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We introduce one- and two-dimensional `exponential shapelets': orthonormal basis functions that efficiently model isolated features in data. They are built from eigenfunctions of the quantum mechanical hydrogen atom, and inherit mathematics…
Hyperspectral Imaging is a crucial tool in remote sensing which captures far more spectral information than standard color images. However, the increase in spectral information comes at the cost of spatial resolution. Super-resolution is a…
Short-and-sparse deconvolution (SaSD) is the problem of extracting localized, recurring motifs in signals with spatial or temporal structure. Variants of this problem arise in applications such as image deblurring, microscopy, neural spike…
In the case of ground-based telescopes equipped with adaptive optics systems, the point spread function (PSF) is only poorly known or completely unknown. Moreover, an accurate modeling of the PSF is in general not available. Therefore in…
We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transform. Our key…
A simple, yet general, formalism for the optimized linear combination of astrophysical images is constructed and demonstrated. The formalism allows the user to combine multiple undersampled images to provide oversampled output at high…
This work presents the construction of a novel spherical wavelet basis designed for incomplete spherical datasets, i.e. datasets which are missing in a particular region of the sphere. The eigenfunctions of the Slepian spatial-spectral…
We develop techniques to solve ill-posed inverse problems on the sphere by sparse regularisation, exploiting sparsity in both axisymmetric and directional scale-discretised wavelet space. Denoising, inpainting, and deconvolution problems,…
Very long baseline interferometry (VLBI) is a radio-astronomical technique in which the correlated signal from various baselines is combined into an image of highest angular resolution. Due to sparsity of the measurements, this imaging…
We propose a deconvolution algorithm for images blurred and degraded by a Poisson noise. The algorithm uses a fast proximal backward-forward splitting iteration. This iteration minimizes an energy which combines a \textit{non-linear} data…
Increasing the resolution of image sensors has been a never ending struggle since many years. In this paper, we propose a novel image sensor layout which allows for the acquisition of images at a higher resolution and improved quality. For…
(arXiv abridged abstract) The current years are seeing huge developments of radio telescopes and a tremendous increase of their capabilities. Such systems make mandatory the design of more sophisticated techniques not only for transporting,…
This paper presents a new family of localized orthonormal bases - sinlets - which are well suited for both signal and image processing and analysis. One-dimensional sinlets are related to specific solutions of the time-dependent harmonic…
We present a method for subtracting point sources from interferometric radio images via forward modeling of the instrument response and involving an algebraic nonlinear minimization. The method is applied to simulated maps of the Murchison…
A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…
Deep cosmic microwave background polarization experiments allow a very precise internal reconstruction of the gravitational lensing signal in pricinple. For this aim, likelihood-based or Bayesian methods are typically necessary, where very…
Access to knowledge of the point spread function (PSF) of adaptive optics(AO)-assisted observations is still a major limitation when processing AO data. This limitation is particularly important when image analysis requires the use of…
Inverse problems in image reconstruction are fundamentally complicated by unknown noise properties. Classical iterative deconvolution approaches amplify noise and require careful parameter selection for an optimal trade-off between…
The problem of imaging extended targets (sources or scatterers) is formulated in the framework of compressed sensing with emphasis on subwavelength resolution. The proposed formulation of the problems of inverse source/scattering is…
We present a dimension-incremental method for function approximation in bounded orthonormal product bases to learn the solutions of various differential equations. Therefore, we decompose the source function of the differential equation…