Related papers: Multiresolution Analysis Based on Coalescence Hidd…
The multiresolution analysis of Alpert is considered. Explicit formulas for the entries in the matrix coefficients of the refinement equation are given in terms of hypergeometric functions. These entries are shown to solve generalized…
Chebyshev Filtered Subspace Iteration (ChFSI) is widely used for computing a small subset of extremal eigenpairs from large matrices, particularly when the eigenpairs must be computed repeatedly as the system matrix evolves within an outer…
The valence of a function $f$ at a point $w$ is the number of distinct, finite solutions to $f(z) = w$. Let $f$ be a complex-valued harmonic function in an open set $R \subseteq \mathbb{C}$. Let $S$ denote the critical set of $f$ and $C(f)$…
We explore the use of multiresolution analysis techniques as texture attributes for seismic image characterization, especially in representing subsurface structures in large migrated seismic data. Namely, we explore the Gaussian pyramid,…
We present a new approach for image reconstruction and weak lensing measurements with interferometers. Based on the shapelet formalism presented in Refregier (2001), object images are decomposed into orthonormal Hermite basis functions. The…
This paper addresses the problem of single view 3D human reconstruction. Recent implicit function based methods have shown impressive results, but they fail to recover fine face details in their reconstructions. This largely degrades user…
Mutiscale analysis represents multiresolution scrutiny of a signal to improve its signal quality. Multiresolution analysis of 1D voice signal and 2D image is conducted using DCT, FFT and different wavelets such as Haar, Deubachies, Morlet,…
Deep learning-based 3D medical image segmentation methods relies on large-scale labeled datasets, yet acquiring such data is difficult due to privacy constraints and the high cost of expert annotation. Formula-Driven Supervised Learning…
We define Sobolev spaces $H^{\mathfrak{s}}(K_q)$ over a local field $K_q$ of finite characteristic $p>0$, where $q=p^c$ for a prime $p$ and $c\in \mathbb{N}$. This paper introduces novel fractal functions, such as the Weierstrass type and…
We construct representations of a q-oscillator algebra by operators on Fock space on positive matrices. They emerge from a multiresolution scaling construction used in wavelet analysis. The representations of the Cuntz Algebra arising from…
Color plays an important role in human visual perception, reflecting the spectrum of objects. However, the existing infrared and visible image fusion methods rarely explore how to handle multi-spectral/channel data directly and achieve high…
Via chirp functions from fractional Fourier transforms, the authors introduce fractional Riesz potentials related to chirp functions, establish their relations with fractional Fourier transforms, fractional Laplace operators related to…
Fourier Transform Interferometry (FTI) is an interferometric procedure for acquiring HyperSpectral (HS) data. Recently, it has been observed that the light source highlighting a (biologic) sample can be coded before the FTI acquisition in a…
Multiplex immunofluorescence (mIF) enables simultaneous single-cell quantification of multiple biomarkers within intact tissue architecture, yet its high reagent cost, multi-round staining protocols, and need for specialized imaging…
Multiresolution Matrix Factorization (MMF) is unusual amongst fast matrix factorization algorithms in that it does not make a low rank assumption. This makes MMF especially well suited to modeling certain types of graphs with complex…
Bayesian image restoration has had a long history of successful application but one of the limitations that has prevented more widespread use is that the methods are generally computationally intensive. The authors recently addressed this…
Multi-modality image fusion aims at fusing modality-specific (complementarity) and modality-shared (correlation) information from multiple source images. To tackle the problem of the neglect of inter-feature relationships, high-frequency…
The focus of this work is on rigorous mathematical analysis of the topological derivative based detection algorithms for the localization of an elastic inclusion of vanishing characteristic size. A filtered quadratic misfit is considered…
Multi-modal image fusion (MMIF) enhances the information content of the fused image by combining the unique as well as common features obtained from different modality sensor images, improving visualization, object detection, and many more…
Guided depth super-resolution is a practical task where a low-resolution and noisy input depth map is restored to a high-resolution version, with the help of a high-resolution RGB guide image. Existing methods usually view this task as a…