相关论文: Using the Navier-Cauchy equation for motion estima…
We consider the inverse shape and parameter problem for detecting corrosion from partial boundary measurements. This problem models the non-destructive testing for a partially buried object from electrostatic measurements on the accessible…
We develop in this paper a generic Bayesian framework for the joint estimation of motion and recovery of missing data in a damaged video sequence. Using standard maximum a posteriori to variational formulation rationale, we derive generic…
We consider the problem of reconstruction of the Cauchy data for the wave equation in $\mathbb{R}^3$ and $\mathbb{R}^2$ by the measurements of its solution on the boundary of the unit ball.
We study regularity and decay properties for the solutions of the Cauchy problem for time-fractional partial differential equations, with tempered initial data, belonging to suitable (weighted) Sobolev spaces, associated with a differential…
This paper proposes a novel framework to reconstruct the dynamic magnetic resonance images (DMRI) with motion compensation (MC). Due to the inherent motion effects during DMRI acquisition, reconstruction of DMRI using motion…
Motion during acquisition of a set of projections can lead to significant motion artifacts in computed tomography reconstructions despite fast acquisition of individual views. In cases such as cardiac imaging, motion may be unavoidable and…
A comprehensive convergence and stability analysis of some probabilistic numerical methods designed to solve Cauchy-type inverse problems is performed in this study. Such inverse problems aim at solving an elliptic partial differential…
Cone Beam Computed Tomography (CBCT) is widely used in dentistry for diagnostics and treatment planning. CBCT Imaging has a long acquisition time and consequently, the patient is likely to move. This motion causes significant artifacts in…
We consider surface finite elements and a semi-implicit time stepping scheme to simulate fluid deformable surfaces. Such surfaces are modeled by incompressible surface Navier-Stokes equations with bending forces. Here, we consider closed…
Direct observation of nanoscale transformations in three dimensions (3D) is essential for understanding materials evolution under operating conditions, yet dynamic electron tomography remains limited by slow tilt series acquisition and by…
The forward problem here is the Cauchy problem for a 1D hyperbolic PDE with a variable coefficient in the principal part of the operator. That coefficient is the spatially distributed dielectric constant. The inverse problem consists of the…
Estimation of internal body motion with high spatio-temporal resolution can greatly benefit MR-guided radiotherapy/interventions and cardiac imaging, but remains a challenge to date. In image-based methods, where motion is indirectly…
The paper presents a reformulation of some of the most basic entities and equations of linear elasticity - the stress and strain tensor, the Cauchy Navier equilibrium equations, material equations for linear isotropic bodies - in a modern…
We consider the Cauchy problem for the wave equation in $\Omega\times{\mathbb R}$ with data given on some part of the boundary $\partial\Omega\times{\mathbb R}$. We provide a reconstruction algorithm for this problem based on analytic…
In fully sampled cardiac MR (CMR) acquisitions, motion can lead to corruption of k-space lines, which can result in artefacts in the reconstructed images. In this paper, we propose a method to automatically detect and correct motion-related…
Numerous applications in signal processing have benefited from the theory of compressed sensing which shows that it is possible to reconstruct signals sampled below the Nyquist rate when certain conditions are satisfied. One of these…
We investigate the problem of estimating the 3D shape of an object defined by a set of 3D landmarks, given their 2D correspondences in a single image. A successful approach to alleviating the reconstruction ambiguity is the 3D deformable…
This paper presents a new iterative reconstruction method to provide high-resolution images of shear modulus and viscosity via the internal measurement of displacement fields in tissues. To solve the inverse problem, we compute the…
Reconstructing high-quality images from undersampled dynamic MRI data is a challenging task and important for the success of this imaging modality. To remedy the naturally occurring artifacts due to measurement undersampling, one can…
Reconstructing dynamic, time-varying scenes with computed tomography (4D-CT) is a challenging and ill-posed problem common to industrial and medical settings. Existing 4D-CT reconstructions are designed for sparse sampling schemes that…