Related papers: Wavelets, Curvelets and Multiresolution Analysis T…
Solving inverse problems is central to a variety of important applications, such as biomedical image reconstruction and non-destructive testing. These problems are characterized by the sensitivity of direct solution methods with respect to…
A new technique is presented for producing images from interferometric data. The method, ``smear fitting'', makes the constraints necessary for interferometric imaging double as a model, with uncertainties, of the sky brightness…
In a standard method of determining electron density for soft X-ray (SXR) flare kernels it is necessary to assume what is the extension of a kernel along the line of sight. This is a source of significant uncertainty of the obtained…
Wavelet scattering networks, which are convolutional neural networks (CNNs) with fixed filters and weights, are promising tools for image analysis. Imposing symmetry on image statistics can improve human interpretability, aid in…
We present experimental and theoretical studies of magnetic levitation of hydrogen gas bubble surrounded by liquid hydrogen confined in a semi-transparent spherical shell of 3 mm internal diameter. Such shells are used as targets for the…
Inspired by the key principle behind the EM algorithm, we propose a general methodology for conducting wavelet estimation with irregularly-spaced data by viewing the data as the observed portion of an augmented regularly-spaced data set. We…
Accurately quantifying swelling of alloys that have undergone irradiation is essential for understanding alloy performance in a nuclear reactor and critical for the safe and reliable operation of reactor facilities. However, typical…
In computer vision, convolutional networks (CNNs) often adopts pooling to enlarge receptive field which has the advantage of low computational complexity. However, pooling can cause information loss and thus is detrimental to further…
We propose a new wavelet-based method for density estimation when the data are size-biased. More specifically, we consider a power of the density of interest, where this power exceeds 1/2. Warped wavelet bases are employed, where warping is…
The wavelet spectra is a common starting point for estimating the Hurst exponent of a self-similar signal using wavelet-based techniques. The decay of the $\log_2$ average energy of the detail wavelet coefficients as a function of the level…
Multiresolution deep learning approaches, such as the U-Net architecture, have achieved high performance in classifying and segmenting images. However, these approaches do not provide a latent image representation and cannot be used to…
The information regarding how the intergalactic medium is reionized by astrophysical sources is contained in the tomographic three-dimensional 21 cm images from the epoch of reionization. In Zhao et al. (2022a) ("Paper I"), we demonstrated…
This note is devoted to an analysis of the so-called peeling algorithm in wavelet denoising. Assuming that the wavelet coefficients of the signal can be modeled by generalized Gaussian random variables, we compute a critical thresholding…
The measurement of weak gravitational lensing is currently limited to a precision of ~10% by instabilities in galaxy shape measurement techniques and uncertainties in their calibration. The potential of large, on-going and future cosmic…
In this paper, we present a theoretical analysis of separating images consisting of pointlike and $C^{ \beta}$-curvelike structures, where $\beta \in (1,2] $. Our approach is based on $l_1$-minimization, in which the sparsity of the desired…
Image deblurring is a classical computer vision problem that aims to recover a sharp image from a blurred image. To solve this problem, existing methods apply the Encode-Decode architecture to design the complex networks to make a good…
We present subarcsecond resolution mid-infrared (mid-IR) photometry in the wavelength range from 8 to 20 micron of eighteen Seyfert galaxies, reporting high spatial resolution nuclear fluxes for the entire sample. We construct spectral…
Radiation symmetry evaluation is critical to the laser driven Inertial Confinement Fusion (ICF), which is usually done by solving a view-factor equation model. The model is nonlinear, and the number of equations can be very large when the…
The application of wavelet transforms to Synthetic Aperture Radar (SAR) imagery has improved despeckling performance. To deduce the problem of filtering the multiplicative noise to the case of an additive noise, the wavelet decomposition is…
We study the X-ray spectra of a sample of 19 obscured, optically-selected Seyfert galaxies (Sy 1.8, 1.9 and 2) in the local universe ($d \leq 175$~Mpc), drawn from the CfA Seyfert sample. Our analysis is driven by the high sensitivity of…