scholarly journals New Classes of Weighted Hölder-Zygmund Spaces and the Wavelet Transform

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Stevan Pilipović ◽  
Dušan Rakić ◽  
Jasson Vindas
Keyword(s):  
Wavelet Transform ◽  
Wavelet Transforms ◽  
Elementary Proof ◽  
Left Inverse ◽  
Regularly Varying Functions ◽  
Continuity Theorem ◽  
New Class ◽  
Zygmund Spaces ◽  
Regularly Varying

We provide a new and elementary proof of the continuity theorem for the wavelet and left-inverse wavelet transforms on the spaces𝒮0(ℝn)and𝒮(ℍn+1). We then introduce and study a new class of weighted Hölder-Zygmund spaces, where the weights are regularly varying functions. The analysis of these spaces is carried out via the wavelet transform and generalized Littlewood-Paley pairs.

Medical Image Feature Matching Based on Wavelet Transform and SIFT Algorithm

2011 ◽  
Vol 65 ◽  
pp. 497-502
Author(s):  
Yan Wei Wang ◽  
Hui Li Yu
Keyword(s):  
Wavelet Transform ◽  
Wavelet Transforms ◽  
Medical Image ◽  
Feature Matching ◽  
Image Feature ◽  
Scale Invariant ◽  
Sift Algorithm ◽  
Matching Algorithm ◽  
Invariant Feature ◽  
Scale Invariant Feature

A feature matching algorithm based on wavelet transform and SIFT is proposed in this paper, Firstly, Biorthogonal wavelet transforms algorithm is used for medical image to delaminating, and restoration the processed image. Then the SIFT (Scale Invariant Feature Transform) applied in this paper to abstracting key point. Experimental results show that our algorithm compares favorably in high-compressive ratio, the rapid matching speed and low storage of the image, especially for the tilt and rotation conditions.

Pseudo-Regularly Varying Functions and Generalized Renewal Processes

2018 ◽  
Author(s):  
Valeriĭ V. Buldygin ◽  
Karl-Heinz Indlekofer ◽  
Oleg I. Klesov ◽  
Josef G. Steinebach
Keyword(s):  
Renewal Processes ◽  
Regularly Varying Functions ◽  
Regularly Varying

Wavelet transform to quantify heart rate variability and to assess its instantaneous changes

1999 ◽  
Vol 86 (3) ◽  
pp. 1081-1091 ◽  
Author(s):  
Vincent Pichot ◽  
Jean-Michel Gaspoz ◽  
Serge Molliex ◽  
Anestis Antoniadis ◽  
Thierry Busso ◽  
...  
Keyword(s):  
Heart Rate ◽  
Heart Rate Variability ◽  
Nervous System ◽  
Fourier Transform ◽  
Wavelet Transform ◽  
Wavelet Transforms ◽  
Autonomous Nervous System ◽  
Dynamic Changes ◽  
Nonstationary Signals ◽  
Higher Doses

Heart rate variability is a recognized parameter for assessing autonomous nervous system activity. Fourier transform, the most commonly used method to analyze variability, does not offer an easy assessment of its dynamics because of limitations inherent in its stationary hypothesis. Conversely, wavelet transform allows analysis of nonstationary signals. We compared the respective yields of Fourier and wavelet transforms in analyzing heart rate variability during dynamic changes in autonomous nervous system balance induced by atropine and propranolol. Fourier and wavelet transforms were applied to sequences of heart rate intervals in six subjects receiving increasing doses of atropine and propranolol. At the lowest doses of atropine administered, heart rate variability increased, followed by a progressive decrease with higher doses. With the first dose of propranolol, there was a significant increase in heart rate variability, which progressively disappeared after the last dose. Wavelet transform gave significantly better quantitative analysis of heart rate variability than did Fourier transform during autonomous nervous system adaptations induced by both agents and provided novel temporally localized information.

scholarly journals Discrete and Dual Tree Wavelet Features for Real-Time Speech/Music Discrimination

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Timur Düzenli ◽  
Nalan Özkurt
Keyword(s):  
Wavelet Transform ◽  
Real Time ◽  
Wavelet Transforms ◽  
Principal Component ◽  
Discrete Wavelet ◽  
Vanishing Moments ◽  
Zero Crossings ◽  
Time Frequency ◽  
Common Time ◽  
Classification Tool

The performance of wavelet transform-based features for the speech/music discrimination task has been investigated. In order to extract wavelet domain features, discrete and complex orthogonal wavelet transforms have been used. The performance of the proposed feature set has been compared with a feature set constructed from the most common time, frequency and cepstral domain features such as number of zero crossings, spectral centroid, spectral flux, and Mel cepstral coefficients. The artificial neural networks have been used as classification tool. The principal component analysis has been applied to eliminate the correlated features before the classification stage. For discrete wavelet transform, considering the number of vanishing moments and orthogonality, the best performance is obtained with Daubechies8 wavelet among the other members of the Daubechies family. The dual tree wavelet transform has also demonstrated a successful performance both in terms of accuracy and time consumption. Finally, a real-time discrimination system has been implemented using the Daubhecies8 wavelet which has the best accuracy.

scholarly journals Certain properties of continuous fractional wavelet transform on Hardy space and Morrey space

2021 ◽  
Vol 41 (5) ◽  
pp. 701-723
Author(s):  
Amit K. Verma ◽  
Bivek Gupta
Keyword(s):  
Wavelet Transform ◽  
Hardy Space ◽  
Morrey Space ◽  
New Class ◽  
Fractional Wavelet Transform

In this paper we define a new class of continuous fractional wavelet transform (CFrWT) and study its properties in Hardy space and Morrey space. The theory developed generalize and complement some of already existing results.

Pattern Changes of Time-Shifted Vibration Signals on Wavelet Time-Scale Maps

1995 ◽  
Author(s):  
Da Jun Chen ◽  
Wei Ji Wang
Keyword(s):  
Wavelet Transform ◽  
Time Scale ◽  
Wavelet Transforms ◽  
Vibration Signal ◽  
Continuous Wavelet ◽  
Time Axis ◽  
Orthogonal Wavelet ◽  
Signal Component ◽  
Analysis Technique ◽  
Map Analysis

Abstract As a multi-resolution signal decomposition and analysis technique, the wavelet transforms have been already introduced to vibration signal processing. In this paper, a comparison on the time-scale map analysis is made between the discrete and the continuous wavelet transform. The orthogonal wavelet transform decomposes the vibration signal onto a series of orthogonal wavelet functions and the number of wavelets on one wavelet level is different from those on the other levels. Since the grids are unevenly distributed on the time-scale map, it is shown that a representation pattern of a vibration component on the map may be significantly altered or even be broken down into pieces when the signal has a shift along the time axis. On contrary, there is no such uneven distribution of grids on the continuous wavelet time-scale map, so that the representation pattern of a vibration signal component will not change its shape when the signal component shifts along the time axis. Therefore, the patterns in the continuous wavelet time-scale map are more easily recognised by human visual inspection or computerised automatic diagnosis systems. Using a Gaussian enveloped oscillation wavelet, the wavelet transform is capable of retaining the frequency meaning used in the spectral analysis, while making the interpretation of patterns on the time-scale maps easier.

Quantum Wavelet Transforms

2021 ◽  
pp. 193-220
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Wavelet Transform ◽  
Tensor Product ◽  
Wavelet Transforms ◽  
Quantum Information Processing ◽  
Complexity Analysis ◽  
Simulation Experiments ◽  
Multi Level

The classical wavelet transform has been widely applied in the information processing field. It implies that quantum wavelet transform (QWT) may play an important role in quantum information processing. This chapter firstly describes the iteration equations of the general QWT using generalized tensor product. Then, Haar QWT (HQWT), Daubechies D4 QWT (DQWT), and their inverse transforms are proposed respectively. Meanwhile, the circuits of the two kinds of multi-level HQWT are designed. What's more, the multi-level DQWT based on the periodization extension is implemented. The complexity analysis shows that the proposed multi-level QWTs on 2n elements can be implemented by O(n3) basic operations. Simulation experiments demonstrate that the proposed QWTs are correct and effective.

Region-Based Fractional Wavelet Transform Using Post Processing Artifact Reduction

2012 ◽  
Vol 8 (8) ◽  
pp. 45-53
Author(s):  
Jassim Abdul-Jabbar ◽  
Alyaa Taqi
Keyword(s):  
Wavelet Transform ◽  
Wavelet Transforms ◽  
Low Cost ◽  
Image Features ◽  
Artifact Reduction ◽  
Digital Cameras ◽  
Wireless Multimedia ◽  
Wavelet Filters ◽  
Fractional Wavelet Transform ◽  
Memory Resources

Wavelet-based algorithms are increasingly used in the source coding of remote sensing, satellite and other geospatial imagery. At the same time, wavelet-based coding applications are also increased in robust communication and network transmission of images. Although wireless multimedia sensors are widely used to deliver multimedia content due to the availability of inexpensive CMOS cameras, their computational and memory resources are still typically very limited. It is known that allowing a low-cost camera sensor node with limited RAM size to perform a multi-level wavelet transform, will in return limit the size of the acquired image. Recently, fractional wavelet filter technique became an interesting solution to reduce communication energy and wireless bandwidth, for resource-constrained devices (e.g. digital cameras). The reduction in the required memory in these fractional wavelet transforms is achieved at the expense of the image quality. In this paper, an adaptive fractional artifacts reduction approach is proposed for efficient filtering operations according to the desired compromise between the effectiveness of artifact reduction and algorithm simplicity using some local image features to reduce boundaries artifacts caused by fractional wavelet. Applying such technique on different types of images with different sizes using CDF 9/7 wavelet filters results in a good performance.

A Multiplicative Analogue of Schur's Tauberian Theorem

2003 ◽  
Vol 46 (3) ◽  
pp. 473-480 ◽  
Author(s):  
Karen Yeats
Keyword(s):  
Power Series ◽  
Asymptotic Behaviour ◽  
Dirichlet Series ◽  
Tauberian Theorem ◽  
Partial Sums ◽  
Regularly Varying Functions ◽  
Regularly Varying

AbstractA theorem concerning the asymptotic behaviour of partial sums of the coefficients of products of Dirichlet series is proved using properties of regularly varying functions. This theorem is a multiplicative analogue of Schur's Tauberian theorem for power series.

Medical Image Compression Using Integer Wavelet Transformations

2011 ◽  
pp. 277-286
Author(s):  
B. Ramakrishnan ◽  
N. Sriraam
Keyword(s):  
Wavelet Transform ◽  
Wavelet Transforms ◽  
Medical Images ◽  
Lossy Compression ◽  
Data Sets ◽  
Optimal Method ◽  
Medical Image Compression ◽  
Integer Wavelet ◽  
Wavelet Transformations ◽  
Lossless And Lossy Compression

In this chapter, we have focused on compression of medical images using integer wavelet transforms. Lifting transforms such as S, TS, S+P(B), S+P(C), 5/3, 2+@, 2, 9/7-M and 9/7-F transforms are used to evaluate the performances of lossless and lossy compression. Four medical images, namely, MRI, CT, ultrasound, and angiograms are used as test data sets. It is found from the experiments that, among the different transforms, the 9/7-M wavelet transform is identified as the optimal method for lossless and lossy compression of medical images.

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