Image processing based acrylamide detection from fried potato chip images using continuous wavelet transform

2018 ◽  
Vol 145 ◽  
pp. 349-362 ◽  
Author(s):  
Anjali Yadav ◽  
Namita Sengar ◽  
Ashish Issac ◽  
Malay Kishore Dutta
Keyword(s):  
Image Processing ◽  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Potato Chip ◽  
Continuous Wavelet

scholarly journals Seismic entangled patterns analyzed via multiresolution decomposition

2009 ◽  
Vol 16 (2) ◽  
pp. 211-217 ◽  
Author(s):  
F. E. A. Leite ◽  
R. Montagne ◽  
G. Corso ◽  
L. S. Lucena
Keyword(s):  
Image Processing ◽  
Wavelet Transform ◽  
Coherent Structures ◽  
Continuous Wavelet Transform ◽  
Original Data ◽  
Continuous Wavelet ◽  
Original Image ◽  
Generating Set ◽  
Multiresolution Decomposition ◽  
Ground Roll

Abstract. This article explores a method for distinguishing entangled coherent structures embedded in geophysical images. The original image is decomposed in a series of j-scale-images using multiresolution decomposition. To improve the image processing analysis each j-image is divided in l-spacial regions generating set of (j, l)-regions. At each (j, l)-region we apply a continuous wavelet transform to evaluate Eν, the spectrum of energy. Eν has two maxima in the original data. Otherwise, at each scale Eν hast typically one peak. The localization of the peaks changes according to the (j, l)-region. The intensity of the peaks is linked with the presence of coherent structures, or patterns, at the respective (j, l)-region. The method is successfully applied to distinguish, in scale and region, the ground roll noise from the relevant geologic information in the signal.

The continuous wavelet transform in n-dimensions

2016 ◽  
Vol 14 (05) ◽  
pp. 1650037 ◽  
Author(s):  
J. N. Pandey ◽  
N. K. Jha ◽  
O. P. Singh
Keyword(s):  
Image Processing ◽  
Wavelet Transform ◽  
Real Number ◽  
Continuous Wavelet Transform ◽  
Inversion Formula ◽  
Spherically Symmetric ◽  
Continuous Wavelet ◽  
Wavelet Inversion ◽  
Translation Parameter

Daubechies obtained the [Formula: see text]-dimensional inversion formula for the continuous wavelet transform of spherically symmetric wavelets in [Formula: see text] with convergence interpreted in the [Formula: see text]-norm. From the wavelet [Formula: see text], Daubechies generated a doubly indexed family of wavelets [Formula: see text] by restricting the dilation parameter [Formula: see text] to be a real number greater than zero and the translation parameter [Formula: see text] belonging to [Formula: see text]. We show that [Formula: see text] can be chosen to be in [Formula: see text] with none of the components [Formula: see text] vanishing. Further, we prove that if [Formula: see text] and [Formula: see text] are continuous in [Formula: see text], then the convergence besides being in [Formula: see text] is also pointwise in [Formula: see text]. We advance our theory further to the case when [Formula: see text] and [Formula: see text] both belong to [Formula: see text] then convergence of the wavelet inversion formula is pointwise at all points of continuity of [Formula: see text]. This result significantly enhances the applicability of the wavelet inversion formula to the image processing.

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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