Related papers: On the difference between solutions of discrete to…
The problem of determining three-dimensional density fields from single two-dimensional projections is hopelessly underdetermined without additional assumptions. While parameterized inversions are typically used to solve this problem, we…
Tomographic image reconstruction can be mapped to a problem of finding solutions to a large system of linear equations which maximize a function that includes \textit{a priori} knowledge regarding features of typical images such as…
Let $X$ be an integral projective variety of codimension two, degree $d$ and dimension $r$ and $Y$ be its general hyperplane section. The problem of lifting generators of minimal degree $\sigma$ from the homogeneous ideal of $Y$ to the…
Interesting data often concentrate on low dimensional smooth manifolds inside a high dimensional ambient space. Random projections are a simple, powerful tool for dimensionality reduction of such data. Previous works have studied bounds on…
We survey known results about the complexity of surjective homomorphism problems, studied in the context of related problems in the literature such as list homomorphism, retraction and compaction. In comparison with these problems,…
The area of inverse problems in mathematics is highly interdisciplinary. In various fields of science, engineering, medicine, and industry, there arises a need to reconstruct information about unknown entities that cannot be directly…
In this paper, we address the problem of finding a correspondence, or matching, between the functions of two programs in binary form, which is one of the most common task in binary diffing. We introduce a new formulation of this problem as…
Discrete tomography focuses on the reconstruction of functions $f: A \to \mathbb{R}$ from their line sums in a finite number $d$ of directions, where $A$ is a finite subset of $\mathbb{Z}^2$. Consequently, the techniques of discrete…
We present a novel algorithm for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. The motivation comes from the problem of establishing a…
We introduce a new non-smooth variational model for the restoration of manifold-valued data which includes second order differences in the regularization term. While such models were successfully applied for real-valued images, we introduce…
This article discusses nonconforming finite element methods for convex minimization problems and systematically derives dual mixed formulations. Duality relations lead to simple error estimates that avoid an explicit treatment of…
Theoretical guarantees for the robust solution of inverse problems have important implications for applications. To achieve both guarantees and high reconstruction quality, we propose learning a pixel-based ridge regularizer with a…
In this paper we consider the problem of image reconstruction in optoacoustic tomography. In particular, we devise a deep neural architecture that can explicitly take into account the band-frequency information contained in the sinogram.…
Higher-dimensional rewriting is founded on a duality of rewrite systems and cell complexes, connecting computational mathematics to higher categories and homotopy theory: the two sides of a rewrite rule are two halves of the boundary of an…
Reconstructing a complete object from its parts is a fundamental problem in many scientific domains. The purpose of this article is to provide a systematic survey on this topic. The reassembly problem requires understanding the attributes…
We consider the problem of reconstructing signals and images from periodic nonlinearities. For such problems, we design a measurement scheme that supports efficient reconstruction; moreover, our method can be adapted to extend to…
Motion blurry images challenge many computer vision algorithms, e.g, feature detection, motion estimation, or object recognition. Deep convolutional neural networks are state-of-the-art for image deblurring. However, obtaining training data…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
We present a novel algorithm for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. A straightforward approach to this problem consists of…
We consider the demixing problem of two (or more) high-dimensional vectors from nonlinear observations when the number of such observations is far less than the ambient dimension of the underlying vectors. Specifically, we demonstrate an…