Related papers: Discrete tomography reconstructions with small bou…
A binary matrix can be scanned by moving a fixed rectangular window (submatrix) across it, rather like examining it closely under a microscope. With each viewing, a convenient measurement is the number of 1s visible in the window, which…
We discuss a notion of convergence for binary trees that is based on subtree sizes. In analogy to recent developments in the theory of graphs, posets and permutations we investigate some general aspects of the topology, such as a…
Mask-based lensless imagers are smaller and lighter than traditional lensed cameras. In these imagers, the sensor does not directly record an image of the scene; rather, a computational algorithm reconstructs it. Typically, mask-based…
While several classes of integer linear optimization problems are known to be solvable in polynomial time, far fewer tractability results exist for integer nonlinear optimization. In this work, we narrow this gap by identifying a broad…
X-ray computed tomography (CT) is one of widely used diagnostic tools for medical and dental tomographic imaging of the human body. However, the standard filtered backprojection reconstruction method requires the complete knowledge of the…
Speckled images of a binary broad band light source (600-670 nm), generated by randomized reflections or transmissions, were used to reconstruct a binary image by use of multi-frame blind deconvolution algorithms. Craft store glitter was…
Thinning is the removal of contour pixels/points of connected components in an image to produce their skeleton with retained connectivity and structural properties. The output requirements of a thinning procedure often vary with…
Hybrid inverse problems are based on the interplay of two types of waves, in order to allow for imaging with both high resolution and high contrast. The inversion procedure often consists of two steps: first, internal measurements involving…
We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…
The problem of reconstructing a sequence of independent and identically distributed symbols from a set of equal size, consecutive, fragments, as well as a dependent reference sequence, is considered. First, in the regime in which the…
In this paper we study the performance of image reconstruction methods from incomplete samples of the 2D discrete Fourier transform. Inspired by requirements in parallel MRI, we focus on a special sampling pattern with a small number of…
Modern deep learning reconstruction algorithms generate impressively realistic scans from sparse inputs, but can often produce significant inaccuracies. This makes it difficult to provide statistically guaranteed claims about the true state…
This article presents a method to perform diffraction tomography in a standard microscope that includes an LED array for illumination. After acquiring a sequence of intensity-only images of a thick sample, a ptychography-based…
We study bounded width algebras which are minimal in the sense that every proper reduct does not have bounded width. We show that minimal bounded width algebras can be arranged into a pseudovariety with one basic ternary operation. We…
The minimum distance graph of a code has the codewords as vertices and edges exactly when the Hamming distance between two codewords equals the minimum distance of the code. A constructive proof for reconstructibility of an extended perfect…
We derive a new estimate of the size of finite sets of points in metric spaces with few distances. The following applications are considered: (1) we improve the Ray-Chaudhuri--Wilson bound of the size of uniform intersecting families of…
Man-made environments typically comprise planar structures that exhibit numerous geometric relationships, such as parallelism, coplanarity, and orthogonality. Making full use of these relationships can considerably improve the robustness of…
Given a tiling of a 2D grid with several types of tiles, we can count for every row and column how many tiles of each type it intersects. These numbers are called the_projections_. We are interested in the problem of reconstructing a tiling…
Consider the projections of a finite set $A\subset R^n$ onto the coordinate hyperplanes. How small can the sum of the sizes of these projections be, given the size of $A$? In a different form, this problem has been studied earlier in the…
In this paper, we present an algorithm for effectively reconstructing an object from a set of its tomographic projections without any knowledge of the viewing directions or any prior structural information, in the presence of pathological…