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Inverse Problem techniques offer powerful tools which deal naturally with marginal data and asymmetric or strongly smoothing kernels, in cases where parameter-fitting methods may be used only with some caution. Although they are typically…
We study the seismic inverse problem for the recovery of subsurface properties in acoustic media. In order to reduce the ill-posedness of the problem, the heterogeneous wave speed parameter to be recovered is represented using a limited…
We study the ability of weak lensing surveys to detect galaxy clusters and constrain cosmological parameters, in particular the equation of state of dark energy. There are two major sources of noise for weak lensing cluster measurements:…
Weak gravitational lensing is becoming a mature technique for constraining cosmological parameters, and future surveys will be able to constrain the dark energy equation of state $w$. When analyzing galaxy surveys, redshift information has…
In this paper, we consider the problem of sparse recovery from nonlinear measurements, which has applications in state estimation and bad data detection for power networks. An iterative mixed $\ell_1$ and $\ell_2$ convex program is used to…
We develop an efficient, non-parametric Bayesian method for reconstructing the time evolution of the dark energy equation of state w(z) from observational data. Of particular importance is the choice of prior, which must be chosen carefully…
We derive an optimal linear filter to suppress the noise from the COBE DMR sky maps for a given power spectrum. We then apply the filter to the first-year DMR data, after removing pixels within $20^\circ$ of the Galactic plane from the…
Weak lensing galaxy surveys are currently undergoing a dramatic revolution as the dawn of the Stage-IV surveys are upon us. Hence, ensuring that our analysis methods are as accurate and precise as the raw data is of upmost importance. This…
Weak gravitational lensing is a powerful probe of the large-scale cosmic matter distribution. Wide-field galaxy surveys allow us to generate the so-called weak lensing maps, but actual observations suffer from noise due to imperfect…
Lensless imaging offers a lightweight, compact alternative to traditional lens-based systems, ideal for exploration in space-constrained environments. However, the absence of a focusing lens and limited lighting in such environments often…
A new method is proposed to recover the water-wave surface elevation from pressure data obtained at the bottom of the fluid. The new method requires the numerical solution of a nonlocal nonlinear equation relating the pressure and the…
Beyond-two-point statistics contain additional information on cosmological as well as astrophysical and observational (systematics) parameters. In this methodology paper we provide an end-to-end simulation-based analysis of a set of…
Weak gravitational lensing is one of the most promising cosmological probes of the late universe. Several large ongoing (DES, KiDS, HSC) and planned (LSST, EUCLID, WFIRST) astronomical surveys attempt to collect even deeper and larger scale…
The two point angular correlation function is an excellent measure of structure in the universe. To extract from it the three dimensional power spectrum, one must invert Limber's Equation. Here we perform this inversion using a Bayesian…
A statistical method for reconstructing large scale structure behind the Zone of Avoidance is presented. It also corrects for shot-noise and for redshift distortion in galaxy surveys. The galaxy distribution is expanded in an orthogonal set…
We apply a mass reconstruction technique to simulated large-scale structure gravitational distortion maps, from 2.5' to 10 degree scales, for different cosmological scenarii. The projected mass is reconstructed using a non-parametric least…
In this paper, we consider the problem of blind signal and image separation using a sparse representation of the images in the wavelet domain. We consider the problem in a Bayesian estimation framework using the fact that the distribution…
We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a…
Weak gravitational lensing observations probe the spectrum and evolution of density fluctuations and the cosmological parameters which govern them. At low redshifts, the non-linear gravitational evolution of large scale structure produces a…
The use of Fourier methods in wave-front reconstruction can significantly reduce the computation time for large telescopes with a high number of degrees of freedom. However, Fourier algorithms for discrete data require a rectangular data…