Related papers: Approximating W projection as a separable kernel
Fractal image compression, Culik's image compression and zerotree prediction coding of wavelet image decomposition coefficients succeed only because typical images being compressed possess a significant degree of self-similarity. Besides…
The recent demonstration of a real-time direct imaging radio interferometry correlator represents a new capability in radio astronomy. However wide field imaging with this method is challenging since wide-field effects and array…
The problem of approximating a sampled function using sums of a fixed number of complex exponentials is considered. We use alternating projections between fixed rank matrices and Hankel matrices to obtain such an approximation. Convergence,…
In this article, we report an imaging method, termed Fourier ptychographic microscopy (FPM), which iteratively stitches together a number of variably illuminated, low-resolution intensity images in Fourier space to produce a wide-field,…
Rahimi and Recht (2007) introduced the idea of decomposing positive definite shift-invariant kernels by randomly sampling from their spectral distribution for machine learning applications. This famous technique, known as Random Fourier…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
The Planet Formation Imager (PFI) is a project for a very large optical interferometer intended to obtain images of the planet formation process at scales as small as the Hill sphere of giant exoplanets. Its main science instruments will…
Convolution kernels are the basic structural component of convolutional neural networks (CNNs). In the last years there has been a growing interest in fisheye cameras for many applications. However, the radially symmetric projection model…
We present and analyze an approximation scheme for a class of highly oscillatory kernel functions, taking the 2D and 3D Helmholtz kernels as examples. The scheme is based on polynomial interpolation combined with suitable pre- and…
The Wide-field Spectroscopic Telescope (WST) is a proposed 12-meter segmented facility optimized for seeing limited observations in the visible and designed to operate both a high-multiplex multi-object spectrograph and a panoramic integral…
Based on the sampling theorem, interpolation should be conducted by employing the sinc functions as the kernels. Inspired by the fact that the discrete Fourier transform (DFT) is sampled from the discrete time Fourier transform, a fast…
The purpose of this article is to study operators whose kernel share some key features of Bergman kernels from complex analysis, and are approximate projectors. It turns out that they must be associated with a rich set of geometric data, on…
Optical stellar interferometers have demonstrated milli-arcsecond resolution with few apertures spaced hundreds of meters apart. To obtain rich direct images, many apertures will be needed, for a better sampling of the incoming wavefront.…
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…
Spatial relations between objects in an image have proved useful for structural object recognition. Structural constraints can act as regularization in neural network training, improving generalization capability with small datasets.…
Computationally efficient numerical methods for high-order approximations of convolution integrals involving weakly singular kernels find many practical applications including those in the development of fast quadrature methods for…
Convolutional neural networks (CNNs) with large kernels, drawing inspiration from the key operations of vision transformers (ViTs), have demonstrated impressive performance in various vision-based applications. To address the issue of…
Foreground segmentation is an essential task in the field of image understanding. Under unsupervised conditions, different images and instances always have variable expressions, which make it difficult to achieve stable segmentation…
Interpolation and approximation of functionals with conditionally positive definite kernels is considered on sets of centers that are not determining for polynomials. It is shown that polynomial consistency is sufficient in order to define…
In order to produce high dynamic range images in radio interferometry, bright extended sources need to be removed with minimal error. However, this is not a trivial task because the Fourier plane is sampled only at a finite number of…