Symmetric MRA tight wavelet frames with three generators and high vanishing moments

Han, Bin; Mo, Qun

doi:10.1016/j.acha.2004.09.001

Cited by 69 publications

(62 citation statements)

References 22 publications

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“…Then we provide a detailed analysis and a complete algorithm to obtain all type I STFFBs with three high-pass filters. Our results not only significantly generalize the results in [1,11], but also help us answer several unresolved problems on STFFBs. Based on [7], we also propose an algorithm to construct all type II STFFBs with three high-pass filters and with the shortest possible filter supports.…”

supporting

confidence: 69%

“…Note that the condition in (1.10) becomes (1.7) when θ = 1. Under the condition that a(1) = 1 and θ(1)θ(−1) = 1, it has been proved in [11,Theorem 1.2] that such a desired Laurent polynomial θ always exists provided that the standard refinable function associated with the low-pass filter a has stable integer shifts. But generally the length of the moment correcting filter Θ in (1.11) is long.…”

Section: Introduction and Motivationsmentioning

confidence: 99%

“…Motivated by the interesting papers by Chui and He [1] and Han and Mo [11], continuing our lines developed in [7,9] on symmetric tight framelet filter banks with a minimum number of generators, in this paper we are particularly interested in systematically studying and developing algorithms to construct all symmetric tight framelet filter banks with three high-pass filters and with the shortest possible filter supports.…”

Section: Introduction and Motivationsmentioning

confidence: 99%

“…In particular, we shall systematically study STFFBs with three high-pass filters which are derived from the oblique extension principle. To our best knowledge, except the papers [1,11], there are no other papers in the literature so far systematically studying this problem. In this paper we show that there are two different types, types I and II, of STFFBs with three high-pass filters.…”

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confidence: 99%

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Symmetric tight framelet filter banks with three high-pass filters

Han

2014

Applied and Computational Harmonic Analysis

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Abstract. In this paper we continue our investigation of symmetric tight framelet filter banks (STFFBs) with a minimum number of generators in [7]. In particular, we shall systematically study STFFBs with three high-pass filters which are derived from the oblique extension principle. To our best knowledge, except the papers [1,11], there are no other papers in the literature so far systematically studying this problem. In this paper we show that there are two different types, types I and II, of STFFBs with three high-pass filters. Then we provide a detailed analysis and a complete algorithm to obtain all type I STFFBs with three high-pass filters. Our results not only significantly generalize the results in [1,11], but also help us answer several unresolved problems on STFFBs. Based on [7], we also propose an algorithm to construct all type II STFFBs with three high-pass filters and with the shortest possible filter supports. Several examples are given to illustrate the results and algorithms in this paper.

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confidence: 69%

Section: Introduction and Motivationsmentioning

confidence: 99%

Section: Introduction and Motivationsmentioning

confidence: 99%

mentioning

confidence: 99%

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Symmetric tight framelet filter banks with three high-pass filters

Han

2014

Applied and Computational Harmonic Analysis

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“…Tight wavelet frames and tight framelet filter banks without symmetry have been extensively studied in a lot of papers, to mention only a few here, see [2,3,4,5,8,12,18,19,20] and many papers therein. Interesting examples of real-valued tight framelet filter banks with symmetry have been obtained in [3,5,6,13,14,15,16,17,18,21].…”

Section: Introductionmentioning

confidence: 99%

Matrix splitting with symmetry and symmetric tight framelet filter banks with two high-pass filters

Han¹

2013

Applied and Computational Harmonic Analysis

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Abstract. The oblique extension principle introduced in [3,5] is a general procedure to construct tight wavelet frames and their associated filter banks. Symmetric tight framelet filter banks with two high-pass filters have been studied in [13,16,17]. Tight framelet filter banks with or without symmetry have been constructed in [1]- [21] and references therein. This paper is largely motivated by several results in [11,13,17] to further study tight wavelet frames and their associated filter banks with symmetry and two high-pass filters. Our study not only leads to a simpler algorithm for the construction of tight framelet filter banks with symmetry and two high-pass filters, but also allows us to obtain a wider class of tight wavelet frames with symmetry which are not available in the current literature. The key ingredient in our investigation is a complete characterization of splitting positive semi-definite 2 × 2 matrices of Laurent polynomials with symmetry. Several examples are provided to illustrate the results and algorithms in this paper.

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Image analysis of heavy oil liberation from host rocks/sands

Zhang

Lin

et al. 2015

Can J Chem Eng

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An essential requirement for efficient heavy oil production is liberation of heavy oil from host rocks, which is determined by the wettability of the rocks, and the interfacial tension and viscosity of heavy oil. Recent progress on the design of an online visualization flow cell allows capture of dynamic heavy oil liberation processes from the surfaces of sand grains in real time under a water flooding environment. However, the accurate assessment of heavy oil liberation remains a challenge, due to uncertainties in defining oil-free areas of heavy oil contaminated rock surfaces. In this study, three new image-processing algorithms of modified empirical, Gridding, and Edge-covering methods were applied to image transformation for heavy oil liberation analysis. These methods were found to be more accurate and robust in determining the threshold value distinguishing liberated from unliberated sand surfaces. The use of wavelet transform theory in the Gridding and Edge-covering methods led to faster calculations with a typical error of less than 2 % in the quantitative analysis on the threshold value determination and the degree of heavy oil liberation. Among these three methods, the Gridding method with a sound theoretical foundation was shown to be the most reliable. The results showed that the threshold value determined was highly dependent on the types of ores and the image capture settings such as lighting conditions, exposure time, and microscope magnification.

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Symmetric MRA tight wavelet frames with three generators and high vanishing moments

Cited by 69 publications

References 22 publications

Symmetric tight framelet filter banks with three high-pass filters

Symmetric tight framelet filter banks with three high-pass filters

Matrix splitting with symmetry and symmetric tight framelet filter banks with two high-pass filters

Image analysis of heavy oil liberation from host rocks/sands

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