Blind image deblurring is a well-known ill-posed inverse problem in the computer vision field. To make the problem well-posed, this paper puts forward a plain but effective regularization method, namely spectral norm regularization (SN), which can be...
This paper introduces a robust waveform design method aimed at reducing the impact of electromagnetic interference in radar systems, thereby enhancing target detection accuracy. We propose utilizing a high-order p-norm to characterize the peak sidelo...
Spectral reflectance reconstruction for multispectral images (such as Weiner estimation) may perform sub-optimally when the object being measured has a texture that is not in the training set. The accuracy of the reconstruction is significantly lower...
The purpose of this study is to analyze and compare pediatric normative data for the retinal nerve fiber layer of Romanian children using two different spectral domain optical coherence tomographs. Due to different scanning speeds and axial and trans...
In this work, a new time-frequency tool based on minimum-norm spectral estimation is introduced for multiple fault detection in induction motors. Several diagnostic techniques are available to identify certain faults in induction machines; however, t...
Norm bounds for circulant-type matrices associated with the bi-periodic Pell–Lucas sequence are examined from a symmetry-driven perspective. By incorporating alternating recurrence coefficients, the results clarify how periodicity and circulant...
The goal of sparse linear hyperspectral unmixing is to determine a scanty subset of spectral signatures of materials contained in each mixed pixel and to estimate their fractional abundances. This turns into an...
In this paper, we present some important approximation properties of Chebyshev polynomials in the Legendre norm. We mainly discuss the Chebyshev interpolation operator at the Chebyshev–Gauss–Lobatto points. The cases of single domain and...
Modeling and design of on-chip interconnect, the interconnection between the components is becoming the fundamental roadblock in achieving high-speed integrated circuits. The scaling of interconnect in nanometer regime had shifted the paradime from d...
Discrete spectral clustering directly obtains the discrete labels of data, but existing clustering methods assume that the real-valued indicator matrices of different views are identical, which is unreasonable in practical applications. Moreover, the...
We used numerical methods to define the normative structure of resting-state EEG (rsEEG) in a pilot study of 37 healthy subjects (10–74 years old), using a double-banana bipolar montage. Artifact-free 120–200 s epoch lengths were visually...
Spectral computed tomography (CT) can divide collected photons into multi-energy channels and gain multi-channel projections synchronously by using photon-counting detectors. However, reconstructed images usually contain severe noise due to the limit...
This study advances the application of the generalized Halmos’ two projections theorem to idempotent operators on Hilbert
The conditioning theory of the generalized inverse
In this study we have given some upper bounds for the spectral and lp norms of Cauchy-Toeplitz and Cauchy-Hankel matrices of the forms T = [1/(1/2 + |i + j|]n×n and H= [1/(1/2 + (i + j))]n×n respectively.
The Pell numbers, named after the English diplomat and mathematician John Pell, are studied by many authors. At this work, by inspiring the definition harmonic numbers, we define harmonic Pell numbers. Moreover, we construct one type of symmetric mat...
The energy
Aiming to assess the role of individual molecular structures in the molecular mechanism of ligand-receptor interaction correlation analysis, the recent Spectral-SAR approach is employed to introduce the Quantum-SAR (QuaSAR) “wave” and “conversion fac...
Tensor-based multi-view spectral clustering methods are promising in practical clustering applications. However, most of the existing methods adopt the
A symmetric spectral method is applied to investigate the two-dimensional Volterra integral equation with weakly singular kernels and delays. In this work, the solution of the equation we considered is assumed to be sufficiently smooth so that the sp...
We present a mathematical analysis of the sterol regulatory element-binding protein 2 (SREBP-2) pathway, a key regulator of intracellular cholesterol homeostasis. Using a compartment model formulated as a nonlinear system of ordinary differential equ...
As a widely used classifier, sparse representation classification (SRC) has shown its good performance for hyperspectral image classification. Recent works have highlighted that it is the collaborative representation mechanism under SRC that makes SR...
The utilization of the inversion-based algorithm for spectral decomposition using constrained least-squares spectral analysis (CLSSA) facilitates a time–frequency spectrum with higher temporal and frequency resolution. The conventional CLSSA al...
This article constructs all the anisotropic spaces of four-dimensional numbers in which the commutative and associative operations of addition and multiplication are defined. In this case, so-called “zero divisors” appear in these spaces....
This paper presents a global and local tensor sparse approximation (GLTSA) model for removing the stripes in hyperspectral images (HSIs). HSIs can easily be degraded by unwanted stripes. Two intrinsic characteristics of the stripes are (1) global spa...
Symmetry plays a crucial role in the study of dual matrices and dual matrix group inverses. This paper is mainly divided into two parts. We present the definition of the spectral norm of a dual real matrix
In this paper, we establish a correlation between the bihyperbolic numbers set and the semi-Euclidean space. There are three different norms on the semi-Euclidean space that allow us to define three different hypersurfaces on semi-Euclidean space. He...
In this paper, we propose a new hyperspectral image (HSI) denoising model with the group sparsity regularized hybrid spatio-spectral total variation (GHSSTV) and low-rank tensor decomposition, which is based on the analysis of structural sparsity of...
Reconstruction of 3D objects in various tomographic measurements is an important problem which can be naturally addressed within the mathematical framework of 3D tensors. In Optical Coherence Tomography, the reconstruction problem can be recast as a...
This study introduces an analysis concerning spacetime perturbations within the context of quantum foam models. Under the framework of Sobolev spaces,
Hyperspectral image (HSI) super-resolution is a vital technique that generates high spatial-resolution HSI (HR-HSI) by integrating information from low spatial-resolution HSI with high spatial-resolution multispectral image (MSI). However, existing s...
Reducing the acquisition time for two-dimensional nuclear magnetic resonance (2D NMR) spectra is important. One way to achieve this goal is reducing the acquired data. In this paper, within the framework of compressed sensing, we proposed to undersam...
Hyperspectral image (HSI) quality is generally degraded by diverse noise contamination during acquisition, which adversely impacts subsequent processing performance. Current techniques predominantly rely on nuclear norms and low-rank matrix approxima...
We propose and investigate two new methods to approximate
Fourier spectral methods for solving some linear stochastic space-fractional partial differential equations perturbed by space-time white noises in the one-dimensional case are introduced and analysed. The space-fractional derivative is defined by us...
We study the exact small deviation asymptotics with respect to the Hilbert norm for some mixed Gaussian processes. The simplest example here is the linear combination of the Wiener process and the Brownian bridge. We get the precise final result in t...
We introduce a novel regularization function for hyperspectral image (HSI), which is based on the nuclear norms of gradient images. Unlike conventional low-rank priors, we achieve a gradient-based low-rank approximation by minimizing the sum of nucle...
Hyperspectral image (HSI) acquisitions are degraded by various noises, among which additive Gaussian noise may be the worst-case, as suggested by information theory. In this paper, we present a novel tensor-based HSI denoising approach by fully ident...
This paper presents the Parallel Primal-Dual (PPD3) algorithm, an innovative approach to solving optimization problems characterized by the minimization of the sum of three convex functions, including a Lipschitz continuous term. The proposed algorit...
Pansharpening refers to the fusion of a panchromatic (PAN) and a multispectral (MS) image aimed at generating a high-quality outcome over the same area. This particular image fusion problem has been widely studied, but until recently, it has been cha...
In this article, a space-time spectral method is considered to approximate third-order differential equations with non-periodic boundary conditions. The Legendre-Petrov-Galerkin discretization is employed in both space and time. In the theoretical an...
Consideration is given to a reaction–diffusion free boundary value problem with one or two turning points arising in oil price modeling. First, an exact (analytical) solution to the reduced problem (i.e., no diffusion term) was obtained for som...
The solution of compressible flow equations is of interest with many aerospace engineering applications. Past literature has focused primarily on the solution of Computational Fluid Dynamics (CFD) problems with low-order finite element and finite vol...
This paper presents and discusses the stability of a discrete multirate sampling system whose sets of sampling rates (or sampling periods) are the integer multiple of those operating on all the preceding substates. Each of such substates is associate...
Conifers are a common type of plant used in ornamental horticulture. The prompt diagnosis of the phenological state of coniferous plants using remote sensing is crucial for forecasting the consequences of extreme weather events. This is the first stu...
Hyperspectral Images (HSIs) contain enriched information due to the presence of various bands, which have gained attention for the past few decades. However, explosive growth in HSIs’ scale and dimensions causes “Curse of dimensionality&r...
Purpose: The purpose was to establish normative data for the macular thicknesses and volume using spectral-domain optical coherence tomography (SD-OCT) in a diabetic population without maculopathies for use as a reference in diabetic retinopathy (DR)...
This study proposes a method for estimating the spectral images of fluorescence spectral distributions emitted from plant grains and leaves without using a spectrometer. We construct two types of multiband imaging systems with six channels, using ord...
We propose a new iterative method for solving a generalized Sylvester matrix equation
The harvest year of maize seeds has a significant impact on seed vitality and maize yield. Therefore, it is vital to identify new seeds. In this study, an on-line near-infrared (NIR) spectra collection device (899–1715 nm) was designed and empl...
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