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• W4285010277 abstract "Three families of super-resolution (SR) wavelets Ψv,ng(x), Ψu,n,ms(x) and Ψw,n,mds(x), to be called Gaussian SR (GSR), spline SR (SSR) and dual-spline SR (DSSR) wavelets, respectively, are introduced in this paper for resolving the super-resolution problem of recovering any point-mass h(y)=∑ℓ=1Lcℓδ(y−σℓ), with |σℓ−σk|≥η for ℓ≠k, σℓ≠0, and |cℓ|>η⁎ for all ℓ,k=1,…,L, where η>0 and η⁎>0 are allowed to be arbitrarily small. Let Ψα,n=Ψv,ng, Ψu,n,ms or Ψw,n,mds, with α=v,u or w, respectively, where m=12,1,2,⋯ is suppressed. The SR wavelets are designed to have the n-th order of vanishing moments, with Fourier transform of their complex conjugates Ψ¯ˆα,n(x) to possess the following properties: (i) Ψ¯ˆα,n(x)≥0 for all x∈R, (ii) maxx⁡Ψ¯ˆα,n(x)=Ψ¯ˆα,n(κ)=ξn, where κ≐2.331122371 and ξ≐1.449222080 are positive constants independent of n,α and m, and (iii) the widths (or standard deviations) of Ψ¯ˆα,n(x), with center at κ, tends to 0 very fast for large values of α. While the most popular approach to resolve this super-resolution problem is to consider the Fourier transform d(x)=∑ℓ=1Lcℓe−iσℓx of h(y) as the “data function” for solving the inverse problem of recovering L, σ1,⋯,σL and c1,⋯,cL of the point-mass d(x), our proposed approach is to consider the “enhanced data function” D(a;α,n):=FΨα,n(a)=∑ℓ=1LcℓΨ¯ˆα,n(aσℓ), where FΨα,n(a), to be called the search function in this paper, is obtained by taking the continuous wavelet transform (CWT): (WΨα,nd)(t,a)=∫−∞∞Ψα,n(y−ta)‾d(y)dya of the data function d(x), with Ψα,n as the analysis wavelet, followed by applying wavelet thresholding to “de-noise” the data function d(x), by choosing an appropriate thresholding parameter γ>0, with γ<η⁎×ξn, in order not to remove any of the coefficients cℓ, where ℓ=1,⋯,L; and finally by setting t=0. Hence, the enhanced data function D(a;α,n) is at least cleaner than the data function d(x). In our proposed approach, instead of directly recovering σ1,⋯,σL as in the published literature, we propose a “divide and conquer” strategy: first by applying “bottom-up thresholding” of the search function FΨα,n(a), with thresholding parameter γ⁎>0 close to but not exceeding η⁎×ξn, to separate the set of the local extrema locations aℓ:=κσℓ of the function FΨα,n(a) in {a∈R:a≠0} into disjoint intervals of clusters, with more and smaller intervals and less number of local extrema aℓ in each interval for larger values of α; and secondly, by applying “top-down thresholding” to extract, one-by-one, of all local maxima, followed by all local minima (after a sign change), for each and every cluster. A desired leeway Δ>0 and lower bounds of the choice of the width parameter α are derived for the iterative application of top-down thresholding. Extension to Rs for s≥2 is also studied in this paper. For s=2, we observe that the imagery of the enhanced data function for a single point-mass at (σ1,σ2) where σ1,σ2≠0, resembles that of an “Airy disk” with center at (κ/σ1,κ/σ2) in light microscopy and celestial telescopy of point-masses." @default.
• W4285010277 created "2022-07-12" @default.
• W4285010277 creator A5080019930 @default.
• W4285010277 date "2022-11-01" @default.
• W4285010277 modified "2023-09-28" @default.
• W4285010277 title "Super-resolution wavelets for recovery of arbitrarily close point-masses with arbitrarily small coefficients" @default.
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• W4285010277 cites W2030521421 @default.
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• W4285010277 cites W2045435533 @default.
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• W4285010277 doi "https://doi.org/10.1016/j.acha.2022.07.003" @default.
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