Related papers: On a link between kernel mean maps and Fraunhofer …

Diffraction is a manifestation of light at edge due to its wavelike nature. The well-known diffraction phenomena are Fresnel and Fraunhofer, they find variety of applications individually. But the synergy of two phenomena is not studied and…

We introduce a novel diffusion-based spectral algorithm to tackle regression analysis on high-dimensional data, particularly data embedded within lower-dimensional manifolds. Traditional spectral algorithms often fall short in such…

We propose a new class of kernels to simplify the design of filters for image interpolation and resizing. Their properties are defined according to two parameters, specifying the width of the transition band and the height of a unique…

Astrophysical images issued from different instruments and/or spectral bands often require to be processed together, either for fitting or comparison purposes. However each image is affected by an instrumental response, also known as PSF,…

Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…

Fourier ptychography is a recently explored imaging method for overcoming the diffraction limit of conventional cameras with applications in microscopy and yielding high-resolution images. In order to splice together low-resolution images…

For more than a century, the diffraction limit has defined the resolution achievable by passive optical imaging systems. Although some resolution improvement can be gained through classical data processing of the image, it is limited by the…

In this paper, we study the feature learning ability of two-layer neural networks in the mean-field regime through the lens of kernel methods. To focus on the dynamics of the kernel induced by the first layer, we utilize a two-timescale…

We revisit Rahimi and Recht (2007)'s kernel random Fourier features (RFF) method through the lens of the PAC-Bayesian theory. While the primary goal of RFF is to approximate a kernel, we look at the Fourier transform as a prior distribution…

We find a new integration transformation which can convert a chirplet function to fractional Fourier transformation kernel, this new transformation is invertible and obeys Parseval theorem. Under this transformation a new relationship…

Metal-dielectric layered stacks for imaging with sub-wavelength resolution are regarded as linear isoplanatic systems - a concept popular in Fourier Optics and in scalar diffraction theory. In this context, a layered flat lens is a…

While achieving excellent results on various datasets, many deep learning methods for image deblurring suffer from limited generalization capabilities with out-of-domain data. This limitation is likely caused by their dependence on certain…

The paper studies machine learning problems where each example is described using a set of Boolean features and where hypotheses are represented by linear threshold elements. One method of increasing the expressiveness of learned hypotheses…

Deep learning-based image reconstruction methods have achieved remarkable success in phase recovery and holographic imaging. However, the generalization of their image reconstruction performance to new types of samples never seen by the…

Lensless imaging methods that account for partial coherence have become very common in the past decade. However, there are no metrics in use for comparing partially coherent light fields, despite the widespread use of such metrics to…

The Fourier inversion of phased coherent diffraction patterns offers images without the resolution and depth-of-focus limitations of lens-based tomographic systems. We report on our recent experimental images inverted using recent…

In this paper, we introduce a new image representation based on a multilayer kernel machine. Unlike traditional kernel methods where data representation is decoupled from the prediction task, we learn how to shape the kernel with…

Recently, the theory of diffusion maps was extended to a large class of local kernels with exponential decay which were shown to represent various Riemannian geometries on a data set sampled from a manifold embedded in Euclidean space.…

Circular and hyperbolic fractional-order Fourier transformations are actually Weyl pseudo-differential operators. Their associated kernels and symbols are written explicitly. Products of fractional-order Fourier transformations are obtained…

One of the main computational bottlenecks when working with kernel based learning is dealing with the large and typically dense kernel matrix. Techniques dealing with fast approximations of the matrix vector product for these kernel…