Phase retrieval in electronic speckle pattern interferometry using the continuous wavelet transform

2001 ◽  
Author(s):  
Alejandro Federico ◽  
Guillermo H. Kaufmann
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Phase Retrieval ◽  
Speckle Pattern ◽  
Electronic Speckle Pattern Interferometry ◽  
Continuous Wavelet

Phase Retrieval Method with Continuous Wavelet Transform Based on Exponent Spacing Scales

2012 ◽  
Vol 32 (7) ◽  
pp. 0712001
Author(s):  
崔世林 Cui Shilin ◽  
田斐 Tian Fei ◽  
李德华 Li Dehua
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Phase Retrieval ◽  
Continuous Wavelet ◽  
Retrieval Method

scholarly journals Continuous Wavelet Transform of Schwartz Distributions in DL2′(Rn), n ≥ 1

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1106
Author(s):  
Jagdish N. Pandey
Keyword(s):  
Wavelet Transform ◽  
Function Space ◽  
Continuous Wavelet Transform ◽  
Inversion Formula ◽  
Continuous Wavelet ◽  
The Real ◽  
Schwartz Distributions ◽  
Distributional Sense ◽  
Wavelet Inversion

We define a testing function space DL2(Rn) consisting of a class of C∞ functions defined on Rn, n≥1 whose every derivtive is L2(Rn) integrable and equip it with a topology generated by a separating collection of seminorms {γk}|k|=0∞ on DL2(Rn), where |k|=0,1,2,… and γk(ϕ)=∥ϕ(k)∥2,ϕ∈DL2(Rn). We then extend the continuous wavelet transform to distributions in DL2′(Rn), n≥1 and derive the corresponding wavelet inversion formula interpreting convergence in the weak distributional sense. The kernel of our wavelet transform is defined by an element ψ(x) of DL2(Rn)∩DL1(Rn), n≥1 which, when integrated along each of the real axes X1,X2,…Xn vanishes, but none of its moments ∫Rnxmψ(x)dx is zero; here xm=x1m1x2m2⋯xnmn, dx=dx1dx2⋯dxn and m=(m1,m2,…mn) and each of m1,m2,…mn is ≥1. The set of such wavelets will be denoted by DM(Rn).

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