Related papers: An explicit reconstruction algorithm for the trans…
We first give a constructive answer to the attenuated tensor tomography problem on simple surfaces. We then use this result to propose two approaches to produce vector-valued integral transforms which are fully injective over tensor fields.…
A new approach is proposed for reconstruction of images from Radon projections. Based on Fourier expansions in orthogonal polynomials of two and three variables, instead of Fourier transforms, the approach provides a new algorithm for the…
We present a new algorithm for recovering paths from their third-order signature tensors, an inverse problem in rough analysis. Our algorithm provides the exact solution to this learning problem and improves upon current approaches by an…
Tensor rank and low-rank tensor decompositions have many applications in learning and complexity theory. Most known algorithms use unfoldings of tensors and can only handle rank up to $n^{\lfloor p/2 \rfloor}$ for a $p$-th order tensor in…
In this article two new algorithms are presented that convert a given data tensor train into either a Tucker decomposition with orthogonal matrix factors or a multi-scale entanglement renormalization ansatz (MERA). The Tucker core tensor is…
Image recovery in optical interferometry is an ill-posed nonlinear inverse problem arising from incomplete power spectrum and bispectrum measurements. We reformulate this nonlin- ear problem as a linear problem for the supersymmetric rank-1…
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…
Recovering the 3D structure of an object from a single image is a challenging task due to its ill-posed nature. One approach is to utilize the plentiful photos of the same object category to learn a strong 3D shape prior for the object.…
We obtain the first polynomial-time algorithm for exact tensor completion that improves over the bound implied by reduction to matrix completion. The algorithm recovers an unknown 3-tensor with $r$ incoherent, orthogonal components in…
A fast 2-dimensional image reconstruction method is presented, which takes as input 1-dimensional data acquired from scans across a central source in different orientations. The resultant reconstructed images do not show artefacts due to…
In this paper, we study the problem of reconstructing a 3D point source model from a set of 2D projections at unknown view angles. Our method obviates the need to recover the projection angles by extracting a set of rotation-invariant…
In this paper, we propose an algorithm that allows joint refinement of camera pose and scene geometry represented by decomposed low-rank tensor, using only 2D images as supervision. First, we conduct a pilot study based on a 1D signal and…
An algorithm for 3D terrain-following area coverage path planning is presented. Multiple adjacent paths are generated that are (i) locally apart from each other by a distance equal to the working width of a machinery, while (ii)…
We present an approach for the planar surface reconstruction of a scene from images with limited overlap. This reconstruction task is challenging since it requires jointly reasoning about single image 3D reconstruction, correspondence…
In this paper, we develop a new method to automatically convert 2D line drawings from three orthographic views into 3D CAD models. Existing methods for this problem reconstruct 3D models by back-projecting the 2D observations into 3D space…
A solution to the inversion problem of scattering would offer aberration-free diffraction-limited 3D images without the resolution and depth-of-field limitations of lens-based tomographic systems. Powerful algorithms are increasingly being…
We study the problem of regularization of inverse problems adopting a purely data driven approach, by using the similarity to the method of regularization by projection. We provide an application of a projection algorithm, utilized and…
The recent years have seen a surge of interest in methods for imaging beyond the direct line of sight. The most prominent techniques rely on time-resolved optical impulse responses, obtained by illuminating a diffuse wall with an ultrashort…
Generating accurate 3D models is a challenging problem that traditionally requires explicit learning from 3D datasets using supervised learning. Although recent advances have shown promise in learning 3D models from 2D images, these methods…
By suitably generalizing the Fourier constraint projection in the difference map phasing algorithm, an object can be reconstructed from its diffraction pattern even when the latter has been incoherently averaged over a discrete group of…