Related papers: Inversion of noisy Radon transform by SVD based ne…
We study integral transforms mapping a function on the Euclidean plane to the family of its integration on plane curves, that is, a function of plane curves. The plane curves we consider in the present paper are given by the graphs of…
We consider unconstrained minimization of smooth convex functions. We propose a novel variational perspective using forced Euler-Lagrange equation that allows for studying high-resolution ODEs. Through this, we obtain a faster convergence…
The article presents an efficient image reconstruction algorithm for single scattering optical tomography (SSOT) in circular geometry of data acquisition. This novel medical imaging modality uses photons of light that scatter once in the…
We study noise in iterative reconstruction from discrete noisy data of a generalized Radon transform in the plane. Our approach builds on Local Reconstruction Analysis (LRA), a framework for analyzing reconstructions at the native scale. We…
A fast algorithm for solving the under-determined 3-D linear gravity inverse problem based on the randomized singular value decomposition (RSVD) is developed. The algorithm combines an iteratively reweighted approach for $L_1$-norm…
This paper proves a novel analytical inversion formula for the so-called modulo Radon transform (MRT), which models a recently proposed approach to one-shot high dynamic range tomography. It is based on the solution of a Poisson problem…
Dynamic mode decomposition (DMD) is an efficient tool for decomposing spatio-temporal data into a set of low-dimensional modes, yielding the oscillation frequencies and the growth rates of physically significant modes. In this paper, we…
We analyze sparse frame based regularization of inverse problems by means of a diagonal frame decomposition (DFD) for the forward operator, which generalizes the SVD. The DFD allows to define a non-iterative (direct) operator-adapted frame…
The method described here performs blind deconvolution of the beamforming output in the frequency domain. To provide accurate blind deconvolution, sparsity priors are introduced with a smooth \ell_1/\ell_2 regularization term. As the mean…
The Radon transform is one of the most useful and applicable tools in functional analysis. First constructed by John Radon in 1917 it has now been adapted to several settings. One of the principle theorems involving the Radon transform is…
A method of determining the optimum number of levels of decomposition in soft-thresholding wavelet denoising using Stationary Wavelet Transform is presented here. The method calculates the risk at each level of decomposition using Steins…
This study introduces a novel formulation to enhance Support Vector Machines (SVMs) in handling class imbalance and noise. Unlike the conventional Soft Margin SVM, which penalizes the magnitude of constraint violations, the proposed model…
This study presents a deep learning-based approach to seismic velocity inversion problem, focusing on both noisy and noiseless training datasets of varying sizes. Our Seismic Velocity Inversion Network (SVInvNet) introduces a novel…
Several methods for solving efficiently the one-dimensional deconvolution problem are proposed. The problem is to solve the Volterra equation ${\mathbf k} u:=\int_0^t k(t-s)u(s)ds=g(t),\quad 0\leq t\leq T$. The data, $g(t)$, are noisy. Of…
In a fissile material, the inherent multiplicity of neutrons born through induced fissions leads to correlations in their detection statistics. The correlations between neutrons can be used to trace back some characteristics of the fissile…
A super-resolution (SR) method for the reconstruction of Navier-Stokes (NS) flows from noisy observations is presented. In the SR method, first the observation data is averaged over a coarse grid to reduce the noise at the expense of losing…
We consider the inverse source problem of thermo- and photoacoustic tomography, with data registered on an open surface partially surrounding the source of acoustic waves. Under the assumption of constant speed of sound we develop an…
For economic and efficiency reasons, blended acquisition of seismic data is becoming more and more commonplace. Seismic deblending methods are always computationally demanding and normally consist of multiple processing steps. Besides, the…
We introduce a data-adaptive inversion method that integrates classical or deep learning-based approaches with iterative graph Laplacian regularization, specifically targeting acoustic impedance inversion - a critical task in seismic…
Benefited from the rapid and sustainable development of synthetic aperture radar (SAR) sensors, change detection from SAR images has received increasing attentions over the past few years. Existing unsupervised deep learning-based methods…