Related papers: Shape reconstruction of a conductivity inclusion u…
In this study, we introduce a Fourier series-based trainable filter for computed tomography (CT) reconstruction within the filtered backprojection (FBP) framework. This method overcomes the limitation in noise reduction by optimizing…
Magnetic resonance imaging (MRI) based electrical properties tomography (EPT) is the quantification of the conductivity and permittivity of different tissues. These electrical properties can be obtained through different reconstruction…
We study the problem of recovering a collection of $n$ numbers from the evaluation of $m$ power sums. This yields a system of polynomial equations, which can be underconstrained ($m < n$), square ($m = n$), or overconstrained ($m > n$).…
In this paper we derive a new recovery procedure for the reconstruction of extended exponential sums of the form $y(t) = \sum_{j=1}^{M} \left( \sum_{m=0}^{n_j} \, \gamma_{j,m} \, t^{m} \right) {\mathrm e}^{2\pi \lambda_j t}$, where the…
A feature-mapping framework for inverse reconstruction of density-based topology optimization results is proposed. Unlike SIMP, whose voxelized outputs are hard to interpret or reuse, the method represents designs with high-level geometric…
Existing depth sensors are imperfect and may provide inaccurate depth values in challenging scenarios, such as in the presence of transparent or reflective objects. In this work, we present a general framework that leverages polarization…
In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…
When constructing high-order schemes for solving hyperbolic conservation laws, the corresponding high-order reconstructions are commonly performed in characteristic spaces to eliminate spurious oscillations as much as possible. For…
In this paper we analyze the shape derivative of a cost functional appearing in image restoration.
We provide a simple and new induction based treatment of the problem of distinguishing cusp forms from the growth of the Fourier coefficients of modular forms. Our approach gives the best possible ranges of the weights for this problem, and…
We first present some identities involving the Pochhammer symbol (rising factorial). We also recall and present some new properties of the Jacobi polynomials. We use them to expand a general hypergeometric function in an orthogonal series…
We improve and generalize a resummation method of post-Newtonian multipolar waveforms from circular compact binaries introduced in Refs. \cite{Damour:2007xr,Damour:2007yf}. One of the characteristic features of this resummation method is to…
In this paper, we develop a factorization method to reconstruct cavities in a heat conductor by knowing the Neumann-to-Dirichlet map at the boundary of this conductor. The factorization method is a very well known reconstruction method for…
The objective of electrical impedance tomography (EIT) is to reconstruct the internal conductivity of a physical body based on current and voltage measurements at the boundary of the body. In many medical applications the exact shape of the…
Phase reconstruction is important in transmission electron microscopy for structural studies. We describe electron Fourier ptychography and its application to phase reconstruction of both radiation-resistant and beam-sensitive materials. We…
We study the shape reconstruction of an inclusion from the {faraway} measurement of the associated electric field. This is an inverse problem of practical importance in biomedical imaging and is known to be notoriously ill-posed. By…
The Taylor expansion of wave fields with respect to shape parameters has a wide range of applications in wave scattering problems, including inverse scattering, optimal design, and uncertainty quantification. However, deriving the high…
We study the use of transformers to reconstruct the compositions of tensor products of two-dimensional rational conformal field theories (RCFTs) based on their low-energy spectra. The task is challenging due to its combinatorial nature. The…
This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…
Recovering the 3D shape of transparent objects using a small number of unconstrained natural images is an ill-posed problem. Complex light paths induced by refraction and reflection have prevented both traditional and deep multiview stereo…