Related papers: Inversion of multiconfiguration complex EMI data w…

Rotation averaging (RA) is a fundamental problem in robotics and computer vision. In RA, the goal is to estimate a set of $N$ unknown orientations $R_{1}, ..., R_{N} \in SO(3)$, given noisy measurements $R_{ij} \sim R^{-1}_{i} R_{j}$ of a…

A new approach of solving the ill-conditioned inverse problem for analytical continuation is proposed. The root of the problem lies in the fact that even tiny noise of imaginary-time input data has a serious impact on the inferred…

In recent work, redressed warped frames have been introduced for the analysis and synthesis of audio signals with non-uniform frequency and time resolutions. In these frames, the allocation of frequency bands or time intervals of the…

We consider the problem of nonlinear dimensionality reduction: given a training set of high-dimensional data whose ``intrinsic'' low dimension is assumed known, find a feature extraction map to low-dimensional space, a reconstruction map…

Plasma diagnostics often employ computerized tomography to estimate emissivity profiles from a finite, and often limited, number of line-integrated measurements. Decades of algorithmic refinement have brought considerable improvements, and…

Compressive sensing is a methodology for the reconstruction of sparse or compressible signals using far fewer samples than required by the Nyquist criterion. However, many of the results in compressive sensing concern random sampling…

An explicit series solution is proposed for the inversion of the spherical mean Radon transform. Such an inversion is required in problems of thermo- and photo- acoustic tomography. Closed-form inversion formulae are currently known only…

Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…

Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…

We consider the Ensemble Kalman Inversion which has been recently introduced as an efficient, gradient-free optimisation method to estimate unknown parameters in an inverse setting. In the case of large data sets, the Ensemble Kalman…

This paper is concerned with the inverse problem of reconstructing an inhomogeneous medium from the acoustic far-field data at a fixed frequency in two dimensions. This inverse problem is severely ill-posed (and also strongly nonlinear),…

We present a machine learning approach to the inversion of Fredholm integrals of the first kind. The approach provides a natural regularization in cases where the inverse of the Fredholm kernel is ill-conditioned. It also provides an…

Fabrication process variations are a major source of yield degradation in the nano-scale design of integrated circuits (IC), microelectromechanical systems (MEMS) and photonic circuits. Stochastic spectral methods are a promising technique…

We present an imaging technique that allows the recovery of the transparency profile of wavelength-scale objects with deep subwavelength resolution based on far-field intensity measurements. The approach, interscale mixing microscopy (IMM),…

This paper develops a new empirical Bayesian inference algorithm for solving a linear inverse problem given multiple measurement vectors (MMV) of under-sampled and noisy observable data. Specifically, by exploiting the joint sparsity across…

Inverse design enables automating the discovery and optimization of devices achieving performance significantly exceeding that of traditional human-engineered designs. However, existing methodologies to inverse-design electromagnetic…

Faraday tomography (or rotation measure synthesis) is a procedure to convert linear polarization spectra into the Faraday dispersion function, which provides us with unique information of magneto-ionic media along the line of sight.…

The de-facto standard approach of promoting sparsity by means of $\ell_1$-regularization becomes ineffective in the presence of simplex constraints, i.e.,~the target is known to have non-negative entries summing up to a given constant. The…

Signal recovery is one of the key techniques of Compressive sensing (CS). It reconstructs the original signal from the linear sub-Nyquist measurements. Classical methods exploit the sparsity in one domain to formulate the L0 norm…

Real-time magnetic resonance imaging (MRI) methods generally shorten the measuring time by acquiring less data than needed according to the sampling theorem. In order to obtain a proper image from such undersampled data, the reconstruction…