysis: Time Series and Image Registration.
The efficacy of Image guided radiation therapy (IGRT) systems relies on accurately extracting, modeling and predicting tumor movement with imaging techniques. This thesis
investigates two key problems associated with such systems: motion modeling and image
processing. For thoracic and upper abdominal tumors, respiratory motion is the dominant
factor for tumor movement. We have studied several special structured time series analysis techniques to incorporate the semi-periodicity characteristics of respiratory motion.
The proposed methods are robust towards large variations among fractions and populations; the algorithms perform stably in the presence of sparse radiographic observations
with noise. We have proposed a subspace projection method to quantitatively evaluate the
semi-periodicity of a given observation trace; a nonparametric local regression approach
for real-time prediction of respiratory motion; a state augmentation scheme to model hysteresis; and an ellipse tracking algorithm to estimate the trend of respiratory motion in
real time. For image processing, we have focused on designing regularizations to account
for prior information in image registration problems. We investigated a penalty function design that accommodates tissue-type-dependent elasticity information. We studied a class of discontinuity preserving regularizers that yield smooth deformation estimates
in most regions, yet allow discontinuities supported by data. We have further proposed a
discriminate regularizer that preserves shear discontinuity, but discourages folding or vacuum generating flows. In addition, we have initiated a preliminary principled study on the
fundamental performance limit of image registration problems. We proposed a statistical
generative model to account for noise effect in both source and target images, and investigated the approximate performance of the maximum-likelihood estimator corresponding
to the generative model and the commonly adopted M-estimator. A simple example suggests that the approximation is reasonably accurate.
Our studies in both time series analysis and image registration constitute essential
building-blocks for clinical applications such as adaptive treatment. Besides their theoretical interests, it is our sincere hope that with further justifications, the proposed techniques
would realize its clinical value, and improve the quality of life for patients.Ph.D.Electrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/60673/1/druan_1.pd
Proceedings of the FEniCS Conference 2017
Proceedings of the FEniCS Conference 2017 that took place 12-14 June 2017 at the University of Luxembourg, Luxembourg
New Directions for Contact Integrators
Contact integrators are a family of geometric numerical schemes which
guarantee the conservation of the contact structure. In this work we review the
construction of both the variational and Hamiltonian versions of these methods.
We illustrate some of the advantages of geometric integration in the
dissipative setting by focusing on models inspired by recent studies in
celestial mechanics and cosmology.Comment: To appear as Chapter 24 in GSI 2021, Springer LNCS 1282