Construction of Nonseparable Multiwavelets for Nonlinear Image Compression

Ruedin, Ana M. C.

doi:10.1155/s1110865702000410

Cited by 9 publications

(2 citation statements)

References 21 publications

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“…See also Bui and Chen ( 1998 ), Huang and Li ( 2011 ), Iyer ( 2001 ), Kessler ( 2009 ), Liang et al. ( 1996 ), Ruedin ( 2002 ), Selesnick ( 1998 , 1999 , 2000 ), Tham et al. ( 2000 ), Vehel and Aldroubi ( 1997 ), Xia ( 1998 ), Xia and Jiang ( 1999 ) and Xia et al.…”

Section: Introduction and Motivationsmentioning

confidence: 99%

Toward new multi-wavelets: associated filters and algorithms. Part I: theoretical framework and investigation of biomedical signals, ECG, and coronavirus cases

et al. 2021

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Biosignals are nowadays important subjects for scientific researches from both theory, and applications, especially, with the appearance of new pandemics threatening the humanity such as the new coronavirus. One aim in the present work is to prove that wavelets may be a successful machinery to understand such phenomena by applying a step forward extension of wavelets to multi-wavelets. We proposed in a first step to improve multi-wavelet notion by constructing more general families using independent components for multi-scaling and multi-wavelet mother functions. A special multi-wavelet is then introduced, continuous, and discrete multi-wavelet transforms are associated, as well as new filters, and algorithms of decomposition, and reconstruction. Applied breakthroughs of the paper may be summarized in three aims. In a first direction, an approximation (reconstruction) of a classical (stationary, periodic) example dealing with Fourier modes has been conducted in order to confirm the efficiency of the HSch multi-wavelets in approximating such signals and in providing fast algorithms. The second experimentation is concerned with the decomposition and reconstruction application of the HSch multi-wavelet on an ECG signal. The last experimentation is concerned with a de-noising application on a strain of coronavirus signal permitting to localize approximately the transmembrane segments of such a series as neighborhoods of the local maxima of an numerized version of the strain. Accuracy of the method has been evaluated by means of error estimates and statistical tests.

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Section: Introduction and Motivationsmentioning

confidence: 99%

Toward new multi-wavelets: associated filters and algorithms. Part I: theoretical framework and investigation of biomedical signals, ECG, and coronavirus cases

et al. 2021

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“…Some interesting cases may be found in [6,?]. See also [15,23,25,32,38,44,46,47,48,54,57,59,60,61] for more methods and applications.…”

Section: Introductionmentioning

confidence: 99%

Towards New Multiwavelets: Associated Filters and Algorithms. Part I: Theoretical Framework and Investigation of Biomedical Signals, ECG and Coronavirus Cases

Jallouli¹,

Zemni²,

Mabrouk³

et al. 2021

Preprint

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Biosignals are nowadays important subjects for scientific researches from both theory and applications especially with the appearance of new pandemics threatening the humanity such as the new Coronavirus. One aim in the present work is to prove that Wavelets may be a successful machinery to understand such phenomena by applying a step forward extension of wavelets to multiwavelets. We proposed in a first step to improve multiwavelet notion by constructing more general families using independent components for multi-scaling and multiwavelet mother functions. A special multiwavelet is then introduced, continuous and discrete multiwavelet transforms are associated, as well as new filters and algorithms of decomposition and reconstruction. The constructed multiwavelet framework is applied for some

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Dilation Matrices for Nonseparable Bidimensional Wavelets

Ruedin

2006

Advanced Concepts for Intelligent Vision Systems

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Construction of Nonseparable Multiwavelets for Nonlinear Image Compression

Cited by 9 publications

References 21 publications

Toward new multi-wavelets: associated filters and algorithms. Part I: theoretical framework and investigation of biomedical signals, ECG, and coronavirus cases

Toward new multi-wavelets: associated filters and algorithms. Part I: theoretical framework and investigation of biomedical signals, ECG, and coronavirus cases

Towards New Multiwavelets: Associated Filters and Algorithms. Part I: Theoretical Framework and Investigation of Biomedical Signals, ECG and Coronavirus Cases

Dilation Matrices for Nonseparable Bidimensional Wavelets

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