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We introduce Schroedinger Eigenmaps, a new semi-supervised manifold learning and recovery technique. This method is based on an implementation of graph Schroedinger operators with appropriately constructed barrier potentials as carriers of…
A new denoising algorithm for hyperspectral complex domain data has been developed and studied. This algorithm is based on the complex domain block-matching 3D filter including the 3D Wiener filtering stage. The developed algorithm is…
The Wigner function for one and two-mode quantum systems is explicitely expressed in terms of the marginal distribution for the generic linearly transformed quadratures. Then, also the density operator of those systems is written in terms…
In machine learning approach to image denoising a network is trained to recover a clean image from a noisy one. In this paper a novel structure is proposed based on training multiple specialized networks as opposed to existing structures…
The aim of this paper is to provide uniform estimates for the eigenvalue spacings of one-dimensional semiclassical Schr\"odinger operators with singular potentials on the half-line. We introduce a new development of semiclassical measures…
In computer-aided diagnosis (CAD) focused on microscopy, denoising improves the quality of image analysis. In general, the accuracy of this process may depend both on the experience of the microscopist and on the equipment sensitivity and…
Autoencoding, which aims to reconstruct the input images through a bottleneck latent representation, is one of the classic feature representation learning strategies. It has been shown effective as an auxiliary task for semi-supervised…
All techniques for denoising involve a notion of a true (noise-free) image, and a hypothesis space. The hypothesis space may reconstruct the image directly as a grayscale valued function, or indirectly by its Fourier or wavelet spectrum.…
Image denoising is of great importance for medical imaging system, since it can improve image quality for disease diagnosis and downstream image analyses. In a variety of applications, dynamic imaging techniques are utilized to capture the…
In this paper we describe active set type algorithms for minimization of a smooth function under general order constraints, an important case being functions on the set of bimonotone r-by-s matrices. These algorithms can be used, for…
I consider random Schr\"odinger operators with exponentially decaying single site potential, which is allowed to change sign. For this model, I prove Anderson localization both in the sense of exponentially decaying eigenfunctions and…
One-dimensional signal decomposition is a well-established and widely used technique across various scientific fields. It serves as a highly valuable pre-processing step for data analysis. While traditional decomposition techniques often…
We present a novel deep learning method for computing eigenvalues of the fractional Schr\"odinger operator. Our approach combines a newly developed loss function with an innovative neural network architecture that incorporates prior…
Image denoising is an important pre-processing step in medical image analysis. Different algorithms have been proposed in past three decades with varying denoising performances. More recently, having outperformed all conventional methods,…
Neat stuff about eigenfunctions, transfer matrices, and a.c. spectrum of one-dimensional Schrodinger operators
For a large family of real-valued Radon measures m on R^d, including the Kato class, the operators -\Delta + C^2 \Delta^2 + m tend to the Schrodinger operator -\Delta +m in the norm resolvent sense as C tends to zero. If the measure is…
Optical image data have been used by the Remote Sensing workforce to study land use and cover since such data is easily interpretable. Synthetic Aperture Radar (SAR) has the characteristic of obtaining images during all-day, all-weather and…
A spectral theory of linear operators on a rigged Hilbert space is applied to Schr\"odinger operators with exponentially decaying potentials and dilation analytic potentials. The theory of rigged Hilbert spaces provides a unified approach…
We consider a semi-classical Schrodinger operator with a degenerate potential V(x,y) =f(x) g(y) . g is assumed to be a homogeneous positive function of m variables and f is a strictly positive function of n variables, with a strict minimum.…
Image denoising is a classical signal processing problem that has received significant interest within the image processing community during the past two decades. Most of the algorithms for image denoising has focused on the paradigm of…