Related papers: Error Correction for Discrete Tomography
Discrete Empirical Interpolation Method (DEIM) is a simple and effective method for reconstructing a function from its incomplete pointwise observations. However, applying DEIM to functions with physically constrained ranges can produce…
This paper presents an innovative set of tools to support a methodology for the multichannel interpolation (MCI) of a discrete signal. It is shown that a bandlimited signal $f$ can be exactly reconstructed from finite samples of $g_k$…
The reconstruction of images from measured data is an increasing field of research. For highly under-determined problems, template-based image reconstruction provides a way of compensating for the lack of sufficient data. A caveat of this…
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…
Light scattering by tissue severely limits how deep beneath the surface one can image, and the spatial resolution one can obtain from these images. Diffuse optical tomography (DOT) is one of the most powerful techniques for imaging deep…
The problem of using proximity (similarity or dissimilarity) data for the purpose of "adding a point to a vector diagram" was first studied by J.C. Gower in 1968. Since then, a number of methods -- mostly kernel methods -- have been…
In this paper, we analyze the error estimate of a wavelet frame based image restoration method from degraded and incomplete measurements. We present the error between the underlying original discrete image and the approximate solution which…
Low Dose Computed Tomography suffers from a high amount of noise and/or undersampling artefacts in the reconstructed image. In the current article, a Deep Learning technique is exploited as a regularization term for the iterative…
We consider the problem of signal reconstruction for computed tomography (CT) under a nonlinear forward model that accounts for exponential signal attenuation, a polychromatic X-ray source, general measurement noise (e.g., Poisson shot…
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…
Let $f$ be an unknown function in $\mathbb R^2$, and $f_\epsilon$ be its reconstruction from discrete Radon transform data, where $\epsilon$ is the data sampling rate. We study the resolution of reconstruction when $f$ has a jump…
The present article proposes a partial answer to the explicit inversion of the tensor tomography problem in two dimensions, by proving injectivity over certain kinds of tensors and providing reconstruction formulas for them. These tensors…
Discrete diffusion language models learn to reconstruct text from randomly masked inputs, yet under mild assumptions their denoiser already implements the exact Bayesian posterior over the original tokens. We prove that the expected…
Line spectral estimation theory aims to estimate the off-the-grid spectral components of a time signal with optimal precision. Recent results have shown that it is possible to recover signals having sparse line spectra from few temporal…
Microstructure reconstruction and compression techniques are designed to find a microstructure with desired properties. While the microstructure reconstruction searches for a microstructure with prescribed statistical properties, the…
We have developed a method for the linear reconstruction of an image from undersampled, dithered data. The algorithm, known as Variable-Pixel Linear Reconstruction, or informally as Drizzle, preserves photometry and resolution, can weight…
The conversion of 2D freehand sketches into 3D models remains a pivotal challenge in computer vision, bridging the gap between fluent sketching and CAD. Traditional monocular depth reconstruction techniques are not suitable for line drawing…
We propose a high-order FDTD scheme based on the correction function method (CFM) to treat interfaces with complex geometry without increasing the complexity of the numerical approach for constant coefficients. Correction functions are…
We consider high-redshift $f(R)$ cosmography adopting the technique of polynomial reconstruction. In lieu of considering Taylor treatments, which turn out to be non-predictive as soon as $z>1$, we take into account the Pad\'e rational…
We introduce a deficiency-based representation and approximation framework for values of the Riemann zeta function. The method is based on comparing two nonlinear accumulation mechanisms: global transformation of a base partial sum and…