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Phase retrieval (PR) is an ill-conditioned inverse problem which can be found in various science and engineering applications. Assuming sparse priority over the signal of interest, recent algorithms have been developed to solve the phase…
This paper studies the recovery of a superposition of point sources from noisy bandlimited data. In the fewest possible words, we only have information about the spectrum of an object in a low-frequency band bounded by a certain cut-off…
This study is motivated by the problem of evaluating reliable false alarm (FA) rates for sinusoid detection tests applied to unevenly sampled time series involving colored noise, when a (small) training data set of this noise is available.…
Hyperspectral images enable precise identification of ground objects by capturing their spectral signatures with fine spectral resolution.While high spatial resolution further enhances this capability, increasing spatial resolution through…
Optical interferometers provide multiple wavelength measurements. In order to fully exploit the spectral and spatial resolution of these instruments, new algorithms for image reconstruction have to be developed. Early attempts to deal with…
A source separation method using a full-rank spatial covariance model has been proposed by Duong et al. ["Under-determined Reverberant Audio Source Separation Using a Full-rank Spatial Covariance Model," IEEE Trans. ASLP, vol. 18, no. 7,…
We present the results of a study to optimize the principal component analysis (PCA) algorithm for planet detection, a new algorithm complementing ADI and LOCI for increasing the contrast achievable next to a bright star. The stellar PSF is…
Sparse principal component analysis (PCA) is a well-established dimensionality reduction technique that is often used for unsupervised feature selection (UFS). However, determining the regularization parameters is rather challenging, and…
Multivariate global polynomial approximations - such as polynomial chaos or stochastic collocation methods - are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses…
Marine Controlled Source Electromagnetic (CSEM) is employed both in large-scale geophysical applications as well as within exploration of hydrocarbons and gas hydrates. Due to the diffusive character of the EM field only very low…
Exoplanetary transit and stellar oscillation surveys require a very high precision photometry. The instrumental noise has therefore to be minimized. First, we perform a semi-analytical model of different noise sources. We show that the…
Weak lensing surveys require accurate correction for the point spread function (PSF) when measuring galaxy shapes. For a diffraction-limited PSF, as arises in space-based missions, this correction depends on each galaxy SED. In the Euclid…
Many circumstellar dust scattering regions have been detected and investigated with polarimetric imaging. However, the quantitative determination of the intrinsic polarization and of dust properties is difficult because of complex…
Ultrasound imaging often suffers from image degradation stemming from phase aberration, which represents a significant contributing factor to the overall image degradation in ultrasound imaging. Frequency-space prediction filtering or FXPF…
We present a variational Bayesian method of joint image reconstruction and point spread function (PSF) estimation when the PSF of the imaging device is only partially known. To solve this semi-blind deconvolution problem, prior…
Cosmic shear requires high precision measurement of galaxy shapes in the presence of the observational Point Spread Function (PSF) that smears out the image. The PSF must therefore be known for each galaxy to a high accuracy. However, for…
The weak gravitational lensing is a powerful tool in modern cosmology. To accurately measure the weak lensing signal, one has to control the systematic bias to a small level. One of the most difficult problems is how to correct the smearing…
A non-parametric smoothing method is presented that reduces noise in multi-wavelength imaging data sets. Using Principle Component Analysis (hereafter PCA) to associate pixels according to their $ugriz$-band colors, smoothing is done over…
We consider the problem of reconstructing one-dimensional point sources from their Fourier measurements in a bounded interval $[-\Omega, \Omega]$. This problem is known to be challenging in the regime where the spacing of the sources is…
We consider the problem of resolving $ r$ point sources from $n$ samples at the low end of the spectrum when point spread functions (PSFs) are not known. Assuming that the spectrum samples of the PSFs lie in low dimensional subspace (let…