Related papers: On a link between kernel mean maps and Fraunhofer …
The method of random Fourier features (RFF), proposed in a seminal paper by Rahimi and Recht (NIPS'07), is a powerful technique to find approximate low-dimensional representations of points in (high-dimensional) kernel space, for…
The kernel mean embedding of probability distributions is commonly used in machine learning as an injective mapping from distributions to functions in an infinite dimensional Hilbert space. It allows us, for example, to define a distance…
Blind deconvolution problems are severely ill-posed because neither the underlying signal nor the forward operator are not known exactly. Conventionally, these problems are solved by alternating between estimation of the image and kernel…
Fraunhofer diffraction is a well-known phenomenon achieved with most wavelength even without lens. A single-shot intensity measurement of diffraction is generally considered inadequate to reconstruct the original light field, because the…
We derive and showcase a novel approach to approximating Fourier transforms in higher dimensions, focusing specifically on the case of 2D radially concentrated ('ring-like') functions. We first reduce the problem to that of evaluating the…
Increasing the angular resolution of an interferometric array requires placing its elements at large separations. This often leads to sparse coverage and introduces challenges to reconstructing images from interferometric data. We introduce…
Kernel mean embedding (KME) is a powerful tool to analyze probability measures for data, where the measures are conventionally embedded into a reproducing kernel Hilbert space (RKHS). In this paper, we generalize KME to that of von…
At present, the principal limitation on the resolution and contrast of astronomical imaging instruments comes from aberrations in the optical path, which may be imposed by the Earth's turbulent atmosphere or by variations in the alignment…
Kernel mean embeddings have recently attracted the attention of the machine learning community. They map measures $\mu$ from some set $M$ to functions in a reproducing kernel Hilbert space (RKHS) with kernel $k$. The RKHS distance of two…
We propose a nonlinear imaging scheme with undetected photons that overcomes the diffraction limit by transferring near-field information at one wavelength to far-field information of a correlated photon with a different wavelength…
In image set classification, a considerable advance has been made by modeling the original image sets by second order statistics or linear subspace, which typically lie on the Riemannian manifold. Specifically, they are Symmetric Positive…
We investigate analytically and numerically the role of quantum fluctuations in reconstruction of optical objects from diffraction-limited images. Taking as example of an input object two closely spaced Gaussian peaks we demonstrate that…
Entangled-photon coincidence imaging is a method to nonlocally image an object by transmitting a pair of entangled photons through the object and a reference optical system, respectively. The image of the object can be extracted from the…
How aesthetically pleasing is your country's diffraction pattern? This work summarizes the calculated and experimental Fraunhofer diffraction patterns obtained from using apertures lithographically formed into shapes of national borders.…
Lithography is fundamental to integrated circuit fabrication, necessitating large computation overhead. The advancement of machine learning (ML)-based lithography models alleviates the trade-offs between manufacturing process expense and…
Precise calibration is a must for high reliance 3D computer vision algorithms. A challenging case is when the camera is behind a protective glass or transparent object: due to refraction, the image is heavily distorted; the pinhole camera…
Quantum-inspired superresolution methods surpass the Rayleigh limit in imaging, or the analogous Fourier limit in spectroscopy. This is achieved by carefully extracting the information carried in the emitted optical field by engineered…
Generalizations and variations of the fundamental lemma by Willems et al. are an active topic of recent research. In this note, we explore and formalize the links between kernel regression and some known nonlinear extensions of the…
Kernel methods are a highly effective and widely used collection of modern machine learning algorithms. A fundamental limitation of virtually all such methods are computations involving the kernel matrix that naively scale quadratically…
The problem of estimating the kernel mean in a reproducing kernel Hilbert space (RKHS) is central to kernel methods in that it is used by classical approaches (e.g., when centering a kernel PCA matrix), and it also forms the core inference…