Hybrid image inpainting using reproducing kernel Hilbert space and dragonfly inspired wavelet transform

2019 ◽  
Vol 8 (3/4) ◽  
pp. 301
Author(s):  
Balasaheb H. Patil ◽  
Pradeep M. Patil
Keyword(s):  
Hilbert Space ◽  
Wavelet Transform ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Image Inpainting

THE IMAGE SPACE OF ONE TYPE OF CONTINUOUS WAVELET TRANSFORM AND ITS PROPERTY

2012 ◽  
Vol 10 (03) ◽  
pp. 1250022 ◽  
Author(s):  
CAIXIA DENG ◽  
ZUOXIAN FU ◽  
SHUAI LI
Keyword(s):  
Hilbert Space ◽  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Fundamental Theorem ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Image Space ◽  
Continuous Wavelet ◽  
Admissible Wavelet ◽  
Linear Transform

In this paper, we show that the space of continuous wavelet transform is a reproducing kernel Hilbert space based on the fundamental theorem of linear transform. An admissible wavelet is got by convolution computation which is made into continuous wavelet transform. By the theory of reproducing kernel we can discuss correlative properties of image space of wavelet transform, which provide theoretic frame for us to study image space of the general wavelet transform.

ON THE CONTINUOUS WAVELET TRANSFORM ON HOMOGENEOUS SPACES

2012 ◽  
Vol 10 (04) ◽  
pp. 1250038 ◽  
Author(s):  
F. ESMAEELZADEH ◽  
R. A. KAMYABI GOL ◽  
R. RAISI TOUSI
Keyword(s):  
Hilbert Space ◽  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Reproducing Kernel ◽  
Homogeneous Spaces ◽  
Reproducing Kernel Hilbert Space ◽  
Compact Subgroup ◽  
Continuous Wavelet ◽  
Square Integrable Representation ◽  
Necessary And Sufficient

Let G be a locally compact group with a compact subgroup H. We define a square integrable representation of a homogeneous space G/H on a Hilbert space [Formula: see text]. The reconstruction formula for G/H is established and as a result it is concluded that the set of admissible vectors is path connected. The continuous wavelet transform on G/H is defined and it is shown that the range of the continuous wavelet transform is a reproducing kernel Hilbert space. Moreover, we obtain a necessary and sufficient condition for the continuous wavelet transform to be onto.

scholarly journals Reproducing kernel Hilbert spaces of CR functions for the Euclidean motion group

2015 ◽  
Vol 13 (03) ◽  
pp. 331-346 ◽  
Author(s):  
D. Barbieri ◽  
G. Citti
Keyword(s):  
Hilbert Space ◽  
Wavelet Transform ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Bargmann Transform ◽  
Euclidean Motion Group ◽  
Cr Functions ◽  
Kernel Hilbert Spaces ◽  
Euclidean Motion ◽  
Hilbert Subspace

We study the geometric structure of the reproducing kernel Hilbert space associated to the continuous wavelet transform generated by the irreducible representations of the group of Euclidean motions of the plane SE(2). A natural Hilbert norm for functions on the group is constructed that makes the wavelet transform an isometry, but since the considered representations are not square integrable, the resulting Hilbert space will not coincide with L2( SE (2)). The reproducing kernel Hilbert subspace generated by the wavelet transform, for the case of a minimal uncertainty mother wavelet, can be characterized in terms of the complex regularity defined by the natural CR structure of the group. Relations with the Bargmann transform are presented.

scholarly journals Lebesgue Decomposition of Non-Commutative Measures

2020 ◽  
Author(s):  
Michael T Jury ◽  
Robert T W Martin
Keyword(s):  
Hilbert Space ◽  
Reproducing Kernel ◽  
Fock Space ◽  
Reproducing Kernel Hilbert Space ◽  
Semigroup Algebra ◽  
Space Theory ◽  
Lebesgue Decomposition ◽  
Sesquilinear Forms ◽  
Positive Linear Functionals ◽  
Algebra Theory

Abstract We extend the Lebesgue decomposition of positive measures with respect to Lebesgue measure on the complex unit circle to the non-commutative (NC) multi-variable setting of (positive) NC measures. These are positive linear functionals on a certain self-adjoint subspace of the Cuntz–Toeplitz $C^{\ast }-$algebra, the $C^{\ast }-$algebra of the left creation operators on the full Fock space. This theory is fundamentally connected to the representation theory of the Cuntz and Cuntz–Toeplitz $C^{\ast }-$algebras; any *−representation of the Cuntz–Toeplitz $C^{\ast }-$algebra is obtained (up to unitary equivalence), by applying a Gelfand–Naimark–Segal construction to a positive NC measure. Our approach combines the theory of Lebesgue decomposition of sesquilinear forms in Hilbert space, Lebesgue decomposition of row isometries, free semigroup algebra theory, NC reproducing kernel Hilbert space theory, and NC Hardy space theory.

scholarly journals Multi-omics-based prediction of hybrid performance in canola

2021 ◽  
Author(s):  
Dominic Knoch ◽  
Christian R. Werner ◽  
Rhonda C. Meyer ◽  
David Riewe ◽  
Amine Abbadi ◽  
...  
Keyword(s):  
Hilbert Space ◽  
Genetic Markers ◽  
Reproducing Kernel ◽  
Prediction Models ◽  
Agronomic Traits ◽  
Reproducing Kernel Hilbert Space ◽  
Hybrid Performance ◽  
Hybrid Prediction ◽  
Gaussian Kernels ◽  
Breeding Programmes

Abstract Key message Complementing or replacing genetic markers with transcriptomic data and use of reproducing kernel Hilbert space regression based on Gaussian kernels increases hybrid prediction accuracies for complex agronomic traits in canola. In plant breeding, hybrids gained particular importance due to heterosis, the superior performance of offspring compared to their inbred parents. Since the development of new top performing hybrids requires labour-intensive and costly breeding programmes, including testing of large numbers of experimental hybrids, the prediction of hybrid performance is of utmost interest to plant breeders. In this study, we tested the effectiveness of hybrid prediction models in spring-type oilseed rape (Brassica napus L./canola) employing different omics profiles, individually and in combination. To this end, a population of 950 F1 hybrids was evaluated for seed yield and six other agronomically relevant traits in commercial field trials at several locations throughout Europe. A subset of these hybrids was also evaluated in a climatized glasshouse regarding early biomass production. For each of the 477 parental rapeseed lines, 13,201 single nucleotide polymorphisms (SNPs), 154 primary metabolites, and 19,479 transcripts were determined and used as predictive variables. Both, SNP markers and transcripts, effectively predict hybrid performance using (genomic) best linear unbiased prediction models (gBLUP). Compared to models using pure genetic markers, models incorporating transcriptome data resulted in significantly higher prediction accuracies for five out of seven agronomic traits, indicating that transcripts carry important information beyond genomic data. Notably, reproducing kernel Hilbert space regression based on Gaussian kernels significantly exceeded the predictive abilities of gBLUP models for six of the seven agronomic traits, demonstrating its potential for implementation in future canola breeding programmes.

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