Related papers: On a link between kernel mean maps and Fraunhofer …
A method to create instructive, nonuniform aperture functions using spatial frequency filtering is described. The diffraction from a single slit in the Fresnel limit and the interference from a double slit in the Fraunhofer limit are…
We consider the problem of improving kernel approximation via randomized feature maps. These maps arise as Monte Carlo approximation to integral representations of kernel functions and scale up kernel methods for larger datasets. Based on…
Diffusion Maps framework is a kernel based method for manifold learning and data analysis that defines diffusion similarities by imposing a Markovian process on the given dataset. Analysis by this process uncovers the intrinsic geometric…
We propose a principled method for kernel learning, which relies on a Fourier-analytic characterization of translation-invariant or rotation-invariant kernels. Our method produces a sequence of feature maps, iteratively refining the SVM…
We propose and demonstrate a new phase retrieval method for imaging through random media. Although methods to recover the Fourier amplitude through random distortions are well established, recovery of the Fourier phase has been a more…
Breaking the diffraction limit in microscopy by utilizing quantum properties of light has been the goal of intense research in the recent years. We propose a quantum superresolution technique based on non-classical emission statistics of…
Kernel mean embeddings -- integrals of a kernel with respect to a probability distribution -- are essential in Bayesian quadrature, but also widely used in other computational tools for numerical integration or for statistical inference…
We resolve the long standing controversy regarding the imaging by a planar lens made of left-handed media and demonstrate theoretically that its far field image has a fundamentally different origin depending on the relationship between…
It is well-known that if a network aims to learn how to deblur, it should understand the blur process. Blurring is naturally caused by the convolution of the sharp image with the blur kernel. Thus, allowing the network to learn the blur…
Optical photothermal microscopy is a powerful, emerging method that overcomes the diffraction limit in infrared hyperspectral imaging by utilizing a visible probe laser beam to detect local temperature-induced modulation at the visible…
Kernel methods provide a flexible and theoretically grounded approach to nonlinear and nonparametric learning. While memory and run-time requirements hinder their applicability to large datasets, many low-rank kernel approximations, such as…
Random Fourier Features (RFF) demonstrate wellappreciated performance in kernel approximation for largescale situations but restrict kernels to be stationary and positive definite. And for non-stationary kernels, the corresponding RFF could…
Random Fourier features is one of the most popular techniques for scaling up kernel methods, such as kernel ridge regression. However, despite impressive empirical results, the statistical properties of random Fourier features are still not…
We show that passing input points through a simple Fourier feature mapping enables a multilayer perceptron (MLP) to learn high-frequency functions in low-dimensional problem domains. These results shed light on recent advances in computer…
We provide a quantitative analysis of super-resolution imaging techniques which exploit temporal fluctuations of luminosity of the sources in order to beat the Rayleigh limit. We define an operationally justified resolution gain figure of…
In some super-resolution techniques, adjacent points are illuminated at different times. Thereby, their locations and light intensities can be detected even if the images are very blurred due to diffraction. According to conventional…
In this paper are reviewed various designs of advanced, multi-aperture optical systems dedicated to high angular resolution imaging or to the detection of exo-planets by nulling interferometry. A simple Fourier optics formalism applicable…
The nonnegative matrix factorization (NMF) is widely used in signal and image processing, including bio-informatics, blind source separation and hyperspectral image analysis in remote sensing. A great challenge arises when dealing with a…
A kernel based procedure for correcting experimental data for distortions due to the finite resolution and limited detector acceptance is presented. The unfolding problem is known to be an ill-posed problem that can not be solved without…
Diffraction tomography aims to recover an object's scattering potential from measured wave fields. In the classical setting, the object is illuminated by plane waves from many directions, and the Fourier diffraction theorem provides a…