Noise Mapping and Removal in Complex-Valued Multi-Channel MRI via Optimal Shrinkage of Singular Values

AbstractIn this paper we study $$L_2$$ L 2 -norm sampling discretization and sampling recovery of complex-valued functions in RKHS on $$D \subset \mathbb {R}^d$$ D ⊂ R d based on random function samples. We only assume the finite trace of the kernel (Hilbert–Schmidt embedding into $$L_2$$ L 2 ) and provide several concrete estimates with precise constants for the corresponding worst-case errors. In general, our analysis does not need any additional assumptions and also includes the case of non-Mercer kernels and also non-separable RKHS. The fail probability is controlled and decays polynomially in n, the number of samples. Under the mild additional assumption of separability we observe improved rates of convergence related to the decay of the singular values. Our main tool is a spectral norm concentration inequality for infinite complex random matrices with independent rows complementing earlier results by Rudelson, Mendelson, Pajor, Oliveira and Rauhut.

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IMPACT OF COMPLEX-VALUED ENERGY FUNCTION SINGULARITIES ON THE BEHAVIOUR OF RAYLEIGH-SCHRÖDINGER PERTURBATION SERIES. H2CO MOLECULE VIBRATIONAL ENERGY SPECTRUM.

Proceedings of the 70th International Symposium on Molecular Spectroscopy ◽

10.15278/isms.2015.rg07 ◽

2015 ◽

Author(s):

Andrey Duchko ◽

Alexandr Bykov

Keyword(s):

Energy Spectrum ◽

Energy Function ◽

Vibrational Energy ◽

Perturbation Series ◽

Schrödinger Perturbation ◽

Complex Valued

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Complex-valued Neural Networks

IEEJ Transactions on Electronics Information and Systems ◽

10.1541/ieejeiss.131.2 ◽

2011 ◽

Vol 131 (1) ◽

pp. 2-8

Author(s):

Akira Hirose

Keyword(s):

Neural Networks ◽

Complex Valued

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Natural Gradient Descent of Complex-Valued Neural Networks Invariant under Rotations

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences ◽

10.1587/transfun.e102.a.1988 ◽

2019 ◽

Vol E102.A (12) ◽

pp. 1988-1996

Author(s):

Jun-ichi MUKUNO ◽

Hajime MATSUI

Keyword(s):

Neural Networks ◽

Gradient Descent ◽

Natural Gradient ◽

Complex Valued

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Stochastic Complex-valued Neural Networks for Radar

2020 28th European Signal Processing Conference (EUSIPCO) ◽

10.23919/eusipco47968.2020.9287425 ◽

2021 ◽

Author(s):

Othmane-Latif Ouabi ◽

Radmila Pribic ◽

Sorin Olaru

Keyword(s):

Neural Networks ◽

Complex Valued

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A SVD and Modified Firefly Optimization Based Robust Digital Image Watermarking Technique

International Journal of Advanced Research in Computer Science and Software Engineering ◽

10.23956/ijarcsse/v7i7/0210 ◽

2017 ◽

Vol 7 (7) ◽

pp. 268

Author(s):

Chauhan Usha ◽

Singh Rajeev Kumar

Keyword(s):

Digital Media ◽

Firefly Algorithm ◽

Image Watermarking ◽

Singular Values ◽

Robust Watermarking ◽

Scaling Factors ◽

Geometric Attacks ◽

Host Image ◽

Firefly Optimization ◽

Value Decomposition

Digital Watermarking is a technology, to facilitate the authentication, copyright protection and Security of digital media. The objective of developing a robust watermarking technique is to incorporate the maximum possible robustness without compromising with the transparency. Singular Value Decomposition (SVD) using Firefly Algorithm provides this objective of an optimal robust watermarking technique. Multiple scaling factors are used to embed the watermark image into the host by multiplying these scaling factors with the Singular Values (SV) of the host image. Firefly Algorithm is used to optimize the modified host image to achieve the highest possible robustness and transparency. This approach can significantly increase the quality of watermarked image and provide more robustness to the embedded watermark against various attacks such as noise, geometric attacks, filtering attacks etc.

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