Related papers: Convergence analysis of pixel-driven Radon and fan…
Differentiable rasterization changes the standard formulation of primitive rasterization -- by enabling gradient flow from a pixel to its underlying triangles -- using distribution functions in different stages of rendering, creating a…
This paper is devoted to a Radon-type transform arising in Photoacoustic Tomography that uses integrating line detectors. We consider two situations: when the line detectors are tangent to the boundary of a cylindrical domain and when the…
We consider a multi-object detection problem over a sensor network (SNET) with limited range sensors. This problem complements the widely considered decentralized detection problem where all sensors observe the same object. While the…
Due to their radiation hardness, kilohertz frame rates, and high dynamic range, hybrid pixel detectors have recently expanded their application range to electron diffraction and recently also electron imaging. However, these detectors…
This revisit gives a survey on the analytical methods for the inverse exponential Radon transform which has been investigated in the past three decades from both mathematical interests and medical applications such as nuclear medicine…
The Discrete Ordinates Method (DOM) is widely used for velocity discretization in radiative transport simulations. However, DOM tends to exhibit the ray effect when the velocity discretization is not sufficiently refined, a limitation that…
Kernel methods for deconvolution have attractive features, and prevail in the literature. However, they have disadvantages, which include the fact that they are usually suitable only for cases where the error distribution is infinitely…
As recent advances in mobile camera technology have enabled the capability to capture high-resolution images, such as 4K images, the demand for an efficient deblurring model handling large motion has increased. In this paper, we discover…
Random features (RFs) are a popular technique to scale up kernel methods in machine learning, replacing exact kernel evaluations with stochastic Monte Carlo estimates. They underpin models as diverse as efficient transformers (by…
The conical Radon transform is an integral transform that maps a given function $f$ to its integral over a conical surface. In this study, we invesgate the conical Radon transform with a fixed central axis and opening angle, considering the…
Convolution neural networks have achieved remarkable performance in many tasks of computing vision. However, CNN tends to bias to low frequency components. They prioritize capturing low frequency patterns which lead them fail when suffering…
Diffusion models achieved great success in image synthesis, but still face challenges in high-resolution generation. Through the lens of discrete cosine transformation, we find the main reason is that \emph{the same noise level on a higher…
Here we present a new non-parametric approach to density estimation and classification derived from theory in Radon transforms and image reconstruction. We start by constructing a "forward problem" in which the unknown density is mapped to…
Inverse imaging problems are inherently under-determined, and hence it is important to employ appropriate image priors for regularization. One recent popular prior---the graph Laplacian regularizer---assumes that the target pixel patch is…
We consider the reconstruction of a two-dimensional discrete image from a set of tomographic measurements corresponding to the Radon projection. Assuming that the image has a structure where neighbouring pixels have a larger probability to…
Several novel imaging applications have lead recently to a variety of Radon type transforms, where integration is done over a family of conical surfaces. We call them \emph{cone transforms} (in 2D they are also called \emph{V-line} or…
This study investigates some of the consequences of representing the sky by a rectangular grid of pixels on the dynamic range of images derived from radio interferometric measurements. In particular, the effects of image pixelization…
In recent years, Rectified flow (RF) has gained considerable popularity largely due to its generation efficiency and state-of-the-art performance. In this paper, we investigate the degree to which RF automatically adapts to the intrinsic…
We establish range characterizations, or data consistency conditions, for an integral transform that maps a function to its weighted integrals over conical surfaces in $\mathbb{R}^n$. We consider two different geometries for the cone…
In this paper, we derive a neural network architecture based on an analytical formulation of the parallel-to-fan beam conversion problem following the concept of precision learning. The network allows to learn the unknown operators in this…