Related papers: Shape reconstruction of a conductivity inclusion u…
We present an image reconstruction algorithm for the Inverse Conductivity Problem based on reformulating the problem in terms of integral equations. We use as data the values of injected electric currents and of the corresponding induced…
The method of filtered back projection (FBP) is a widely used reconstruction technique in X-ray computerized tomography (CT), which is particularly important in clinical diagnostics. To reduce scanning times and radiation doses in medical…
In this paper, we are concerned with the recovery of the geometric shapes of inhomogeneous inclusions from the associated far field data in electrostatics and acoustic scattering. We present a local resolution analysis and show that the…
Iterative Fast Fourier Transform methods are useful for calculating the fields in composite materials and their macroscopic response. By iterating back and forth until convergence, the differential constraints are satisfied in Fourier…
In certain three-dimensional (3D) applications of photoacoustic computed tomography (PACT), including \textit{in vivo} breast imaging, hemispherical measurement apertures that enclose the object within their convex hull are employed for…
Shape from Polarization (SfP) estimates surface normals using photos captured at different polarizer rotations. Fundamentally, the SfP model assumes that light is reflected either diffusely or specularly. However, this model is not valid…
Today, three-dimensional reconstruction of objects has many applications in various fields, and therefore, choosing a suitable method for high resolution three-dimensional reconstruction is an important issue and displaying high-level…
We propose a data-driven method for recovering miss-ing parts of 3D shapes. Our method is based on a new deep learning architecture consisting of two sub-networks: a global structure inference network and a local geometry refinement…
We are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-field measurement. Using the intrinsic geometric properties…
This paper concerns a fast, one-step iterative technique of imaging extended perfectly conducting cracks with Dirichlet boundary condition. In order to reconstruct the shape of cracks from scattered field data measured at the boundary, we…
A fully algebraic approach to reconstructing one-dimensional reflectionless potentials is described. A simple and easily applicable general formula is derived, using the methods of the theory of determinants. In particular, useful…
We discuss efficient algorithms for the accurate forward and reverse evaluation of the discrete Fourier-Bessel transform (dFBT) as numerical tools to assist in the 2D polar convolution of two radially symmetric functions, relevant, e.g., to…
Calculation of the vacuum polarization, $<\phi^2(x)>$, and expectation value of the stress tensor, $<T_{\mu\nu}(x)>$, has seen a recent resurgence, notably for black hole spacetimes. To date, most calculations of this type have been done…
A two-step shape reconstruction method for diffuse optical tomography (DOT) is presented which uses adjoint fields and level sets. The propagation of near-infrared photons in tissue is modeled by the time-dependent linear transport…
The differentiable shift-variant filtered backprojection (FBP) model enables the reconstruction of cone-beam computed tomography (CBCT) data for any non-circular trajectories. This method employs deep learning technique to estimate the…
The advent of synchrotron sources has led to an increasing availability of high resolution Compton Profiles J(pz) and a consequent renewed interest in the reconstruction of the corresponding full momentum densities rho(p). We present…
We study polytopes associated to factorisations of prime powers. These polytopes have explicit descriptions either in terms of their vertices or as intersections of closed halfspaces associated to their facets. We give formulae for their…
We consider the problem of reconstructing of the boundary of an unknown inclusion together with its conductivity from the localized Dirichlet-to-Neumann map. We give an exact reconstruction procedure and apply the method to an inverse…
The Fourier transform of the indicator function of arbitrary polygons and polyhedra is computed for complex wavevectors. Using the divergence theorem and Stokes' theorem, closed expressions are obtained. Apparent singularities, all…
A robust single-shot 3D shape reconstruction technique integrating the fringe projection profilometry (FPP) technique with the deep convolutional neural networks (CNNs) is proposed in this letter. The input of the proposed technique is a…