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Journal articles on the topic 'Wavelet transforms'

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Author: Grafiati

Published: 4 June 2021

Last updated: 7 September 2023

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1

Romanchak, V. M. "Local transformations with a singular wavelet." Informatics 17, no. 1 (March 29, 2020): 39–46. http://dx.doi.org/10.37661/1816-0301-2020-17-1-39-46.

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The paper considers a local wavelet transform with a singular basis wavelet. The problem of nonparametric approximation of a function is solved by the use of the sequence of local wavelet transforms. Traditionally believed that the wavelet should have an average equal to zero. Earlier, the author considered singular wavelets when the average value is not equal to zero. As an example, the delta-shaped functions, participated in the estimates of Parzen – Rosenblatt and Nadara – Watson, were used as a wavelet. Previously, a sequence of wavelet transforms for the entire numerical axis and finite interval was constructed for singular wavelets. The paper proposes a sequence of local wavelet transforms, a local wavelet transform is defined, the theorems that formulate the properties of a local wavelet transform are proved. To confirm the effectiveness of the algorithm an example of approximating the function by use of the sum of discrete local wavelet transforms is given.

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2

Zeelan Basha, CMAK, K. M. Sricharan, Ch Krishna Dheeraj, and R. Ramya Sri. "A Study on Wavelet Transform Using Image Analysis." International Journal of Engineering & Technology 7, no. 2.32 (May 31, 2018): 94. http://dx.doi.org/10.14419/ijet.v7i2.32.13535.

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The wavelet transforms have been in use for variety of applications. It is widely being used in signal analysis and image analysis. There have been lot of wavelet transforms for compression, decomposition and reconstruction of images. Out of many transforms Haar wavelet transform is the most computationally feasible wavelet transform to implement. The wave analysis technique has an understandable impact on the removal of noise within the signal. The paper outlines the principles and performance of wavelets in image analysis. Compression performance and decomposition of images into different layers have been discussed in this paper. We used Haar distinct wavelet remodel (HDWT) to compress the image. Simulation of wavelet transform was done in MATLAB. Simulation results are conferred for the compression with Haar rippling with totally different level of decomposition. Energy retention and PSNR values are calculated for the wavelets. Result conjointly reveals that the extent of decomposition will increase beholding of the photographs goes on decreasing however the extent of compression is incredibly high. Experimental results demonstrate the effectiveness of the Haar wavelet transform in energy retention in comparison to other wavelet transforms.

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TODA, HIROSHI, ZHONG ZHANG, and TAKASHI IMAMURA. "PERFECT-TRANSLATION-INVARIANT CUSTOMIZABLE COMPLEX DISCRETE WAVELET TRANSFORM." International Journal of Wavelets, Multiresolution and Information Processing 11, no. 04 (July 2013): 1360003. http://dx.doi.org/10.1142/s0219691313600035.

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The theorems, giving the condition of perfect translation invariance for discrete wavelet transforms, have already been proven. Based on these theorems, the dual-tree complex discrete wavelet transform, the 2-dimensional discrete wavelet transform, the complex wavelet packet transform, the variable-density complex discrete wavelet transform and the real-valued discrete wavelet transform, having perfect translation invariance, were proposed. However, their customizability of wavelets in the frequency domain is limited. In this paper, also based on these theorems, a new type of complex discrete wavelet transform is proposed, which achieves perfect translation invariance with high degree of customizability of wavelets in the frequency domain.

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Jansen, Maarten. "Non-equispaced B-spline wavelets." International Journal of Wavelets, Multiresolution and Information Processing 14, no. 06 (November 2016): 1650056. http://dx.doi.org/10.1142/s0219691316500569.

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This paper has three main contributions. The first is the construction of wavelet transforms from B-spline scaling functions defined on a grid of non-equispaced knots. The new construction extends the equispaced, biorthogonal, compactly supported Cohen–Daubechies–Feauveau wavelets. The new construction is based on the factorization of wavelet transforms into lifting steps. The second and third contributions are new insights on how to use these and other wavelets in statistical applications. The second contribution is related to the bias of a wavelet representation. It is investigated how the fine scaling coefficients should be derived from the observations. In the context of equispaced data, it is common practice to simply take the observations as fine scale coefficients. It is argued in this paper that this is not acceptable for non-interpolating wavelets on non-equidistant data. Finally, the third contribution is the study of the variance in a non-orthogonal wavelet transform in a new framework, replacing the numerical condition as a measure for non-orthogonality. By controlling the variances of the reconstruction from the wavelet coefficients, the new framework allows us to design wavelet transforms on irregular point sets with a focus on their use for smoothing or other applications in statistics.

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5

Pathak, R. S., and S. K. Singh. "The wavelet transform on spaces of type S." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 136, no. 4 (August 2006): 837–50. http://dx.doi.org/10.1017/s0308210500004753.

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The continuous wavelet transform is studied on certain Gel'fand–Shilov spaces of type S. It is shown that, for wavelets belonging to the one type of S-space defined on R, the wavelet transform is a continuous linear map of the other type of the S-space into a space of the same type (latter type) defined on R × R+. The wavelet transforms of certain ultradifferentiable functions are also investigated.

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6

Guido, Rodrigo Capobianco, Fernando Pedroso, André Furlan, Rodrigo Colnago Contreras, Luiz Gustavo Caobianco, and Jogi Suda Neto. "CWT × DWT × DTWT × SDTWT: Clarifying terminologies and roles of different types of wavelet transforms." International Journal of Wavelets, Multiresolution and Information Processing 18, no. 06 (August 28, 2020): 2030001. http://dx.doi.org/10.1142/s0219691320300017.

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Wavelets have been placed at the forefront of scientific researches involving signal processing, applied mathematics, pattern recognition and related fields. Nevertheless, as we have observed, students and young researchers still make mistakes when referring to one of the most relevant tools for time–frequency signal analysis. Thus, this correspondence clarifies the terminologies and specific roles of four types of wavelet transforms: the continuous wavelet transform (CWT), the discrete wavelet transform (DWT), the discrete-time wavelet transform (DTWT) and the stationary discrete-time wavelet transform (SDTWT). We believe that, after reading this correspondence, readers will be able to correctly refer to, and identify, the most appropriate type of wavelet transform for a certain application, selecting relevant and accurate material for subsequent investigation.

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7

Abdullah, Shahrum, S. N. Sahadan, Mohd Zaki Nuawi, and Zulkifli Mohd Nopiah. "Fatigue Data Analysis Using Continuous Wavelet Transform and Discrete Wavelet Transform." Key Engineering Materials 462-463 (January 2011): 461–66. http://dx.doi.org/10.4028/www.scientific.net/kem.462-463.461.

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The wavelet transform is well known for its ability in vibration analysis in fault detection. This paper presents the ability of wavelet transform in fatigue data analysis starts from high amplitude events detection and it is then followed by fatigue data extraction based on wavelet coefficients. Since the wavelet transform has two main categories, i.e. the continuous wavelet transforms (CWT) and the discrete wavelet transform (DWT), the comparison study were carried out in order to investigate performance of both wavelet for fatigue data analysis. CWT represents by the Morlet wavelet while DWT with the form of the 4th Order Daubechies wavelet (Db4) was also used for the analysis. An analysis begins with coefficients plot using the time-scale representation that associated to energy coefficients plot for the input value in fatigue data extraction. Ten extraction levels were used and all levels gave the damage difference, (%∆D) less than 10% with respect to original signal. From the study, both wavelet transforms gave almost similar ability in editing fatigue data but the Morlet wavelet provided faster analysis time compared to the Db4 wavelet. In comparison to have the value of different at 5%, the Morlet wavelet achieved at L= 5 while the Db4 wavelet at L=7. Even though it gave slower analysis time, both wavelets can be used in fatigue data editing but at different time consuming.

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8

Kekre, H. B., Tanuja Sarode, and Shachi Natu. "Performance Comparison of Wavelets Generated from Four Different Orthogonal Transforms for Watermarking With Various Attacks." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 9, no. 3 (July 15, 2013): 1139–52. http://dx.doi.org/10.24297/ijct.v9i3.3340.

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This paper proposes a watermarking technique using different orthogonal wavelet transforms like Hartley wavelet, Kekrewavelet, Slant wavelet and Real Fourier wavelet transform generated from corresponding orthogonal transform. Theseorthogonal wavelet transforms have been generated using different sizes of component orthogonal transform matrices.For example 256*256 size orthogonal wavelet transform can be generated using 128*128 and 2*2 size componentorthogonal transform. It can also be generated using 64*64 and 4*4, 32*32 and 8*8, 16*16 and 16*16 size componentorthogonal transform matrices. In this paper the focus is to compare the performance of above mentioned transformsgenerated using 128*128 and 2*2 size component orthogonal transform and 64*64 and 4*4 size component orthogonaltransform in digital image watermarking. The other two combinations are not considered as their performance iscomparatively not as good. Comparison shows that wavelet transforms generated using (128,2) combination of orthogonalÂ transform give better performances than wavelet transforms generated using (64,4) combination of orthogonaltransformfor contrast stretching, cropping, Gaussian noise, histogram equalization and resizing attacks. Real Fourierwavelet and Slant wavelet prove to be better for histogram equalization and resizing attack respectively than DCT waveletand Walsh wavelet based watermarking presented in previous work.

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9

Taha, Saleem, and Walid Mahmood. "New techniques for Daubechies wavelets and multiwavelets implementation using quantum computing." Facta universitatis - series: Electronics and Energetics 26, no. 2 (2013): 145–56. http://dx.doi.org/10.2298/fuee1302145t.

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In this paper, new techniques to implement the Daubechies wavelets and multiwavelets are presented using quantum computing synthesis structures. Also, a new quantum implementation of inverse Daubechies multiwavelet transform is proposed. The permutation matrices, particular unitary matrices, play a pivotal role. The particular set of permutation matrices arising in quantum wavelet and multiwavelet transforms is considered, and efficient quantum circuits that implement them are developed. This allows the design of efficient and complete quantum circuits for the quantum wavelet and multiwavelet transforms.

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10

TODA, HIROSHI, ZHONG ZHANG, and TAKASHI IMAMURA. "THE DESIGN OF COMPLEX WAVELET PACKET TRANSFORMS BASED ON PERFECT TRANSLATION INVARIANCE THEOREMS." International Journal of Wavelets, Multiresolution and Information Processing 08, no. 04 (July 2010): 537–58. http://dx.doi.org/10.1142/s0219691310003638.

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The useful theorems for achieving perfect translation invariance have already been proved, and based on these theorems, dual-tree complex discrete wavelet transforms with perfect translation invariance have been proposed. However, due to the complication of frequency divisions with wavelet packets, it is difficult to design complex wavelet packet transforms with perfect translation invariance. In this paper, based on the aforementioned theorems, novel complex wavelet packet transforms are designed to achieve perfect translation invariance. These complex wavelet packet transforms are based on the Meyer wavelet, which has the important characteristic of possessing a wide range of shapes. In this paper, two types of complex wavelet packet transforms are designed with the optimized Meyer wavelet. One of them is based on a single Meyer wavelet and the other is based on a number of different shapes of the Meyer wavelets to create good localization of wavelet packets.

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11

R. S. Pathak. "Variation-Diminishing Wavelets and Wavelet Transforms." Real Analysis Exchange 37, no. 1 (2012): 147. http://dx.doi.org/10.14321/realanalexch.37.1.0147.

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12

Hamdi, Med. "A Comparative Study in Wavelets, Curvelets and Contourlets as Denoising biomedical Images." Image Processing & Communications 16, no. 3-4 (January 1, 2011): 13–20. http://dx.doi.org/10.2478/v10248-012-0007-1.

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A Comparative Study in Wavelets, Curvelets and Contourlets as Denoising biomedical ImagesA special member of the emerging family of multi scale geometric transforms is the contourlet transform which was developed in the last few years in an attempt to overcome inherent limitations of traditional multistage representations such as curvelets and wavelets. The biomedical images were denoised using firstly wavelet than curvelets and finally contourlets transform and results are presented in this paper. It has been found that the contourlets transform outperforms the curvelets and wavelet transform in terms of signal noise ratio

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13

AVERBUCH, AMIR Z., and VALERY A. ZHELUDEV. "WAVELET TRANSFORMS GENERATED BY SPLINES." International Journal of Wavelets, Multiresolution and Information Processing 05, no. 02 (March 2007): 257–91. http://dx.doi.org/10.1142/s0219691307001756.

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In this paper, we design a new family of biorthogonal wavelet transforms that are based on polynomial and discrete splines. The wavelet transforms are constructed via lifting steps, where the prediction and update filters are derived from various types of interpolatory and quasi-interpolatory splines. The transforms use finite and infinite impulse response (IIR) filters and are implemented in a fast lifting mode. We analyze properties of the generated scaling functions and wavelets. In the case when the prediction filter is derived from a polynomial interpolatory spline of even order, the synthesis scaling function and wavelet are splines of the same order. We formulate conditions for the IIR filter to generate an exponentially decaying scaling function.

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14

Ashurov, Ravshan. "On the almost-everywhere convergence of the continuous wavelet transforms." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 142, no. 6 (November 27, 2012): 1121–29. http://dx.doi.org/10.1017/s030821051000123x.

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Almost-everywhere convergence of wavelet transforms of Lp-functions under minimal conditions on wavelets was proved by Rao et al. in 1994. However, results on convergence almost everywhere do not provide any information regarding the exceptional set (of Lebesgue measure zero), where convergence does not hold. We prove that if a wavelet ψ satisfies a single additional condition xψ(x) ∈ L1 (R), then, instead of almost-everywhere convergence, we have a more sophisticated result, i.e. convergence of wavelet transforms everywhere on the entire Lebesgue set of Lp-functions. For example, wavelets with compact support, used frequently in applications, obviously satisfy this extra condition. Moreover, we prove that our conditions on wavelets ensure the Riemann localization principle in L1 for the wavelet transforms.

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Ashory, Mohammad-Reza, Ahmad Ghasemi-Ghalebahman, and Mohammad-Javad Kokabi. "Damage detection in laminated composite plates via an optimal wavelet selection criterion." Journal of Reinforced Plastics and Composites 35, no. 24 (September 30, 2016): 1761–75. http://dx.doi.org/10.1177/0731684416667563.

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Delamination is a potential risk of failure considered as one of the failure modes and frequently occurs in composites due to its relatively low inter-laminar fracture toughness. In recent years, the majority of activities in this field have been focused on raising the level of sensitivity of these devising methods for detecting tiny damages. In this article, damage detection method via wavelet transform has been examined, and an appropriate procedure has been proposed to increase sensitivity of this transform for damage detection. Among the inherent impediments of classical wavelet transforms, the generality of these transforms and ignoring the studied signal can be mentioned. Consequently, various wavelet selection algorithms leading to provide appropriate wavelet functions with respect to the characteristics of the signal have been examined. As a novelty in the field, the correlation between wavelet and strain energy signal is considered as a criterion for optimal wavelet selection. In wavelet transforms, in addition to original wavelet functions, the signals used for damage detection are also of high importance. To achieve this goal, the frequency-weighted strain energy ratio signals resulting from intact and damaged forms have been exploited. Also, the edges’ effects were removed through stringing of plane mode shape signals. Moreover, by summing wavelet coefficients in all scale factors plus natural frequencies, the focus can bring to the detection of one or more damages in a laminated composite plate with symmetric layup. Finally, a quantitative measure to compare different wavelets has been presented.

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16

ANIELLO, PAOLO. "EXTENDED WAVELET TRANSFORMS." International Journal of Geometric Methods in Modern Physics 03, no. 03 (May 2006): 341–73. http://dx.doi.org/10.1142/s0219887806001223.

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We introduce the notion of extended wavelet transform for locally compact topological groups that are semidirect products with abelian normal factor, and we study its main properties. In particular, we show that this notion allows to define a weak wavelet transform — enjoying 'essentially' the same properties as a standard wavelet transform — associated with a group representation which is not square integrable, provided that suitable conditions are satisfied. As an application, we show that this construction allows to define (weak) wavelet transforms for (the universal covering of) the Poincaré group, in spite of the fact that the discrete series of representations of this group is empty, so opening the possibility of achieving a remarkable representation of relativistic particles.

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Qin, Jun, and Pengfei Sun. "Applications and Comparison of Continuous Wavelet Transforms on Analysis of A-wave Impulse Noise." Archives of Acoustics 40, no. 4 (December 1, 2015): 503–12. http://dx.doi.org/10.1515/aoa-2015-0050.

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Abstract Noise induced hearing loss (NIHL) is a serious occupational related health problem worldwide. The A-wave impulse noise could cause severe hearing loss, and characteristics of such kind of impulse noise in the joint time-frequency (T-F) domain are critical for evaluation of auditory hazard level. This study focuses on the analysis of A-wave impulse noise in the T-F domain using continual wavelet transforms. Three different wavelets, referring to Morlet, Mexican hat, and Meyer wavelets, were investigated and compared based on theoretical analysis and applications to experimental generated A-wave impulse noise signals. The underlying theory of continuous wavelet transform was given and the temporal and spectral resolutions were theoretically analyzed. The main results showed that the Mexican hat wavelet demonstrated significant advantages over the Morlet and Meyer wavelets for the characterization and analysis of the A-wave impulse noise. The results of this study provide useful information for applying wavelet transform on signal processing of the A-wave impulse noise.

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18

Strang, Gilbert. "Wavelet transforms versus Fourier transforms." Bulletin of the American Mathematical Society 28, no. 2 (April 1, 1993): 288–306. http://dx.doi.org/10.1090/s0273-0979-1993-00390-2.

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Mandal, U. K., Sandeep Verma, and Akhilesh Prasad. "Composition of wavelet transforms and wave packet transform involving Kontorovich-Lebedev transform." Filomat 35, no. 1 (2021): 47–60. http://dx.doi.org/10.2298/fil2101047m.

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The main objective of this paper is to study the composition of continuous Kontorovich-Lebedev wavelet transform (KL-wavelet transform) and wave packet transform (WPT) based on the Kontorovich-Lebedev transform (KL-transform). Estimates for KL-wavelet and KL-wavelet transform are obtained, and Plancherel?s relation for composition of KL-wavelet transform and WPT-transform are derived. Reconstruction formula for WPT associated to KL-transform is also deduced and at the end Calderon?s formula related to KL-transform using its convolution property is obtained.

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LEWALLE, JACQUES. "FIELD RECONSTRUCTION FROM SINGLE SCALE CONTINUOUS WAVELET COEFFICIENTS." International Journal of Wavelets, Multiresolution and Information Processing 07, no. 01 (January 2009): 131–42. http://dx.doi.org/10.1142/s0219691309002738.

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The redundancy of continuous wavelet transforms implies that the wavelet coefficients are not independent of each other. This interdependence allows the reconstruction or approximation of the wavelet transform, and of the original field, from a subset of the wavelet coefficients. Contrasting with lines of modulus maxima, known to provide useful partition functions and some data compaction, the reconstruction from single-scale coefficients is derived for the Hermitian family of wavelets. The formula is exact in the continuum for d-dimensional fields, and its limitations under discretization are illustrated.

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ASHUROV, RAVSHAN. "CONVERGENCE OF THE CONTINUOUS WAVELET TRANSFORMS ON THE ENTIRE LEBESGUE SET OF Lp-FUNCTIONS." International Journal of Wavelets, Multiresolution and Information Processing 09, no. 04 (July 2011): 675–83. http://dx.doi.org/10.1142/s0219691311004262.

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The almost everywhere convergence of wavelets transforms of Lp-functions under minimal conditions on wavelets is well known. But this result does not provide any information about the exceptional set (of Lebesgue measure zero), where convergence does not hold. In this paper, under slightly stronger conditions on wavelets, we prove convergence of wavelet transforms everywhere on the entire Lebesgue set of Lp-functions. On the other hand, practically all the wavelets, including Haar and "French hat" wavelets, used frequently in applications, satisfy our conditions. We also prove that the same conditions on wavelets guarantee the Riemann localization principle in L1 for the wavelet transforms.

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Indrusiak, M. L. S., A. J. Kozakevicius, and S. V. Möller. "WAVELET ANALYSIS CONSIDERATIONS FOR EXPERIMENTAL NONSTATIONARY FLOW PHENOMENA." Revista de Engenharia Térmica 15, no. 1 (June 30, 2016): 67. http://dx.doi.org/10.5380/reterm.v15i1.62149.

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In this work, wavelet transforms are the analysis tools for studying transient and discontinuous phenomena associated to turbulent flows. The application in quest results from velocity measurements with hot wire anemometry in the transient wake considering a circular cylinder in an aerodynamic channel. Continuous and discrete wavelet transforms are applied and compared with the corresponding results given by the Fourier transform. For the continuous wavelet transform, the Morlet function was adopted as transform basis, and for the discrete case, the Daubechies orthonormal wavelet with 20 null moments. Results using the discrete wavelet packet transform are also presented and compared. A wake past a cylinder was analytically simulated and compared with the actual one, both in transient flow. The ability of the wavelet transforms in the analysis of unsteady phenomena and the potential of the wavelet approach as a complementary tool to the Fourier spectrum for the analysis of stationary phenomena is presented and discussed.

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23

Xiang-Gen Xia and Zhen Zhang. "On sampling theorem, wavelets, and wavelet transforms." IEEE Transactions on Signal Processing 41, no. 12 (1993): 3524–35. http://dx.doi.org/10.1109/78.258090.

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24

Heinlein, Peter. "Discretizing continuous wavelet transforms using integrated wavelets." Applied and Computational Harmonic Analysis 14, no. 3 (May 2003): 238–56. http://dx.doi.org/10.1016/s1063-5203(03)00005-8.

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Li, Yaoguo, and Douglas W. Oldenburg. "Rapid construction of equivalent sources using wavelets." GEOPHYSICS 75, no. 3 (May 2010): L51—L59. http://dx.doi.org/10.1190/1.3378764.

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We have developed a fast algorithm for generating an equivalent source by using fast wavelet transforms based on orthonormal, compactly supported wavelets. We apply a 2D wavelet transform to each row and column of the coefficient matrix and subsequently threshold the transformed matrix to generate a sparse representation in the wavelet domain. The algorithm then uses this sparse matrix to construct the the equivalent source directly in the wavelet domain. Performing an inverse wavelet transform then yields the equivalent source in the space domain. Using upward continuation of total-field magnetic data between uneven surfaces as examples, we have compared this approach with the direct solution using the dense matrix in the space domain. We have shown that the wavelet approach can reduce the CPU time by as many as two orders of magnitude.

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Nigam, Vaibhav, Smriti Bhatnagar, and Sajal Luthra. "Image Denoising Using Wavelet Transform and Wavelet Transform with Enhanced Diversity." Advanced Materials Research 403-408 (November 2011): 866–70. http://dx.doi.org/10.4028/www.scientific.net/amr.403-408.866.

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This paper is a comparative study of image denoising using previously known wavelet transform and new type of wavelet transform, namely, Diversity enhanced discrete wavelet transform. The Discrete Wavelet Transform (DWT) has two parameters: the mother wavelet and the number of iterations. For every noisy image, there is a best pair of parameters for which we get maximum output Peak Signal to Noise Ratio, PSNR. As the denoising algorithms are sensitive to the parameters of the wavelet transform used, in this paper comparison of DEDWT to DWT has been presented. The diversity is enhanced by computing wavelet transforms with different parameters. After the filtering of each detail coefficient, the corresponding wavelet transforms are inverted and the estimated image, having a higher PSNR, is extracted. To benchmark against the best possible denoising method three thresholding techniques have been compared. In this paper we have presented a more practical, implementation oriented work.

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Bochkarev, A. V. "Resolving of Overlapping Asymmetrical Chromatographic Peaks by Using Wavelet-Transform and Gram-Charlier Peak Model." Journal of Physics: Conference Series 2096, no. 1 (November 1, 2021): 012068. http://dx.doi.org/10.1088/1742-6596/2096/1/012068.

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Abstract The paper describes a method for resolving overlapping asymmetric peaks that make up a chromatogram. The presented method uses the Gram-Charlier model in the form of the first three terms of the Gram-Charlier series as a basis. Using the wavelet transform, the parameters of this model are determined, which is used to describe a single or overlapping chromatographic peak. Hermitian wavelets of the first four orders are used in the computation of the wavelet transform. To speed up the computation of multiple wavelet transforms, the possibility of coding a signal using the Chebyshev-Hermite functions is considered in order to further restore the set of wavelet transforms simultaneously. According to the presented method, the parameters of the peaks are determined by analytical expressions without using the numerical approximation of the chromatogram by the peak model, which avoids the disadvantages of the numerical approach. The resulting method is used to resolve overlapping asymmetric peaks. The advantage of the method over others is shown by calculating the area of each of the resolved peaks.

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Lu, X. J., A. Katz, N. P. Caviris, and E. G. Kanterakis. "Joint transform correlator that uses wavelet transforms." Optics Letters 17, no. 23 (December 1, 1992): 1700. http://dx.doi.org/10.1364/ol.17.001700.

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29

Rubin, Boris. "Spherical Radon Transform and Related Wavelet Transforms." Applied and Computational Harmonic Analysis 5, no. 2 (April 1998): 202–15. http://dx.doi.org/10.1006/acha.1997.0228.

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30

Pathak, R. S., and C. P. Pandey. "Laguerre wavelet transforms." Integral Transforms and Special Functions 20, no. 7 (July 2009): 505–18. http://dx.doi.org/10.1080/10652460802047809.

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31

Gong, Bo, Benjamin Schullcke, Sabine Krueger-Ziolek, and Knut Moeller. "Regularization of EIT reconstruction based on multi-scales wavelet transforms." Current Directions in Biomedical Engineering 2, no. 1 (September 1, 2016): 423–26. http://dx.doi.org/10.1515/cdbme-2016-0094.

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AbstractElectrical Impedance Tomography (EIT) intends to obtain the conductivity distribution of a domain from the electrical boundary conditions. This is an ill-posed inverse problem usually solved on finite element meshes. Wavelet transforms are widely used for medical image reconstruction. However, because of the irregular form of the finite element meshes, the canonical wavelet transforms is impossible to perform on meshes. In this article, we present a framework that combines multi-scales wavelet transforms and finite element meshes by viewing meshes as undirected graphs and applying spectral graph wavelet transform on the meshes.

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Rao, I. Umamaheswar. "Discrete Wavelet Transforms using Daubechies Wavelet." IETE Journal of Research 47, no. 3-4 (May 2001): 169–71. http://dx.doi.org/10.1080/03772063.2001.11416221.

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Pathak, R. S., and Ashish Pathak. "Asymptotic Expansions of the Wavelet Transform for Large and Small Values ofb." International Journal of Mathematics and Mathematical Sciences 2009 (2009): 1–13. http://dx.doi.org/10.1155/2009/270492.

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Asymptotic expansions of the wavelet transform for large and small values of the translation parameterbare obtained using asymptotic expansions of the Fourier transforms of the function and the wavelet. Asymptotic expansions of Mexican hat wavelet transform, Morlet wavelet transform, and Haar wavelet transform are obtained as special cases. Asymptotic expansion of the wavelet transform has also been obtained for small values ofbwhen asymptotic expansions of the function and the wavelet near origin are given.

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Prasad, Akhilesh, and U. K. Mandal. "Wavelet transforms associated with the Kontorovich–Lebedev transform." International Journal of Wavelets, Multiresolution and Information Processing 15, no. 02 (February 7, 2017): 1750011. http://dx.doi.org/10.1142/s0219691317500114.

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The main objective of this paper is to study continuous wavelet transform (CWT) using the convolution theory of Kontorovich–Lebedev transform (KL-transform) and discuss some of its basic properties. Plancherel’s as well as Parseval’s relation and Reconstruction formula for CWT are obtained and some examples are also given. The discrete version of the wavelet transform associated with KL-transform is also given and reconstruction formula is derived.

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Ma, Guangsheng, Hongbo Li, and Jiman Zhao. "Windowed Fourier transform and general wavelet algorithms in quantum computation." Quantum Information and Computation 19, no. 3&4 (March 2019): 237–51. http://dx.doi.org/10.26421/qic19.3-4-4.

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In this paper, we define the quantum windowed Fourier transform and study some of its properties, then we develop two useful operations called quantum convolution and `integral'. Quantum `integral' allows us to implement the integral transforms quantum-mechanically with a certain probability, including general wavelet kernel transforms. Furthermore, we propose an improved wavelet kernel transform for quantum computation.

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Kittisuwan, Pichid, Sanparith Marukatat, Thitiporn Chanwimaluang, and Widhyakorn Asdornwised. "Image Denoising Employing Two-Sided Gamma Random Vectors with Cycle-Spinning in Wavelet Domain." ECTI Transactions on Electrical Engineering, Electronics, and Communications 9, no. 2 (January 16, 2009): 255–63. http://dx.doi.org/10.37936/ecti-eec.201192.172503.

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In this work, we present new Bayesian estimator for circularly-contoured Two-Sided Gamma random vector in additive white Gaussian noise (AWGN). This PDF is used in view of the fact that it is more peaked and the tails are heavier to be incorporated in the probabilistic modeling of the wavelet coefficients. One of the cruxes of the Bayesian image denoising methods is to estimate statistical parameters for a shrinkage function. We employ maximum a posterior (MAP) estimation to calculate local variances with Rayleigh density prior for local observed variances and Gaussian distribution for noisy wavelet coefficients. Several denoising methods (ProbShrink with redundant wavelet transform) using undecimated wavelet transforms provide good results. The undecimated wavelet transforms can also be viewed as applying an orthogonal wavelet transform to a set of shifted versions of the signal. This procedure wasfirst suggested by Coifman and Donoho where they termed it cycle-spinning method. We apply cycle spinning with orthogonal wavelet transforms in our work. The experimental results show that the proposed method yields good denoising results.

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Rubin, Boris. "Inversion of Radon transforms using wavelet transforms generated by wavelet measures." MATHEMATICA SCANDINAVICA 85, no. 2 (December 1, 1999): 285. http://dx.doi.org/10.7146/math.scand.a-18278.

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Kuznetsov, Nikolay A. "METHOD FOR CONSTRUCTING NONLINEAR WAVELET CODE TO ENSURE DATA INTEGRITY IN COMMUNICATION CHANNELS." T-Comm 15, no. 2 (2021): 26–32. http://dx.doi.org/10.36724/2072-8735-2021-15-2-26-32.

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A method for constructing a nonlinear wavelet code (NVC) to ensure data integrity in communication channels, taking into account current threats to information security in a modern dynamic stochastic environment, is proposed. A special place among the methods of combating threats to the integrity of information is occupied by noise-resistant encoding. The article presents a computationally effective method for ensuring data integrity in communication channels by using nonlinear transformations and wavelets. The approximation of the wavelet transform refers to the division of the signal into approximating and detailing components. Continuous and discrete wavelet transforms are widely used [2] for signal analysis in modern communication channels. The set of functions defining the wavelet transform belongs to the space of square-integrable functions on a straight line and provides a necessary condition for constructing constructions of nonlinear codes based on the theory of wavelet decomposition. As is known, in the process of wavelet analysis, the signal is decomposed along the orthogonal basis formed by shifts of the wavelet function. A distinctive feature of this approach is that convolution of the signal with wavelets allows us to identify the characteristic features of the signal in the area of localization of these wavelets. To perform computational calculations, you need a set of scaling function coefficients and a wavelet. The wavelet transform matrix depends on the coefficients of the scaling function. The results presented in the article describe a new approach to ensuring data integrity in communication channels using nvcs. A computational example is presented.

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Cohen, Albert, Ingrid Daubechies, and Pierre Vial. "Wavelets on the Interval and Fast Wavelet Transforms." Applied and Computational Harmonic Analysis 1, no. 1 (December 1993): 54–81. http://dx.doi.org/10.1006/acha.1993.1005.

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Wachowiak, Mark P., Renata Wachowiak-Smolíková, Michel J. Johnson, Dean C. Hay, Kevin E. Power, and F. Michael Williams-Bell. "Quantitative feature analysis of continuous analytic wavelet transforms of electrocardiography and electromyography." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2126 (July 9, 2018): 20170250. http://dx.doi.org/10.1098/rsta.2017.0250.

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Theoretical and practical advances in time–frequency analysis, in general, and the continuous wavelet transform (CWT), in particular, have increased over the last two decades. Although the Morlet wavelet has been the default choice for wavelet analysis, a new family of analytic wavelets, known as generalized Morse wavelets, which subsume several other analytic wavelet families, have been increasingly employed due to their time and frequency localization benefits and their utility in isolating and extracting quantifiable features in the time–frequency domain. The current paper describes two practical applications of analysing the features obtained from the generalized Morse CWT: (i) electromyography, for isolating important features in muscle bursts during skating, and (ii) electrocardiography, for assessing heart rate variability, which is represented as the ridge of the main transform frequency band. These features are subsequently quantified to facilitate exploration of the underlying physiological processes from which the signals were generated. This article is part of the theme issue ‘Redundancy rules: the continuous wavelet transform comes of age’.

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Prasad, Akhilesh, Jeetendrasingh Maan, and Sandeep Kumar Verma. "Wavelet transforms associated with the index Whittaker transform." Mathematical Methods in the Applied Sciences 44, no. 13 (April 21, 2021): 10734–52. http://dx.doi.org/10.1002/mma.7440.

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Usta, Fuat, Hüseyin Budak, and Mehmet Sarikaya. "Approximating the finite Mellin and Sumudu transforms utilizing wavelet transform." Filomat 34, no. 13 (2020): 4513–22. http://dx.doi.org/10.2298/fil2013513u.

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In this study, some approximates for the finite Wavelet transform of different classes of absolutely continues mappings are presented using Wavelet transform of unit function. Then, with the help of these approximates, some other approximates for the finite Mellin and Sumudu transforms are given.

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Knowles, G. "Hardware Architectures for the Orthogonal and Biorthogonal Wavelet Transform." VLSI Design 15, no. 2 (January 1, 2002): 499–506. http://dx.doi.org/10.1080/1065514021000012110.

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In this note, optimal hardware architectures for the orthogonal and biorthogonal wavelet transforms are presented. The approach used here is not the standard lifting method, but takes advantage of the symmetries inherent in the coefficients of the transforms and the decimation/interpolation operators. The design is based on a highly optimized datapath, which seamlessly integrates both orthogonal and biorthogonal transforms, data extension at the edges and the forward and inverse transforms. The datapath design could be further optimized for speed or low power. The datapath is controlled by a small fast control unit which is hard programmed according to the wavelet or wavelets required by the application. Example circuits are given, including one for the Daubechies 9-7 wavelet which requires only 2.5 multipliers for each input data value, when the equivalent for lifting is 3.

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Prosser, R., and R. S. Cant. "The theoretical development of wavelets in reacting flows." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 214, no. 11 (November 1, 2000): 1363–73. http://dx.doi.org/10.1243/0954406001523335.

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This paper focuses on the simulation of turbulent reacting flows via recent developments in wavelet-based analyses. The unique data compression properties of wavelet methods render them especially attractive for such simulations, in which the length and time-scales of interest originate from both physical and chemical processes and may span several orders of magnitude. The particular difficulties encountered when representing reacting flow problems on non-periodic domains, and how these difficulties have led to the adoption of a biorthogonal wavelet framework, are discussed. This leads to consideration of interpolating wavelet transforms based on second-generation wavelets, for which a fast transform algorithm is presented. Issues raised by the application of wavelet transform methods to the reacting Navier-Stokes equations, including the calculation of differential operators, the extension to two and three dimensions and the evaluation of non-linear terms, are examined. The implications of the wavelet approach for the representation of the turbulent energy cascade are explored briefly. Finally, some future directions for research into the extension of wavelet analysis as an underpinning technology for computational fluid dynamics are indicated.

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Zhang, Xi, and Noriaki Fukuda. "Lossy to lossless image coding based on wavelets using a complex allpass filter." International Journal of Wavelets, Multiresolution and Information Processing 12, no. 04 (July 2014): 1460002. http://dx.doi.org/10.1142/s0219691314600029.

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Wavelet-based image coding has been adopted in the international standard JPEG 2000 for its efficiency. It is well-known that the orthogonality and symmetry of wavelets are two important properties for many applications of signal processing and image processing. Both can be simultaneously realized by the wavelet filter banks composed of a complex allpass filter, thus, it is expected to get a better coding performance than the conventional biorthogonal wavelets. This paper proposes an effective implementation of orthonormal symmetric wavelet filter banks composed of a complex allpass filter for lossy to lossless image compression. First, irreversible real-to-real wavelet transforms are realized by implementing a complex allpass filter for lossy image coding. Next, reversible integer-to-integer wavelet transforms are proposed by incorporating the rounding operation into the filtering processing to obtain an invertible complex allpass filter for lossless image coding. Finally, the coding performance of the proposed orthonormal symmetric wavelets is evaluated and compared with the D-9/7 and D-5/3 biorthogonal wavelets. It is shown from the experimental results that the proposed allpass-based orthonormal symmetric wavelets can achieve a better coding performance than the conventional D-9/7 and D-5/3 biorthogonal wavelets both in lossy and lossless coding.

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Akdemir, Bayram, and Şaban Öztürk. "Glass Surface Defects Detection with Wavelet Transforms." International Journal of Materials, Mechanics and Manufacturing 3, no. 3 (2015): 170–73. http://dx.doi.org/10.7763/ijmmm.2015.v3.189.

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Kautský, Jaroslav. "An algebraic construction of discrete wavelet transforms." Applications of Mathematics 38, no. 3 (1993): 169–93. http://dx.doi.org/10.21136/am.1993.104545.

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Holschneider, M. "Inverse Radon transforms through inverse wavelet transforms." Inverse Problems 7, no. 6 (December 1, 1991): 853–61. http://dx.doi.org/10.1088/0266-5611/7/6/008.

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CAPOBIANCO, ENRICO. "WAVELET TRANSFORMS FOR THE STATISTICAL ANALYSIS OF RETURNS GENERATING STOCHASTIC PROCESSES." International Journal of Theoretical and Applied Finance 04, no. 03 (June 2001): 511–34. http://dx.doi.org/10.1142/s0219024901001097.

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We study high frequency Nikkei stock index series and investigate what certain wavelet transforms suggest in terms of volatility features underlying the observed returns process. Several wavelet transforms are applied for exploratory data analysis. One of the scopes is to use wavelets as a pre-processing smoothing tool so to de-noise the data; we believe that this procedure may help in identifying, estimating and predicting the latent volatility. Evidence is shown on how a non-parametric statistical procedure such as wavelets may be useful for improving the generalization power of GARCH models when applied to de-noised returns.

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Zhang, Zhihua. "The Improvement of the Discrete Wavelet Transform." Mathematics 11, no. 8 (April 7, 2023): 1770. http://dx.doi.org/10.3390/math11081770.

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Discrete wavelet transforms are widely used in signal processing, data compression and spectral analysis. For discrete data with finite sizes, one always pads the data with zeros or extends the data into periodic data before performing the discrete periodic wavelet transform. Due to discontinuity on the boundaries of the original data, the obtained wavelet coefficients always decay slowly, leading to data compression ratios that are significantly lower. In order to solve this issue, in this study, we coupled polynomial fitting into classic discrete periodic wavelet transforms to mitigate these boundary effects.

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