Indirect Image Registration with Large Diffeomorphic Deformations

The paper adapts the large deformation diffeomorphic metric mapping framework for image registration to the indirect setting where a template is registered against a target that is given through indirect noisy observations. The registration uses diffeomorphisms that transform the template through a (group) action. These diffeomorphisms are generated by solving a flow equation that is defined by a velocity field with certain regularity. The theoretical analysis includes a proof that indirect image registration has solutions (existence) that are stable and that converge as the data error tends so zero, so it becomes a well-defined regularization method. The paper concludes with examples of indirect image registration in 2D tomography with very sparse and/or highly noisy data.Comment: 43 pages, 4 figures, 1 table; revise

Phase retrieval via non-rigid image registration

Phase retrieval is the numerical procedure of recovering a complex-valued signal from knowledge about its amplitude and some additional information. Here, an indirect registration procedure, based on the large deformation diffeomorphic metric mapping (LDDMM) formalism, is investigated as a phase retrieval method for coherent diffractive imaging. The method attempts to find a deformation which transforms an initial, template image to match an unknown target image by comparing the diffraction pattern to the data. The exterior calculus framework is used to treat different types of deformations in a unified and coordinate-free way. The algorithm performance with respect to measurement noise, image topology, and particular action are explored through numerical examples

Image reconstruction through metamorphosis

International audienceThis article adapts the framework of metamorphosis to the resolution of inverse problems with shape prior. The metamorphosis framework allows to transform an image via a balance between geometrical deformations and changes in intensities (that can for instance correspond to the appearance of a new structure). The idea developed here is to reconstruct an image from noisy and indirect observations by registering, via metamorphosis, a template to the observed data. Unlike a registration with only geometrical changes, this framework gives good results when intensities of the template are poorly chosen. We show that this method is a well-defined regularization method (proving existence, stability and convergence) and present several numerical examples

A method for quantitative analysis of regional lung ventilation using deformable image registration of CT and hybrid hyperpolarized gas/H-1 MRI

Hyperpolarized gas magnetic resonance imaging (MRI) generates highly detailed maps of lung ventilation and physiological function while CT provides corresponding anatomical and structural information. Fusion of such complementary images enables quantitative analysis of pulmonary structure-function. However, direct image registration of hyperpolarized gas MRI to CT is problematic, particularly in lungs whose boundaries are difficult to delineate due to ventilation heterogeneity. This study presents a novel indirect method of registering hyperpolarized gas MRI to CT utilizing 1H-structural MR images that are acquired in the same breath-hold as the gas MRI. The feasibility of using this technique for regional quantification of ventilation of specific pulmonary structures is demonstrated for the lobes. The direct and indirect methods of hyperpolarized gas MRI to CT image registration were compared using lung images from 15 asthma patients. Both affine and diffeomorphic image transformations were implemented. Registration accuracy was evaluated using the target registration error (TRE) of anatomical landmarks identified on 1H MRI and CT. The Wilcoxon signed-rank test was used to test statistical significance. For the affine transformation, the indirect method of image registration was significantly more accurate than the direct method (TRE = 14.7  ±  3.2 versus 19.6  ±  12.7 mm, p = 0.036). Using a deformable transformation, the indirect method was also more accurate than the direct method (TRE = 13.5  ±  3.3 versus 20.4  ±  12.8 mm, p = 0.006). Accurate image registration is critical for quantification of regional lung ventilation with hyperpolarized gas MRI within the anatomy delineated by CT. Automatic deformable image registration of hyperpolarized gas MRI to CT via same breath-hold 1H MRI is more accurate than direct registration. Potential applications include improved multi-modality image fusion, functionally weighted radiotherapy planning, and quantification of lobar ventilation in obstructive airways disease

Joint Image Reconstruction and Motion Estimation for Spatiotemporal Imaging

International audienceWe propose a variational model for joint image reconstruction and motion estimation applicable to spatiotemporal imaging. This model consists of two parts, one that conducts image reconstruction in a static setting and another that estimates the motion by solving a sequence of coupled indirect image registration problems, each formulated within the large deformation diffeomorphic metric mapping framework. The proposed model is compared against alternative approaches (optical flow based model and diffeomorphic motion models). Next, we derive efficient algorithms for a time-discretized setting and show that the optimal solution of the time-discretized formulation is consistent with that of the time-continuous one. The complexity of the algorithm is characterized and we conclude by giving some numerical examples in 2D space + time tomography with very sparse and/or highly noisy dat

Template-Based Image Reconstruction from Sparse Tomographic Data

Funder: University of CambridgeAbstract: We propose a variational regularisation approach for the problem of template-based image reconstruction from indirect, noisy measurements as given, for instance, in X-ray computed tomography. An image is reconstructed from such measurements by deforming a given template image. The image registration is directly incorporated into the variational regularisation approach in the form of a partial differential equation that models the registration as either mass- or intensity-preserving transport from the template to the unknown reconstruction. We provide theoretical results for the proposed variational regularisation for both cases. In particular, we prove existence of a minimiser, stability with respect to the data, and convergence for vanishing noise when either of the abovementioned equations is imposed and more general distance functions are used. Numerically, we solve the problem by extending existing Lagrangian methods and propose a multilevel approach that is applicable whenever a suitable downsampling procedure for the operator and the measured data can be provided. Finally, we demonstrate the performance of our method for template-based image reconstruction from highly undersampled and noisy Radon transform data. We compare results for mass- and intensity-preserving image registration, various regularisation functionals, and different distance functions. Our results show that very reasonable reconstructions can be obtained when only few measurements are available and demonstrate that the use of a normalised cross correlation-based distance is advantageous when the image intensities between the template and the unknown image differ substantially