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In this paper, we investigate the relations between the Radon and weighted divergent beam and cone transforms. Novel inversion formulas are derived for the latter two. The weighted cone transform arises, for instance, in image…
In this work, we develop efficient solvers for linear inverse problems based on randomized singular value decomposition (RSVD). This is achieved by combining RSVD with classical regularization methods, e.g., truncated singular value…
Wavefront-free behavior and the resulting quantification difficulties are intrinsic limitations of vibrothermography due to the diffusive nature of thermal fields. This work proposes a generalized virtual wave reconstruction framework to…
An optical imaging system forms an object image by recollecting light scattered by the object. However, intact optical information of the object delivered through the imaging system is deteriorated by imperfect optical elements and unwanted…
Let $\mathscr Q$ be the quaternion Heisenberg group, and let $\mathbf P$ be the affine automorphism group of $\mathscr Q$. We develop the theory of continuous wavelet transform on the quaternion Heisenberg group via the unitary…
Blind face inpainting refers to the task of reconstructing visual contents without explicitly indicating the corrupted regions in a face image. Inherently, this task faces two challenges: (1) how to detect various mask patterns of different…
Low dose computed tomography is a mainstream for clinical applications. How-ever, compared to normal dose CT, in the low dose CT (LDCT) images, there are stronger noise and more artifacts which are obstacles for practical applications. In…
In this paper we present a new approach to deblur the effect of atmospheric turbulence in the case of long range imaging. Our method is based on an analytical formulation, the Fried kernel, of the atmosphere modulation transfer function…
In this work, we consider compressible single-phase flow problems in a porous media containing a fracture. In the latter, a non-linear pressure-velocity relation is prescribed. Using a non-overlapping domain decomposition procedure, we…
This paper establishes $L^p$-improving estimates for a variety of Radon-like transforms which integrate functions over submanifolds of intermediate dimension. In each case, the results rely on a unique notion of curvature which relates to,…
This paper considers the problem of undersampled MRI reconstruction. We propose a novel Transformer-based framework for directly processing signal in k-space, going beyond the limitation of regular grids as ConvNets do. We adopt an implicit…
This paper introduces a neural network approach for solving two-dimensional traveltime tomography (TT) problems based on the eikonal equation. The mathematical problem of TT is to recover the slowness field of a medium based on the boundary…
Passive radar has key advantages over its active counterpart in terms of cost and stealth. In this paper, we address passive radar imaging problem by interferometric inversion using a spectral estimation method with a priori information…
Deep learning (DL) has shown unprecedented performance for many image analysis and image enhancement tasks. Yet, solving large-scale inverse problems like tomographic reconstruction remains challenging for DL. These problems involve…
This report describes the solution that secured the first place in the "View Synthesis Challenge for Human Heads (VSCHH)" at the ICCV 2023 workshop. Given the sparse view images of human heads, the objective of this challenge is to…
We study a Radon-like transform that takes functions on the Grassmannian of $j$-dimensional affine planes in $\Bbb R ^n$ to functions on a similar manifold of $k$-dimensional planes by integration over the set of all $j$-planes that meet a…
A core challenge in Machine Learning is to learn to disentangle natural factors of variation in data (e.g. object shape vs. pose). A popular approach to disentanglement consists in learning to map each of these factors to distinct subspaces…
Dimensionality reduction is an essential technique for multi-way large-scale data, i.e., tensor. Tensor ring (TR) decomposition has become popular due to its high representation ability and flexibility. However, the traditional TR…
Radon transform and its inverse operation are important techniques in medical imaging tasks. Recently, there has been renewed interest in Radon transform for applications such as content-based medical image retrieval. However, all studies…
The reconstruction of images from their corresponding noisy Radon transform is a typical example of an ill-posed linear inverse problem as arising in the application of computerized tomography (CT). As the (naive) solution does not depend…