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A nearly optimal explicitly-sparse representation for oscillatory kernels is presented in this work by developing a curvelet based method. Multilevel curvelet-like functions are constructed as the transform of the original nodal basis. Then…
A novel spherical convolution is defined through the sifting property of the Dirac delta on the sphere. The so-called sifting convolution is defined by the inner product of one function with a translated version of another, but with the…
Multivariate problems are typically governed by anisotropic features such as edges in images. A common bracket of most of the various directional representation systems which have been proposed to deliver sparse approximations of such…
Wavefront sensing and reconstruction are widely used for adaptive optics, aberration correction, and high-resolution optical phase imaging. Traditionally, interference and/or microlens arrays are used to convert the optical phase into…
At millimeter wavelengths, the atmospheric emission is circularly polarized owing to the Zeeman splitting of molecular oxygen by the Earth's magnetic field. We report a measurement of the signal in the 150 GHz band using 3 years of…
Direct detection of exoplanets requires high dynamic range imaging. Coronagraphs could be the solution, but their performance in space is limited by wavefront errors (manufacturing errors on optics, temperature variations, etc.), which…
Shuffled linear regression (SLR) seeks to estimate latent features through a linear transformation, complicated by unknown permutations in the measurement dimensions. This problem extends traditional least-squares (LS) and Least Absolute…
Spatial field correlation functions represent a key quantity for the description of mesoscopic phenomena in disordered media and the optical characterization of complex materials. Yet many aspects related to the vector nature of light waves…
Sampling and budgeting training examples are two essential factors in tracking algorithms based on support vector machines (SVMs) as a trade-off between accuracy and efficiency. Recently, the circulant matrix formed by dense sampling of…
As galaxy surveys become larger and more complex, keeping track of the completeness, magnitude limit, and other survey parameters as a function of direction on the sky becomes an increasingly challenging computational task. For example,…
We consider a fast, data-sparse directional method to realize matrix-vector products related to point evaluations of the Helmholtz kernel. The method is based on a hierarchical partitioning of the point sets and the matrix. The considered…
A novel algorithm is proposed for quantitative comparisons between compact surfaces embedded in the three-dimensional Euclidian space. The key idea is to identify those objects with the associated surface measures and compute a weak…
The performance of adaptive optics systems is partially dependant on the algorithms used within the real-time control system to compute wavefront slope measurements. We demonstrate use of a matched filter algorithm for the processing of…
In astronomy and microscopy, distortions in the wavefront affect the dynamic range of a high contrast imaging system. These aberrations are either imposed by a turbulent medium such as the atmosphere, by static or thermal aberrations in the…
Pairing coherent correlation OTDR with low-complexity analysis methods, we investigate the detection of fast temperature changes and vibrations in optical fibers. A localization accuracy of ~2 m and extraction of vibration amplitudes and…
We present a new method to estimate three-point correlations in Cosmic Microwave Background maps. Our Fast Fourier Transform based implementation estimates three-point functions using all possible configurations (triangles) at a controlled…
Spherical regression explores relationships between variables on spherical domains. We develop a nonparametric model that uses a diffeomorphic map from a sphere to itself. The restriction of this mapping to diffeomorphisms is natural in…
Wave propagation and acoustic scattering problems require vast computational resources to be solved accurately at high frequencies. Asymptotic methods can make this cost potentially frequency independent by explicitly extracting the…
The Easy Path Wavelet Transform is an adaptive transform for bivariate functions (in particular natural images) which has been proposed in [1]. It provides a sparse representation by finding a path in the domain of the function leveraging…
We present a solver for the 2D high-frequency Helmholtz equation in heterogeneous acoustic media, with online parallel complexity that scales optimally as $\mathcal{O}(\frac{N}{L})$, where $N$ is the number of volume unknowns, and $L$ is…