Related papers: Revisiting Homomorphic Wavelet Estimation and Phas…
Finding low-dimensional interpretable models of complex physical fields such as turbulence remains an open question, 80 years after the pioneer work of Kolmogorov. Estimating high-dimensional probability distributions from data samples…
A new phase-coherent technique for the calibration of polarimetric data is presented. Similar to the one-dimensional form of convolution, data are multiplied by the response function in the frequency domain. Therefore, the system response…
Deconvolution is the most commonly used image processing method to remove the blur caused by the point-spread-function (PSF) in optical imaging systems. While this method has been successful in deblurring, it suffers from several…
Unmixing the disk-integrated spectra of exoplanets provides hints about heterogeneous surfaces that we cannot directly resolve in the foreseeable future. It is particularly important for terrestrial planets with diverse surface compositions…
In image deconvolution problems, the diagonalization of the underlying operators by means of the FFT usually yields very large speedups. When there are incomplete observations (e.g., in the case of unknown boundaries), standard…
In this paper, we introduce a total variation based variational model for denoising wrapped phase images. Our model improves on former methods by preserving discontinuities of the phase map and enforcing the fundamental Pythagorean…
We consider deconvolution from repeated observations with unknown error distribution. So far, this model has mostly been studied under the additional assumption that the errors are symmetric. We construct an estimator for the non-symmetric…
We present a novel surface convolution operator acting on vector fields that is based on a simple observation: instead of combining neighboring features with respect to a single coordinate parameterization defined at a given point, we have…
The visualization of pure phase objects by wavefront sensing has important applications ranging from surface profiling to biomedical microscopy, and generally requires bulky and complicated setups involving optical spatial filtering,…
In recent years, astronomical photometry has been revolutionised by space missions such as MOST, CoRoT and Kepler. However, despite this progress, high-quality spectroscopy is still required as well. Unfortunately, high-resolution spectra…
Wavelet estimators for a probability density f enjoy many good properties, however they are not "shape-preserving" in the sense that the final estimate may not be non-negative or integrate to unity. A solution to negativity issues may be to…
In astronomy or biological imaging, refractive index inhomogeneities of e.g. atmosphere or tissues induce optical aberrations which degrade the desired information hidden behind the medium. A standard approach consists in measuring these…
Quantum phase is not a direct observable and is usually determined by interferometric methods. We present a method to map complete electron wave functions, including internal quantum phase information, from measured single-state probability…
In this paper, we propose a novel hyperspectral unmixing technique based on deep spectral convolution networks (DSCN). Particularly, three important contributions are presented throughout this paper. First, fully-connected linear operation…
We consider sequential and parallel decomposition methods for a dual problem of a general total variation minimization problem with applications in several image processing tasks, like image inpainting, estimation of optical flow and…
We describe the implementation of a topological constraint in finite element simulations of phase field models which ensures path-connectedness of preimages of intervals in the phase field variable. Two main applications of our method are…
Seismic denoising is an important processing step before subsequent imaging and interpretation, which consumes a significant amount of time, whether it is for Quality control or for the associated computations. We present results of our…
In this paper, a hard thresholding wavelet estimator is constructed for a deconvolution model in a periodic setting that has long-range dependent noise. The estimation paradigm is based on a maxiset method that attains a near optimal rate…
We present in this paper new multiscale transforms on the sphere, namely the isotropic undecimated wavelet transform, the pyramidal wavelet transform, the ridgelet transform and the curvelet transform. All of these transforms can be…
We provide a new algorithm for the treatment of the deconvolution problem on the sphere which combines the traditional SVD inversion with an appropriate thresholding technique in a well chosen new basis. We establish upper bounds for the…