Related papers: Discrete tomography reconstructions with small bou…
Medical imaging is an invaluable resource in medicine as it enables to peer inside the human body and provides scientists and physicians with a wealth of information indispensable for understanding, modelling, diagnosis, and treatment of…
3D image reconstruction from a set of X-ray projections is an important image reconstruction problem, with applications in medical imaging, industrial inspection and airport security. The innovation of X-ray emitter arrays allows for a…
We investigate the problem of reconstructing signals from a subsampled convolution of their modulated versions and a known filter. The problem is studied as applies to specific imaging systems relying on spatial phase modulation by randomly…
This paper is concerned with the question of reconstructing a vector in a finite-dimensional real Hilbert space when only the magnitudes of the coefficients of the vector under a redundant linear map are known. We analyze various Lipschitz…
We propose and analyze an online algorithm for reconstructing a sequence of signals from a limited number of linear measurements. The signals are assumed sparse, with unknown support, and evolve over time according to a generic nonlinear…
This paper is concerned with the question of reconstructing a vector in a finite-dimensional real or complex Hilbert space when only the magnitudes of the coefficients of the vector under a redundant linear map are known. We present new…
In tomographic reconstruction, the goal is to reconstruct an unknown object from a collection of line integrals. Given a complete sampling of such line integrals for various angles and directions, explicit inverse formulas exist to…
Super-resolution imaging aims at improving the resolution of an image by enhancing it with other images or data that might have been acquired using different imaging techniques or modalities. In this paper we consider the task of doubling,…
Motivated by applications to DNA storage, we study reconstruction and list-reconstruction schemes for integer vectors that suffer from limited-magnitude errors. We characterize the asymptotic size of the intersection of error balls in…
To date, high-resolution (< 1 nm) imaging of extended objects in three-dimensions (3D) has not been possible. A restriction known as the Crowther criterion forces a tradeoff between object size and resolution for 3D reconstructions by…
In many tomographic imaging problems the data consist of integrals along lines or curves. Increasingly we encounter "rich tomography" problems where the quantity imaged is higher dimensional than a scalar per voxel, including vectors…
Generic 3D reconstruction from a single image is a difficult problem. A lot of data loss occurs in the projection. A domain based approach to reconstruction where we solve a smaller set of problems for a particular use case lead to greater…
We review boundary rigidity theorems assessing that, under appropriate conditions, Riemannian manifolds with the same spectrum of boundary geodesics are isometric. We show how to apply these theorems to the problem of reconstructing a $d+1$…
Tomography is the three-dimensional reconstruction of an object from images taken at different angles. The term classical tomography is used, when the imaging beam travels in straight lines through the object. This assumption is valid for…
We study the problem of reconstructing a signal from its projection on a subspace. The proposed signal reconstruction algorithms utilize a guiding subspace that represents desired properties of reconstructed signals. We show that optimal…
Conventional inversion of the discrete Fourier transform (DFT) requires all DFT coefficients to be known. When the DFT coefficients of a rasterized image (represented as a matrix) are known only within a pass band, the original matrix…
In this work, we develop a novel technique for reconstructing images from projection-based nano- and microtomography. Our contribution focuses on enhancing reconstruction quality, particularly for specimen composed of homogeneous material…
Random field and random cluster theory are used to describe certain mathematical results concerning the probability distribution of image pixel intensities characterized as generic $2D$ integer arrays. The size of the smallest bounded…
We consider a mathematical model of thermoacoustic tomography and other multi-wave imaging techniques with variable sound speed and attenuation. We find that a Neumann series reconstruction algorithm, previously studied under the assumption…
We investigate the recovery of structures from large-area, low dose exposures that distribute the dose over many identical copies of an object. The reconstruction is done via a maximum likelihood approach that does neither require to…