Shape-based image reconstruction using linearized deformations

Öktem, Ozan; Chen, Chong; Domaniç, Nevzat Onur; Ravikumar, Pradeep; Bajaj, Chandrajit L.

doi:10.1088/1361-6420/aa55af

Cited by 13 publications

(30 citation statements)

References 55 publications

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“…Remark 3. The time-discretized version (42) can be also written such that the image in the first gate is the template:…”

Section: Time-discretized Versionmentioning

confidence: 99%

“…More precisely, a fixed velocity field ν yields the flow of diffeomorphisms φ t through ODE (11). Hence, the spatiotemporal reconstruction problem (42) reduces to the following modified static image reconstruction problem:…”

Section: Time-discretized Versionmentioning

confidence: 99%

“…More importantly, the optimal solution of the timediscretized problem is consistent with that of the time-continuous one. Most of the computationally demanding parts relate to implementing the linearized deformations [42].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A New Variational Model for Joint Image Reconstruction and Motion Estimation in Spatiotemporal Imaging

Chen¹,

Gris²,

Öktem³

2019

SIAM J. Imaging Sci.

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We propose a new variational model for joint image reconstruction and motion estimation in spatiotemporal imaging, which is investigated along a general framework that we present with shape theory. This model consists of two components, one for conducting modified static image reconstruction, and the other performs sequentially indirect image registration. For the latter, we generalize the large deformation diffeomorphic metric mapping framework into the sequentially indirect registration setting. The proposed model is compared theoretically against alternative approaches (optical flow based model and diffeomorphic motion models), and we demonstrate that the proposed model has desirable properties in terms of the optimal solution. The theoretical derivations and efficient algorithms are also presented for a time-discretized scenario of the proposed model, which show that the optimal solution of the time-discretized version is consistent with that of the time-continuous one, and most of the computational components is the easy-implemented linearized deformation. The complexity of the algorithm is analyzed as well. This work is concluded by some numerical examples in 2D space + time tomography with very sparse and/or highly noisy data.

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“…Remark 3. The time-discretized version (42) can be also written such that the image in the first gate is the template:…”

Section: Time-discretized Versionmentioning

confidence: 99%

Section: Time-discretized Versionmentioning

confidence: 99%

See 1 more Smart Citation

A New Variational Model for Joint Image Reconstruction and Motion Estimation in Spatiotemporal Imaging

Chen¹,

Gris²,

Öktem³

2019

SIAM J. Imaging Sci.

Self Cite

View full text Add to dashboard Cite

show abstract

“…In image registration, the goal is to find a reasonable deformation of a given template image so that it matches a given target image as closely as possible according to a predefined similarity measure, see [40,39] for an introduction. When the target image is unknown and only given through indirect measurements, it is referred to as indirect image registration and has been explored only recently [12,24,31,45]. As a result, a deformation together with a transformed template can be computed from tomographic data.…”

Section: Introductionmentioning

confidence: 99%

“…In comparison to abovementioned existing methods for indirect image registration, such as [12,24,31,45], our method is conceptually different in several ways. The first difference concerns the discretisation.…”

Section: Introductionmentioning

confidence: 99%

Template-Based Image Reconstruction from Sparse Tomographic Data

et al. 2019

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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 massand 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.

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Incorporation of a Deformation Prior in Image Reconstruction

Gris

2019

J Math Imaging Vis

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This article presents a method to incorporate a deformation prior in image reconstruction via the formalism of deformation modules. The framework of deformation modules allows to build diffeomorphic deformations that satisfy a given structure. The idea is to register a template image against the indirectly observed data via a modular deformation, incorporating this way the deformation prior in the reconstruction method. We show that this is a well-defined regularization method (proving existence, stability and convergence) and present numerical examples of reconstruction from 2-D tomographic simulations and partially-observed images.

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Shape-based image reconstruction using linearized deformations

Cited by 13 publications

References 55 publications

A New Variational Model for Joint Image Reconstruction and Motion Estimation in Spatiotemporal Imaging

A New Variational Model for Joint Image Reconstruction and Motion Estimation in Spatiotemporal Imaging

Template-Based Image Reconstruction from Sparse Tomographic Data

Incorporation of a Deformation Prior in Image Reconstruction

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