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The measurement of cellular traction forces on soft elastic substrates has become a standard tool for many labs working on mechanobiology. Here we review the basic principles and different variants of this approach. In general, the…
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…
A novel computational, non-iterative and noise-robust reconstruction method is introduced for the planar anisotropic inverse conductivity problem. The method is based on bypassing the unstable step of the reconstruction of the values of the…
In vector tomography (VT), the aim is to reconstruct an unknown multi-dimensional vector field using line integral data. In the case of a 2-dimensional VT, two types of line integral data are usually required. These data correspond to…
We study extensions of compressive sensing and low rank matrix recovery (matrix completion) to the recovery of low rank tensors of higher order from a small number of linear measurements. While the theoretical understanding of low rank…
On the lattice, a renormalization group (RG) flow for two-dimensional partition functions expressed as a tensor network can be obtained using the tensor network renormalization (TNR) algorithm [G. Evenbly, G. Vidal, Phys. Rev. Lett. 115…
In this work, we study a set of generalized Radon transforms over symmetric $m$-tensor fields in $\mathbb{R}^n$. The longitudinal/transversal Radon transform and corresponding weighted integral transforms for symmetric $m$-tensor field are…
Structural reconstruction of plant roots from MRI is challenging, because of low resolution and low signal-to-noise ratio of the 3D measurements which may lead to disconnectivities and wrongly connected roots. We propose a two-stage…
The relation between Radon transform and orthogonal expansions of a function on the unit ball in $\RR^d$ is exploited. A compact formula for the partial sums of the expansion is given in terms of the Radon transform, which leads to…
We present a reconstruction method that stably recovers the real valued, symmetric tensors compactly supported in the Euclidean plane, from knowledge of their attenuated momenta ray transform. The problem is recast as an inverse boundary…
In this paper various extensions of the design strategy of transformation media are proposed. We show that it is possible to assign different transformed spaces to the field strength tensor (electric field and magnetic induction) and to the…
Deep learning has been widely employed to solve the Electrical Impedance Tomography (EIT) image reconstruction problem. Most existing physical model-based and learning-based approaches focus on 2D EIT image reconstruction. However, when…
X-ray tomography has been studied in various fields. Although a great deal of effort has been directed at reconstructing the projection image set from a rigid-type specimen, little attention has been addressed to the reconstruction of…
We propose a method for deriving equivalent one-dimensional models for slender non-linear structures. The approach is designed to be broadly applicable, and can handle in principle finite strains, finite rotations, arbitrary cross-sections…
We present a novel numerical method that allows the calculation of nonlinear force-free magnetostatic solutions above a boundary surface on which only the distribution of the normal magnetic field component is given. The method relies on…
A light field records numerous light rays from a real-world scene. However, capturing a dense light field by existing devices is a time-consuming process. Besides, reconstructing a large amount of light rays equivalent to multiple light…
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…
This paper considers the reconstruction problem in Acousto-Electrical Tomography, i.e., the problem of estimating a spatially varying conductivity in a bounded domain from measurements of the internal power densities resulting from…
This paper concerns the reconstruction of a complex-valued anisotropic tensor $\gamma=\sigma+\i\omega\varepsilon$ from knowledge of several internal magnetic fields $H$, where $H$ satisfies the anisotropic Maxwell system on a bounded domain…
In dual-energy computed tomography (DECT), the X-ray tube energy pair often changes depending on the target organ or patient obesity. In practice, it makes difficult to apply deep learning (DL) based algorithms for image reconstruction…