Related papers: Image representation and denoising using squared e…
Sparse representation of real-life images is a very effective approach in imaging applications, such as denoising. In recent years, with the growth of computing power, data-driven strategies exploiting the redundancy within patches…
The behaviour of the photon renormalization function in strong coupling QED has been recently studied by Kondo, Mino and Nakatani. We find that the sharp decrease in its behaviour at intermediate photon momenta is an artefact of the method…
Many imaging modalities involve reconstruction of unknown objects from collections of noisy projections related by random rotations. In one of these modalities, cryogenic electron microscopy (cryo-EM), the extremely low signal-to-noise…
This paper investigates quantum simulation algorithms for the Liouville equation in geometrical optics with partial transmission and reflection at sharp interfaces, based on the Schr\"odingerization method. By means of a warped phase…
The bilateral filter has diverse applications in image processing, computer vision, and computational photography. In particular, this non-linear filter is quite effective in denoising images corrupted with additive Gaussian noise. The…
This paper gives an introduction to the theory of orthogonal projection of functions or signals. Several kinds of decomposition are explored: Fourier, Fourier-Legendre, Fourier-Bessel series for 1D signals, and Spherical Harmonic series for…
Functional graphs (FGs) model the graph structures used to analyse the behaviour of functions from a discrete set to itself. In turn, such functions are used to study real complex phenomena evolving in time. As the systems involved can be…
We analyze the Schr\"odingerization method for quantum simulation of a general class of non-unitary dynamics with inhomogeneous source terms. The Schr\"odingerization technique, introduced in [31], transforms any linear ordinary and partial…
Diagonalization, or eigenvalue decomposition, is very useful in many areas of applied mathematics, including signal processing and quantum physics. Matrix decomposition is also a useful tool for approximating matrices as the product of a…
Spherical confinement in 3D harmonic, quartic and other higher oscillators of even order is studied. The generalized pseudospectral method is employed for accurate solution of relevant Schr\"odinger equation in an \emph{optimum,…
Joint diagonalization, the process of finding a shared set of approximate eigenvectors for a collection of matrices, arises in diverse applications such as multidimensional harmonic analysis or quantum information theory. This task is…
The recent statistical theory of neural networks focuses on nonparametric denoising problems that treat randomness as additive noise. Variability in image classification datasets does, however, not originate from additive noise but from…
Sparse coding of images is traditionally done by cutting them into small patches and representing each patch individually over some dictionary given a pre-determined number of nonzero coefficients to use for each patch. In lack of a way to…
In this paper we point out an connection between eigenfunctions of one-dimensional Schrodinger operator with polynomial potentials of degree 3, 4 and eigenfunctions of rank two commuting ordinary differential operators.
Image restoration has been an extensively researched topic in numerous fields. With the advent of deep learning, a lot of the current algorithms were replaced by algorithms that are more flexible and robust. Deep networks have demonstrated…
Wavelet denoising is a classical and effective approach for reducing noise in images and signals. Suggested in 1994, this approach is carried out by rectifying the coefficients of a noisy image in the transform domain, using a set of scalar…
The main object of this work is to show how some rather elementary techniques based upon certain inverse pairs of symbolic operators would lead us easily to several decomposition formulas associated with confluent hypergeometric functions…
Reconstruction fidelity of sparse signals contaminated by sparse noise is considered. Statistical mechanics inspired tools are used to show that the l1-norm based convex optimization algorithm exhibits a phase transition between the…
When capturing and storing images, devices inevitably introduce noise. Reducing this noise is a critical task called image denoising. Deep learning has become the de facto method for image denoising, especially with the emergence of…
Recovering a signal from auto-correlations or, equivalently, retrieving the phase linked to a given Fourier modulus, is a wide-spread problem in imaging. This problem has been tackled in a number of experimental situations, from optical…