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Face super-resolution aims to reconstruct a high-resolution face image from a low-resolution face image. Previous methods typically employ an encoder-decoder structure to extract facial structural features, where the direct downsampling…
The parametric nonlinear Schrodinger equation models a variety of parametrically forced and damped dispersive waves. For the defocusing regime, we derive a normal velocity for the evolution of curved dark-soliton fronts that represent a…
Optical focusing at depths in tissue is the Holy Grail of biomedical optics that may bring revolutionary advancement to the field. Wavefront shaping is a widely accepted approach to solve this problem, but most implementations thus far have…
Wavefront shaping has revolutionized the concepts of optical imaging and focusing. Contrary to what was believed, strong scattering in the optical paths can be exploited in favor of light focusing through turbid media and ultimately improve…
In this article, we investigate the application of wavelet packet transform as a novel spectrum sensing approach. The main attraction for wavelet packets is the tradeoffs they offer in terms of satisfying various performance metrics such as…
Wavelet Transforms are a widely used technique for decomposing a signal into coefficient vectors that correspond to distinct frequency/scale bands while retaining time localization. This property enables an adaptive analysis of signals at…
During the past few years, metasurfaces have been used to demonstrate optical elements and systems with capabilities that surpass those of conventional diffractive optics. Here we review some of these recent developments with a focus on…
With the increasing growth of technology and the entrance into the digital age, we have to handle a vast amount of information every time which often presents difficulties. So, the digital information must be stored and retrieved in an…
In this paper, we have studied continuous fractional wavelet transform (CFrWT) in $n$-dimensional Euclidean space $\mathbb{R}^n$ with dilation parameter $\boldsymbol a=(a_{1},a_{2},\ldots,a_{n}),$ such that none of $a_{i}'s$ are zero.…
This document describes the implementation of the external module ITKIsotropicWavelets, a multiresolution (MRA) analysis framework using isotropic and steerable wavelets in the frequency domain. This framework provides the backbone for…
Wavelet (Besov) priors are a promising way of reconstructing indirectly measured fields in a regularized manner. We demonstrate how wavelets can be used as a localized basis for reconstructing permeability fields with sharp interfaces from…
Over the past fifty years, wavefront sensing technology has continuously evolved from basic techniques to high-precision systems, serving as a core methodology in adaptive optics (AO). Beyond traditional wavefront retrieval methods based on…
Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are…
A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of the wavelet formalism developed by Antoine & Vandergheynst (1999) and Wiaux…
A perfectly collimated beam can be spread out by multiple scattering, creating a speckle pattern and increasing the etendue of the system. Standard optical systems conserve etendue, and thus are unable to reverse the process by transforming…
Image registration is the process of transforming different sets of data into one coordinate system and is required for various remote sensing applications like change detection, image fusion, and other related areas. The effect of…
This paper is a continuation of a paper by the authors: arXiv:0706.0415, where short range perturbations of the flat Euclidian metric where considered. Here, we generalize the results of the paper to long-range perturbations (in particular,…
In the paper we design a Parseval wavelet frame with a compact support and many vanishing moments. The corresponding refinement mask approximates an arbitrary continuous periodic function $f$, $f(0)=1$. The refinable function has stable…
We consider an extension of the continuous shearlet transform which additionally uses higher order shears. This extension, called the Taylorlet transform, allows for a detection of the position, the orientation, the curvature and other…
Recent work has highlighted several advantages of enforcing orthogonality in the weight layers of deep networks, such as maintaining the stability of activations, preserving gradient norms, and enhancing adversarial robustness by enforcing…