Reverse Biorthogonal Spline Wavelets in Undecimated Transform for Image Denoising

Tilak, T. N.; Krishnakumar, S.

doi:10.26438/ijcse/v6i2.6672

Cited by 4 publications

(5 citation statements)

References 11 publications

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“…This allows using non-symmetrical filters of non-trivial lengths and obtaining consequent desirable properties, in addition to obtaining signal flexibility. In this way, as biorthogonal wavelets, rbio wavelet matrices are reversible and allow a perfect signal reconstruction . Regarding this wavelet, the inner product of two functions x ( t ) and y ( t ) is defined as where y *( t ) is the complex conjugate of y ( t ).…”

Section: Resultsmentioning

confidence: 99%

“…In this way, as biorthogonal wavelets, rbio wavelet matrices are reversible and allow a perfect signal reconstruction. 45 Regarding this wavelet, the inner product of two functions x(t) and y(t) 46 is defined as…”

mentioning

confidence: 99%

“…It is important to choose symmetric filters because they provide phase linearity, minimize perceptual error, and enable better handling of boundaries. 45 These characteristics are important for the treatment of signs of flexible organic systems since this type of system could present greater signal flexibility, which allows obtaining more representative relevant conformations that more realistically represent the behavior of the system.…”

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confidence: 99%

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Improved Protocol for the Selection of Structures from Molecular Dynamics of Organic Systems in Solution: The Value of Investigating Different Wavelet Families

Gonçalves

França

et al. 2022

J. Chem. Theory Comput.

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Wavelets are mathematical tools used to decompose and represent another function described in the time domain, allowing the study of each component of the original function with a scale-compatible resolution. Thus, these transforms have been used to select conformations from molecular dynamics (MD) trajectories in systems of fundamental and technological interest. Recently, our research group has used wavelets to develop and validate a method, meant to select structures from MD trajectories, which we named OWSCA (optimal wavelet signal compression algorithm). Here, we moved forward on this project by demonstrating the efficacy of this method on the study of three different systems (non-flexible organic, flexible organic, and protein). For each system, 93 wavelets were investigated to verify which is the best one for a given organic system. The results show that the best wavelets were different for each system and, also, very close to the experimental values, with the wavelets db1, rbio 3.1, and bior1.1 being selected for the non-flexible, flexible organic, and protein systems, respectively. This reinforces our OWSCA as a very efficient and promising method for the selection of structures from MD trajectories of different classes of compounds. Our findings also point out that additional studies considering wavelet families are needed for defining the best wavelet for representing each system under study.

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Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Improved Protocol for the Selection of Structures from Molecular Dynamics of Organic Systems in Solution: The Value of Investigating Different Wavelet Families

Gonçalves

França

et al. 2022

J. Chem. Theory Comput.

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“…In this study the Biorthogonal (Bior1.5), Coiflets (Coif1), Daubechies (Db3), Discrete Meyer (Dmey), Haar , Reverse Biorthogonal (Rbio1.5), and Symlets (Sym2) wavelet families [ 24 ] were considered. The following are the main applications of wavelet families: Biorthogonal : commonly used for denoising, in particular when white Gaussian noise is present [ 25 ]; Reverse Biorthogonal : used for compression [ 26 ] and denoising [ 27 ]; Coiflet : used for compression [ 28 ] and denoising [ 29 ]; Daubechies : provides excellent performance in compression and are popular choice in medical imaging applications [ 30 ]; Discrete Meyer : in general used for multi-resolution analysis [ 31 ] and some variants for edge and blocking artifact reduction [ 32 ]; Haar : is the first introduced and several generalizations and modifications were proposed [ 33 ]. It is one of the most widely used and has many medical imaging applications, including image fusion [ 34 ] and compression in radiography [ 35 ], CT, and MRI [ 36 ]; Symlets : is a modified version of Daubechies wavelets with increased symmetry [ 37 ], used for signal decomposition including characterization of fabric texture [ 38 ].…”

Section: Materials and Methodsmentioning

confidence: 99%

Impact of Wavelet Kernels on Predictive Capability of Radiomic Features: A Case Study on COVID-19 Chest X-ray Images

et al. 2023

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Radiomic analysis allows for the detection of imaging biomarkers supporting decision-making processes in clinical environments, from diagnosis to prognosis. Frequently, the original set of radiomic features is augmented by considering high-level features, such as wavelet transforms. However, several wavelets families (so called kernels) are able to generate different multi-resolution representations of the original image, and which of them produces more salient images is not yet clear. In this study, an in-depth analysis is performed by comparing different wavelet kernels and by evaluating their impact on predictive capabilities of radiomic models. A dataset composed of 1589 chest X-ray images was used for COVID-19 prognosis prediction as a case study. Random forest, support vector machine, and XGBoost were trained (on a subset of 1103 images) after a rigorous feature selection strategy to build-up the predictive models. Next, to evaluate the models generalization capability on unseen data, a test phase was performed (on a subset of 486 images). The experimental findings showed that Bior1.5, Coif1, Haar, and Sym2 kernels guarantee better and similar performance for all three machine learning models considered. Support vector machine and random forest showed comparable performance, and they were better than XGBoost. Additionally, random forest proved to be the most stable model, ensuring an appropriate balance between sensitivity and specificity.

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“…In this way, as biorthogonal wavelets, rbio wavelet matrices are reversible and allow a perfect signal reconstruction 45 . Regarding to this wavelet, the inner product of two functions x(t) and y(t) 46 is defined as:…”

Section: 2-a Comparative Analysis Of Wavelet Familiesmentioning

confidence: 99%

An improved protocol for the selection of structures from molecular dynamics of organic systems in solution: the value of investigating different wavelet families

Gonçalves

França

et al. 2022

Preprint

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Wavelets are mathematical tools used to decompose and represent another function described in the time domain, allowing the study of each component of the original function with a scale-compatible resolution. Thus, these transforms have been used to select conformations from Molecular Dynamics (MD) trajectories in systems of fundamental and technological interest. Recently our research group has used wavelets to develop and validate a method, meant to select structures from MD trajectories, which we named OWSCA (Optimal Wavelet Signal Compression algorithm). Here we moved forward on this project by demonstrating the efficacy of this method on the study of 3 different systems (non-flexible organic, flexible organic and protein). For each system, 93 wavelets were investigated in order to verify which is the best one for a given organic system. The results show that the best wavelets were different for each system and, also, very close to the experimental values, with the wavelets db1, rbio 3.1 and bior1.1 being selected for the non-flexible, flexible organic, and protein systems, respectively. This reinforces our OWSCA as a very efficient and promising method for the selection of structures from MD trajectories of different classes of compounds. Our findings also point out that additional studies considering wavelets families is needed for defining the best wavelet for representing each system under study.

show abstract

Reverse Biorthogonal Spline Wavelets in Undecimated Transform for Image Denoising

Cited by 4 publications

References 11 publications

Improved Protocol for the Selection of Structures from Molecular Dynamics of Organic Systems in Solution: The Value of Investigating Different Wavelet Families

Improved Protocol for the Selection of Structures from Molecular Dynamics of Organic Systems in Solution: The Value of Investigating Different Wavelet Families

Impact of Wavelet Kernels on Predictive Capability of Radiomic Features: A Case Study on COVID-19 Chest X-ray Images

An improved protocol for the selection of structures from molecular dynamics of organic systems in solution: the value of investigating different wavelet families

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