A biorthogonal wavelet design technique using Karhunen–Loéve transform approximation

Kale, Mehmet Cemil; Atac, Gizem; Gerek, Ömer Nezih

doi:10.1016/j.dsp.2015.06.002

Cited by 7 publications

(3 citation statements)

References 15 publications

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“…Extensive investigation has also been done for the development of a technique to define the wavelet transform as a transform matrix: block wavelet transform (BWT) [6][7][8]. Instead of a conventional discrete wavelet transform, the discrete wavelet transform is achieved using matrix multiplications.…”

Section: Introductionmentioning

confidence: 99%

“…The first research of the author consisted of the iterative development of a 2 N × 2 N BWT matrix development algorithm (from smaller BWT counterparts) and the design of a filter by considering the orthogonality limitations of BWT matrices of the lifting scheme. In the same research, the author proposed another filter whose output BWT matrices converged to the Karhunen-Loéve transform matrices of test images [7,8]. Here, there was a problem: The wavelets were signal-dependent.…”

Section: Introductionmentioning

confidence: 99%

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Development of computationally eﬀicient biorthogonal wavelets

Kale¹

2021

Turk J Elec Eng & Comp Sci

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Daubechies 5-tap/3-tap (Daub 5/3) wavelet and Kale 5-tap/3-tap (Kale 5/3) wavelet are computationally efficient wavelets which can be implemented by bitwise shifts and additions in the lifting scheme. In this work, presented is a formulation for computationally efficient wavelet prediction (P) and update (U) filters of two-channel lifting structures.Their subband decomposition scheme counterparts are also given. This research bases itself on the Daub 5/3 and Kale 5/3 wavelets and develops a formula for wavelets (which can be implemented with bitwise shifts and additions) that are derived from these two wavelets. The proposed wavelets are tried on 16 test images for three-level wavelet decompositions and better decorrelation results are achieved for the proposed wavelets for higher-level decompositions.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Development of computationally eﬀicient biorthogonal wavelets

Kale¹

2021

Turk J Elec Eng & Comp Sci

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“…Kaldırma düzeni etkin olarak çift dikgen dalgacık dönüşümlerinde kullanılmaktadır [15][16][17][18][19][20][21][22][23]. Öte yandan, geleneksel kafes yapısı, 2 kanallı DAF bankalarında uygulanmaktadır ve bir altbant filtre bankası uygulamasıdır [24][25].…”

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Kaldırma Düzeninde Kafes Uygulaması

Kale¹

2019

Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi

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ÖZFiltre bankalarında altbant, kaldırma ve altbantın bir parçası olarak kafes düzenleri kullanılmaktadır. Bunların içinden kaldırma düzeni, işareti alt örneklemeyi daha önce yaparak aritmetik işlem sayısını yarı yarıya indirdiği için daha avantajlıdır. Ancak, kafes tekniği kaldırma düzeninde kullanılmamaktadır. Bu makalede anlatılan araştırmada, filtre bankaları için kaldırma düzeninde kafes uygulaması geliştirilmiştir. Mükemmel geri oluşturulma için tüm koşullar ele alınmış ve detaylıca açıklanmıştır. Geliştirilen düzen 4 test resmi üzerinde denenmiş ve geleneksel kafes düzenine göre daha iyi sonuçlar elde edilmiştir. ABSTRACTIn the filter banks, subband scheme, lifting scheme and as a part of the subband scheme, the lattice scheme are used. Among these, lifting scheme has the advantage of decreasing the arithmetic operations by half, because it downsamples the signal first. However, lattice is not used in the lifting scheme. In the research described in this article, lattice application for filter banks on the lifting scheme has been developed. Also, the constraints for the perfect reconstruction are given in detail. The performance of the new scheme is tested on 4 test images and better results are obtained compared to the traditional lattice scheme.

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