We present a novel Asymptotic-Preserving Neural Network (APNN) approach utilizing even-odd decomposition to tackle the nonlinear gray radiative transfer equations (GRTEs). Our AP loss demonstrates consistent stability concerning small Knudsen number, ensuring neural network solution uniformly converges macro solution. This APNN method alleviates rigorous conservation requirements while simultaneously incorporating an auxiliary deep network, distinguishing it from based on micro-macro for...

In this paper, we study ℓ1 − αℓ2 (0 < α ⩽ 1) minimization methods for signal and image reconstruction with impulsive noise removal. The data fitting term is based on fidelity between the output observational data, regularization nonconvex of or its total variation. Theoretically, show that under generalized restricted isometry property underlying can be recovered exactly. Numerical algorithms are also developed to solve resulting optimization problems. Experimental results have shown...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 8 September 2020Accepted: 29 December 2020Published online: 03 May 2021Keywordscompressed sensing, restricted isometry property, $\ell_1-\ell_2$ minimization, sparse representation, recoveryAMS Subject Headings65F50Publication DataISSN (online): 1936-4954Publisher: Society for Industrial and Applied MathematicsCODEN: sjisbi

Let $\mu$ be a Borel measure on $\mathbb{R}^d$ which may non-doubling. The only condition that must satisfy is $\mu(Q)\leq c_0l(Q)^n$ for any cube $Q\subset \mathbb{R}^d$ with sides parallel to the coordinate axes, some fixed $n$ $0 < n\leq d$. In this note we consider commutators of fractional integrals functions new BMO introduced by X. Tolsa.

The null space property (NSP), which depends only on the of column measurement matrix, has received much attention in compressed sensing. This letter considers NSP truncated l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-2</sub> minimization. It provides two versions minimization, under we present sufficient conditions for minimization to recover sparse and compressible signals. In addition, discuss that stable holds by Gaussian matrices...

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Transformed $L_1$ (TL1) regularization has been shown to have comparable signal recovery capability with $L_1-L_2$ and $L_1/L_2$ regularization, regardless of whether the measurement matrix satisfies restricted isometry property (RIP). In spirit TL1 method, we introduce a transformed total variation (TTV) minimization model investigate robust image from certain number noisy measurements by proposed TTV in this paper. An optimal error bound, up logarithmic factor, compressed via is...

.The nonconvex optimization method has attracted increasing attention due to its excellent ability of promoting sparsity in signal processing, image restoration, and machine learning. In this paper, we consider a new minimization \(L_1-\beta L_q\) \(((\beta,q)\in [0,1]\times [1,\infty )\setminus (1,1))\) applications recovery reconstruction because provides an effective way solve the \(q\) -ratio model. Our main contributions are establish convex hull decomposition for investigate RIP-based...

Let $\mu$ be a non-negative Radon measure on $\mathbb {R}^d$ which only satisfies some growth condition. In this paper, the authors obtain boundedness of Calderón-Zygmund operators in Hardy space $H^1(\mu )$.

This paper studies the pointwise estimates of a class oscillatory integrals related to dispersive equations under geometric assumptions finite type. As applications, these can be used set up solutions for different types including classical and general wave equations, Klein-Gordon Schrödinger so on.

This note shows the existence of a sharp bilinear estimate for Bourgain-type space and gives its application to optimal local well/ill-posedness Cauchy problem Benjamin equation.