Related papers: A General Approach to Regularizing Inverse Problem…
We investigate the Slepian spatiospectral localization problem within subdomains of the $d$-dimensional ball. Opposed to the more classical setups of the Euclidean space or the sphere, the ball lacks a standard or universally accepted…
We derive and analyse a new variant of the iteratively regularized Landweber iteration, for solving linear and nonlinear ill-posed inverse problems. The method takes into account training data, which are used to estimate the interior of a…
We examine holographic renormalization by the singular value decomposition (SVD) of matrix data generated by the Monte Carlo snapshot of the 2D classical Ising model at criticality. To take the continuous limit of the SVD enables us to find…
The Bayesian statistical framework provides a systematic approach to enhance the regularization model by incorporating prior information about the desired solution. For the Bayesian linear inverse problems with Gaussian noise and Gaussian…
Convolutional Neural Networks are widely used in various machine learning domains. In image processing, the features can be obtained by applying 2D convolution to all spatial dimensions of the input. However, in the audio case, frequency…
Low-rank approximation of images via singular value decomposition is well-received in the era of big data. However, singular value decomposition (SVD) is only for order-two data, i.e., matrices. It is necessary to flatten a higher order…
Super-resolution is a classical problem in image processing, with numerous applications to remote sensing image enhancement. Here, we address the super-resolution of irregularly-sampled remote sensing images. Using an optimal interpolation…
We analyse the Krylov solvability of inverse linear problems on Hilbert space $\mathcal{H}$ where the underlying operator is compact and normal. Krylov solvability is an important feature of inverse linear problems that has profound…
A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…
We consider the inverse medium scattering of reconstructing the medium contrast using Born data, including the full aperture, limited-aperture, and multi-frequency data. We propose data-driven basis functions for these inverse problems…
We propose a class of spherical wavelet bases for the analysis of geophysical models and forthe tomographic inversion of global seismic data. Its multiresolution character allows for modeling with an effective spatial resolution that varies…
Continuous optimization is an important problem in many areas of AI, including vision, robotics, probabilistic inference, and machine learning. Unfortunately, most real-world optimization problems are nonconvex, causing standard convex…
Representations learned via self-supervised learning (SSL) can be susceptible to dimensional collapse, where the learned representation subspace is of extremely low dimensionality and thus fails to represent the full data distribution and…
We propose an unsupervised approach for learning end-to-end reconstruction operators for ill-posed inverse problems. The proposed method combines the classical variational framework with iterative unrolling, which essentially seeks to…
Distributed optimization plays an important role in modern large-scale machine learning and data processing systems by optimizing the utilization of computational resources. One of the classical and popular approaches is Local Stochastic…
The Lomb-Scargle periodogram is a common tool in the frequency analysis of unequally spaced data equivalent to least-squares fitting of sine waves. We give an analytic solution for the generalisation to a full sine wave fit, including an…
We study the inverse problem of estimating n locations $t_1, ..., t_n$ (up to global scale, translation and negation) in $R^d$ from noisy measurements of a subset of the (unsigned) pairwise lines that connect them, that is, from noisy…
The regularity of refinable functions has been investigated deeply in the past 25 years using Fourier analysis, wavelet analysis, restricted and joint spectral radii techniques. However the shift-invariance of the underlying regular setting…
Most algorithms for solving optimization problems or finding saddle points of convex-concave functions are fixed-point algorithms. In this work we consider the generic problem of finding a fixed point of an average of operators, or an…
Inverse medium problems involve the reconstruction of a spatially varying unknown medium from available observations by exploring a restricted search space of possible solutions. Standard grid-based representations are very general but all…