Related papers: Localization of point scatterers via sparse optimi…

In this paper, we consider the inverse problem of determining the location and the shape of a sound-soft obstacle from the modulus of the far-field data for a single incident plane wave. By adding a reference ball artificially to the…

Weak lensing convergence maps - upon which higher order statistics can be calculated - can be recovered from observations of the shear field by solving the lensing inverse problem. For typical surveys this inverse problem is ill-posed…

The problem of recovering acoustic sources, more specifically monopoles, from point-wise measurements of the corresponding acoustic pressure at a limited number of frequencies is addressed. To this purpose, a family of sparse optimization…

In many statistical learning problems, it is desired that the optimal solution conforms to an a priori known sparsity structure represented by a directed acyclic graph. Inducing such structures by means of convex regularizers requires…

We present the framework of slowly varying regression under sparsity, allowing sparse regression models to exhibit slow and sparse variations. The problem of parameter estimation is formulated as a mixed-integer optimization problem. We…

We consider a bilevel optimatisation method for inverse linear atmospheric dispersion problems where both linear and non-linear model parameters are to be determined. We propose that a smooth weighted Mahalanobis distance function is used…

The inverse scattering problem is of critical importance in a number of fields, including medical imaging, sonar, sensing, non-destructive evaluation, and several others. The problem of interest can vary from detecting the shape to the…

The time domain linear sampling method (TD-LSM) solves inverse scattering problems using time domain data by creating an indicator function for the support of the unknown scatterer. It involves only solving a linear integral equation called…

We propose a method to reconstruct sparse signals degraded by a nonlinear distortion and acquired at a limited sampling rate. Our method formulates the reconstruction problem as a nonconvex minimization of the sum of a data fitting term and…

Computational time reversal imaging can be used to locate the position of multiple scatterers in a known background medium. The current methods for computational time reversal imaging are based on the null subspace projection operator,…

We consider model selection and estimation for partial spline models and propose a new regularization method in the context of smoothing splines. The regularization method has a simple yet elegant form, consisting of roughness penalty on…

We consider in this work an inverse acoustic scattering problem when only phaseless data is available. The inverse problem is highly nonlinear and ill-posed due to the lack of the phase information. Solving inverse scattering problems with…

In many compressive sensing problems today, the relationship between the measurements and the unknowns could be nonlinear. Traditional treatment of such nonlinear relationships have been to approximate the nonlinearity via a linear model…

In this work, we propose an easy-to-implement fixed-point algorithm for reconstructing a space-time dependent source in a subdiffusion model from lateral boundary measurements. The numerical scheme combines a Galerkin finite element method…

We introduce the localized Lasso, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality $d$ and small sample size $n$. More specifically, we consider a function…

Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…

In many areas of imaging science, it is difficult to measure the phase of linear measurements. As such, one often wishes to reconstruct a signal from intensity measurements, that is, perform phase retrieval. In several applications the…

We discuss a time-harmonic inverse scattering problem for the Helmholtz equation with compactly supported penetrable and possibly inhomogeneous scattering objects in an unbounded homogeneous background medium, and we develop a monotonicity…

Direct imaging methods recover the presence, position, and shape of the unknown obstacles in time-harmonic inverse scattering without a priori knowledge of either the physical properties or the number of disconnected components of the…

We propose a novel iterative numerical method to solve the three-dimensional inverse obstacle scattering problem of recovering the shape of the obstacle from far-field measurements. To address the inherent ill-posed nature of the inverse…