Related papers: On reconstruction formulas for the ray transform a…
This paper concerns the reconstruction of a scalar diffusion coefficient $\sigma(x)$ from redundant functionals of the form $H_i(x)=\sigma^{2\alpha}(x)|\nabla u_i|^2(x)$ where $\alpha\in\Rm$ and $u_i$ is a solution of the elliptic problem…
We perform a recursive reduction of one-loop $n$-point rank $R$ tensor Feynman integrals [in short: $(n,R)$-integrals] for $n\leq 6$ with $R\leq n$ by representing $(n,R)$-integrals in terms of $(n,R-1)$- and $(n-1,R-1)$-integrals. We use…
Weighted V-line transforms map a symmetric tensor field of order $m\ge0$ to a linear combination of certain integrals of those fields along two rays emanating from the same vertex. A significant focus of current research in integral…
We introduce a method to reconstruct an element of a Hilbert space in terms of an arbitrary finite collection of linearly independent reconstruction vectors, given a finite number of its samples with respect to any Riesz basis. As we…
Practical applications of thermoacoustic tomography require numerical inversion of the spherical mean Radon transform with the centers of integration spheres occupying an open surface. Solution of this problem is needed (both in 2-D and…
Inverse problems, such as accelerated MRI reconstruction, are ill-posed and an infinite amount of possible and plausible solutions exist. This may not only lead to uncertainty in the reconstructed image but also in downstream tasks such as…
We develop sampling formulas for high-dimensional functions in reproducing kernel Hilbert spaces, where we rely on irregular samples that are taken at determining sequences of data points. We place particular emphasis on sampling formulas…
This paper presents an iterative inversion algorithm for computed tomography image reconstruction that performs well in terms of accuracy and speed using limited data. The computational method combines an image domain technique and…
The representation theory of tensor functions is essential to constitutive modeling of materials including both mechanical and physical behaviors. Generally, material symmetry is incorporated in the tensor functions through a structural or…
The present paper deals with the discrete inverse problem of reconstructing binary matrices from their row and column sums under additional constraints on the number and pattern of entries in specified minors. While the classical…
Radio-frequency (RF) tomographic imaging is a promising technique for inferring multi-dimensional physical space by processing RF signals traversed across a region of interest. However, conventional RF tomography schemes are generally based…
The theory and computation of tensors with different tensor products play increasingly important roles in scientific computing and machine learning. Different products aim to preserve different algebraic properties from the matrix algebra,…
A unique inversion of the exponential X-ray transform of some class of symmetric 2-tensor field in a two dimensional strictly convex set is considered. The approach to inversion is based on the Cauchy problem for a Beltrami-like equation…
In this article, we study various aspects of the mixed ray transform of $(k + \ell)$-tensor fields that are symmetric in its first $k$ and last $\ell$ indices. As a first result, we derive an inversion algorithm to recover the solenoidal…
Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…
A radial transverse resonance model for two cylindrical concentric layers with different complex dielectric constants is presented. An inverse problem with four unknowns - 3 physical material parameters and one dimensional dielectric layer…
Computed Tomography (CT) reconstruction of objects with cylindrical symmetry can be performed with a single projection. When the measured rays are parallel, and the axis of symmetry is perpendicular to the optical axis, the data can be…
In this paper we study the problem of photoacoustic inversion in a weakly attenuating medium. We present explicit reconstruction formulas in such media and show that the inversion based on such formulas is moderately ill--posed. Moreover,…
We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where…
We introduce a technique for recovering a sufficiently smooth function from its ray transform over a wide class of curves in a general region of Euclidean space. The method is based on a complexification of the underlying vector fields…