Zhihua Zhang

Zhihua Zhang
Shandong University | SDU

PhD
Taishan Distinguished Professor

About

109
Publications
40,737
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997
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September 2019 - present
Shandong University
Position
  • Professor

Publications

Publications (109)
Article
Due to global warming, the quantity of Arctic sea ice has been drastically reduced in recent decades, consequently navigating the Arctic is becoming increasingly commercially feasible during part of the year. It will bring huge transportation benefits due to reduction in navigational time, fossil energy consumption and related carbon emissions. In...
Book
Full-text available
Climate change mechanisms, impacts, risks, mitigation, adaption, and governance are widely recognized as the biggest, most interconnected problem facing humanity. Big Data Mining for Climate Change addresses one of the fundamental issues facing scientists of climate or the environment: how to manage the vast amount of information available and anal...
Book
THIS BOOK: - Enhances the understanding of climate, paleoclimate, and paleoenvironmental changes in Europe, America, Africa, Middle East, and Asia, but mainly focuses on the Mediterranean environment and surrounding regions. - Provides new insights on sustainable water characterization, evaluation, management, and protection. - Includes case studi...
Article
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In time–frequency analysis, an increasing interest is to develop various tools to split a signal into a set of non-overlapping frequency regions without the influence of their adjacent regions. Although the framelet is an ideal tool for time–frequency analysis, most of the framelets only give an overlapping partition of the frequency domain. In ord...
Article
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Signals are often destroyed by various kinds of noises. A common way to statistically assess the significance of a broad spectral peak in signals and the synchronization between signals is to compare with simple noise processes. At present, wavelet analysis of red noise is studied limitedly and there is no general formula on the distribution of the...
Article
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Fourier approximation plays a key role in qualitative theory of deterministic and random differential equations. In this paper, we will develop a new approximation tool. For an m -order differentiable function f on [ 0 , 1 ], we will construct an m -degree algebraic polynomial P m depending on values of f and its derivatives at ends of [ 0 , 1 ] su...
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Dynamic accurate predictions of Arctic sea ice, ocean, atmosphere, and ecosystem are necessary for safe and efficient Arctic maritime transportation; however a related technical roadmap has not yet been established. In this paper, we propose a management system for trans-Arctic maritime transportation supported by near real-time streaming data from...
Article
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Based on temperature and rainfall recorded at 34 meteorological stations in Bangladesh during 1989–2018, the trends of yearly average maximum and minimum temperatures have been found to be increasing at the rates of 0.025 ∘ C and 0.018 ∘ C per year. Analysis of seasonal average maximum temperature showed increasing trend for all seasons except the...
Article
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Framelets have been widely used in narrowband signal processing, data analysis, and sampling theory, due to their resilience to background noise, stability of sparse reconstruction, and ability to capture local time-frequency information. The well-known approach to construct framelets with useful properties is through frame multiresolution analysis...
Article
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Due to resilience to background noise, stability of sparse reconstruction, and ability to capture local time-frequency information, the frame theory is becoming a dynamic forefront topic in data science. In this study, we overcome the disadvantages in the construction of traditional framelet packets derived by frame multiresolution analysis and squ...
Article
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Purpose Climatic extreme events are predicted to occur more frequently and intensely and will significantly threat the living of residents in arid and semi-arid regions. Therefore, this study aims to assess climatic extremes’ response to the emerging climate change mitigation strategy using a marine cloud brightening (MCB) scheme. Design/methodolo...
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The increasing carbon emissions from fossil fuel combustion and land use change will lead to disastrous global warming in the near future, so it is widely recognised as one of the most challenges facing human societies. In this paper, we will assess the atmospheric carbon dioxide removal and recycling utilisation which can turn anthropogenic carbon...
Article
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For a d-dimensional smooth target function f on the cube [0,1]d, we propose the Hermite-wavelet transform to overcome boundary effects. In details, we first give a decomposition of f based on its even-order Hermite interpolation on sections of the cube [0,1]d: f=G+r, where G is a combination of polynomials and the restriction of derivative function...
Article
Under rapid Arctic warming, the vast amount of labile organic carbon stored in Arctic permafrost soils poses a potentially huge threat. Thawing permafrost will release hundreds of billion tons of soil carbon into the atmosphere in the form of CO2 and CH4 that would further intensify global warming and bring more challenges to human society. In this...
Book
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This edited volume is based on the best papers accepted for presentation during the 1st Springer Conference of the Arabian Journal of Geosciences (CAJG-1), Tunisia 2018. The book is of interest to all researchers in the fields of climate, paleo-climate and paleo-environmental studies. Middle East and Mediterranean region is located at a crossroad...
Cover Page
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International Journal of Big Data Mining for Global Warming
Conference Paper
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Purpose: Currently, negotiation on global carbon emissions reduction is very difficult owing to lack of international willingness. In response, geoengineering (climate engineering) strategies are proposed to artificially cool the planet. Meanwhile, as the harbor around one-third of all described marine species, coral reefs are the most sensitive ec...
Article
The most serious desertification in China occurs in the agro-pastoral ecotone of Northeast China and in the oases in Northwest China. It has resulted in the reduce of land productivity and serious ecological/environmental consequences. In this paper, we assessed the mechanisms of land desertification and the key strategies to monitor, control and m...
Chapter
Climate change and its social, environmental, and ethical consequences are widely recognized as the major set of interconnected problems facing human societies.
Chapter
Multivariate harmonic analysis technique has been employed widely in determining cyclic variations of multivariate time series.
Chapter
Multivariate time series analysis in climate and environmental research always requires to process huge amount of data. Inspired by human nervous system, the artificial neural network methodology is a powerful tool to handle this kind of difficult and challenge problems and has been widely used to investigate mechanism of climate change and predict...
Chapter
Stochastic methods are a crucial tool for the analysis of multivariate time series in contemporary climate and environmental research.
Chapter
Wavelet analysis offers an alternative to harmonic analysis of multivariate time series and is particularly useful when the amplitudes and periods of dominant cycles are time dependent.
Chapter
Global warming of the climate system is unequivocal, as is now evident from observations of increases in global average air and ocean temperatures, widespread melting of snow and ice, and rising global average sea level.
Chapter
The ability to reconstruct past climates has expanded in recent years with a better understanding of present and future climate variability and climate change.
Chapter
Global climate change is one of the greatest threats to human survival and social stability that has occurred in human history. The main factor causing climate change is the increase of global carbon emissions produced by human activities such as deforestation and burning of fossil fuels.
Chapter
The global carbon cycle is the fluxes of carbon among four main reservoirs: fossil carbon, the atmosphere, the oceans, and the land surface.
Chapter
The complexity of climatic and environmental variability on all timescales requires the use of advanced methods to unravel its primary dynamics from observations, so various spectral methods for multivariate stochastic processes are developed and applied to unravel amplitudes and phases of periodic components embedded in climatic and environmental...
Article
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Due to discontinuity on the boundary, traditional Fourier approximation does not work efficiently for d−variate functions on [0, 1]d. In this paper, we will give a recursive method to reconstruct/approximate functions on [0, 1]d well. The main process is as follows: We reconstruct a d−variate function by using all of its (d−1)–variate boundary func...
Article
Full-text available
Purpose Currently, negotiation on global carbon emissions reduction is very difficult owing to lack of international willingness. In response, geoengineering (climate engineering) strategies are proposed to artificially cool the planet. Meanwhile, as the harbor around one-third of all described marine species, coral reefs are the most sensitive ec...
Article
Full-text available
For a bivariate function on a square, in general, its Fourier coefficients decay slowly, so one cannot reconstruct it by few Fourier coefficients. In this paper we will develop a new approximation scheme to overcome the weakness of Fourier approximation. In detail, we will use Lagrange interpolation and linear interpolation on the boundary of the s...
Article
In data analysis, one needs to study Fourier sine analysis on the unit cube. However, for this kind of non-periodic case, no exact result is available. In this paper, firstly, based on our multivariate function decomposition, we deduce an asymptotic formula of Fourier sine coefficients of continuously differentiable functions f on [0, 1](d). Second...
Book
Full-text available
Most environmental data involve a large degree of complexity and uncertainty. Environmental Data Analysis is created to provide modern quantitative tools and techniques designed specifi cally to meet the needs of environmental sciences and related fi elds. This book has an impressive coverage of the scope. Main techniques described in this book inc...
Article
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The Tibetan Plateau is situated in one of Earth's extreme continental climate settings and is influenced by numerous climatic regimes such as the East Asian and Indian monsoons and westerlies. It is the largest region of the world where permafrost is present at mid-latitudes and its relative warmth and shallow thickness makes it more sensitive to c...
Article
In application, one often expands the functions f on [0,1](2) into Fourier sine series and uses few Fourier sine coefficients to reconstruct f. In this paper, we give a decomposition formula of Fourier sine coefficients. Based on it, we discuss hyperbolic cross approximations of Fourier sine series and Fourier sine expansion with simple polynomial...
Chapter
The Fourier transform of a signal can provide only global frequency information. While a time-frequency distribution of a signal can provide information about how the frequency content of the signal evolves with time. This is performed by mapping a one-dimensional time domain signal into a two-dimensional time-frequency representation of the signal...
Chapter
Empirical orthogonal function (EOF) analyses are often used to study possible spatial patterns of climate variability and how they change with time. One of the important results from EOF analysis is the discovery of several oscillations in the climate system, including the Pacific Decadal Oscillation and the Arctic Oscillation. Similarly to Fourier...
Chapter
Earth’s atmosphere is composed of a mixture of gases such as nitrogen, oxygen, carbon dioxide, water vapor, and ozone. A wide variety of fluid flows take place in the atmosphere. In this chapter, we show how the theory of fluid dynamics in Chapter ?? is applied to the atmosphere. For this purpose, we introduce the Navier-Stokes equation, hydrostati...
Chapter
Glaciers and ice sheets cover about 10% of Earth’s land surface. Most mountain glaciers have been retreating since the end of the “Little Ice Age.” The present volume of Earth’s glacier ice, if totally melted, represents about 80 m in potential sea level rise. Sea level changes, especially in densely populated, low-lying coastal areas and on island...
Chapter
Compared with in situ observation, remote sensing gathers information concerning Earth’s surface by using data acquired from aircraft and satellites. The traditional and physics-based concepts are now complemented with signal and image processing concepts, so remote sensing is capable of managing the interface between the signal acquired and the ph...
Chapter
The oceans are an important component of the climate system. They have a profound influence on global climate and ecosystems. Therefore, the understanding of oceanic dynamics is a prerequisite for understanding the present climate, including both the mean climate state and the superimposed natural climate variability. In this chapter, we cover vari...
Chapter
Earth’s atmosphere and oceans exhibit complex patterns of fluid motion over a vast range of space and time scales. These patterns combine to establish the climate in response to solar radiation that is inhomogeneously absorbed by the materials composing air, water, and land. Therefore, fluid dynamics is fundamental for understanding, modeling, and...
Chapter
Various models are used to study the climate system and its natural variability, and to simulate the interaction between the physical climate and the biosphere, and the chemical constituents of the land, atmosphere, and ocean. Models are the best tools available to test hypotheses about the factors causing climate change and to assess future Earth...
Chapter
Climatic data and theoretical considerations suggest that a large part of climatic variability has a random nature and can be analyzed using the theory of random processes. In this chapter, we describe the random approach to the study of changes in the climate system, including stationary random processes, calculus of random processes, power spectr...
Chapter
Data assimilation is a powerful technique which has been widely applied in investigations of the atmosphere, ocean, and land surface. It combines observation data and the underlying dynamical principles governing the system to provide an estimate of the state of the system which is better than could be obtained using just the data or the model alon...
Chapter
Basic probability theory and statistics have a wide application in climate change research, ranging from the mean climate state and uncertainty of climatic parameters to the dynamics of the climate system. They provide powerful tools for climatologists to explain and analyze climatic data as well as to model and predict climate change. In this chap...
Article
Full-text available
We model background noise in time series of climate data as AR(1) red noise. To extract significant features of these time series, we use comparisons of wavelet power spectrum time series with that of AR(1) red noise. We improve on earlier work which has so far only relied on empirical formulas for the distribution of AR(1) red noise in Morlet wave...
Article
Full-text available
Carbon capture and storage (CCS) facilities coupled to coal-fired power plants provide a climate change mitigation strategy that potentially permits the continued use of coal whilst reducing the carbon dioxide emissions. However, the still-high cost of CCS is one of the major obstacles, especially for developing countries. In this paper, we will as...
Article
Full-text available
Based on calculus of random processes, we present a kind of Fourier expansions with simple polynomial terms via our decomposition method of random processes. Using our method, the expectations and variances of the corresponding coefficients decay fast and partial sum approximations attain the best approximation order. Moreover, since we remove boun...
Article
Full-text available
Climate change and its social, environmental, economic and ethical consequences are widely recognized as the major set of interconnected problems facing human societies. Its impacts and costs will be large, serious, and unevenly spread, globally for decades. The main factor causing climate change and global warming is the increase of global carbon...
Article
Fourier cosine transforms are applied widely in applied mathematics, PDEs, and signal processing. In this paper we give some asymptotic representations in stochastic Fourier cosine analyses based on our decomposition. More importantly, we propose a stochastic Fourier cosine expansion with a polynomial term. In this expansion, Fourier cosine coeffic...
Article
Full-text available
Based on our decomposition of stochastic processes and our asymptotic representations of Fourier cosine coefficients, we deduce an asymptotic formula of approximation errors of hyperbolic cross truncations for bivariate stochastic Fourier cosine series. Moreover we propose a kind of Fourier cosine expansions with polynomials factors such that the c...
Article
Full-text available
The support of the Fourier transform of a wavelet is said to be its frequency domain. In the research of geometric structures of frequency domains of band-limited wavelets, it is well known that the frequency domain of any band-limited wavelet has a hole, in which the origin lies. In Zhang (J. Approx. Theory 148:128-147, 2007), we further study mea...
Article
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A function is called a wavelet if its integral translations and dyadic dilations form an orthonormal basis for L 2(ℝ). The support of the Fourier transform of a wavelet is called its frequency band. In this paper, we study the relation between diameters and measures of frequency bands of wavelets, precisely say, we study the ratio of the measure to...
Article
Full-text available
In order to extract the intrinsic information of climatic time series from background red noise, in this paper, we will first give an analytic formula on the distribution of Haar wavelet power spectra of red noise in a rigorous statistical framework. After that, by comparing the difference of wavelet power spectra of real climatic time series and r...
Article
Full-text available
For a smooth bivariate function defined on a general domain with arbitrary shape, it is difficult to do Fourier approximation or wavelet approximation. In order to solve these problems, in this paper, we give an extension of the bivariate function on a general domain with arbitrary shape to a smooth, periodic function in the whole space or to a smo...
Article
Full-text available
Climate change is now widely recognized as the major environmental problem facing human societies. Its impacts and costs will be large, serious, and unevenly spread. Due to the observed increases in temperature, decreases in snow & ice extent and increases in sea level, global warming is unequivocal. The main factor causing climate change and globa...
Article
Full-text available
We propose an efficient nonlinear approximation scheme using the Polyharmonic Local Sine Transform (PHLST) of N. Saito and J.-F. Remy [Appl. Comput. Harmon. Anal. 20, No. 1, 41–73 (2006; Zbl 1089.94003)] combined with an algorithm to tile a given image automatically and adaptively according to its local smoothness and singularities. To measure such...
Article
Based on multiresolution analysis (MRA) structures combined with the unitary extension principle (UEP), many frame wavelets were constructed, which are called UEP framelets. The aim of this letter is to derive general properties of UEP framelets based on the spectrum of the center space of the underlying MRA structures. We first give the existence...
Article
In this paper, we present a decomposition method of multivariate functions. This method shows that any multivariate function f on [0, 1]d is a finite sum of the form Σj ϕj ψj , where each ϕ j can be extended to a smooth periodic function, each ψ j is an algebraic polynomial, and each φ j ψ j is a product of separated variable type and its smoothnes...
Article
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As the main result in Ge's paper, Ge announced that he proved a formula on the distribution of Morlet wavelet power spectrum of continuous-time Gaussian white noise in a rigorous statistical framework. In this paper, we will show that Ge's formula is wrong and each step of Ge's proof is wrong. Moreover, we give and prove a correct formula in a rigo...
Article
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It is well known that smooth periodic functions can be expanded into Fourier series and can be approximated by trigonometric polynomials. The purpose of this paper is to do Fourier analysis for smooth functions on planar domains. A planar domain can often be divided into some trapezoids with curved sides, so first we do the Fourier analysis for smo...
Article
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It is well-known that the different kinds of multiresolution analysis (MRA) structures generate different wavelets. In this paper, we give two uniform formulas on the number of mother functions for various wavelets associated with MRA structures. These formulas show that the number of mother functions of wavelets is determined by the support of the...
Article
The notion of quasi-biorthogonal frame wavelets is a generalization of the notion of orthogonal wavelets. A quasi-biorthogonal frame wavelet with the cardinality r consists of r pairs of functions. In this paper we first analyze the local property of the quasi-biorthogonal frame wavelet and show that its each pair of functions generates reconstruct...
Article
Modularity design is a comon method in product design. This essay is about the analyzing of the application of modularity in military product design,study on the developing trend and value of modularity in military products by analyzing the advantages of moularity and it's major features in military products.
Article
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Since the wavelet power spectra are distorted at data boundaries (the cone of influence, COI), using traditional methods, one cannot judge whether there is a significant region in COI or not. In this paper, with the help of a first-order autoregressive (AR1) extension and using our simple and rigorous method, we can obtain realistic significant reg...
Article
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When one applies the discrete Fourier transform to analyze finite-length time series, discontinuities at the data boundaries will distort its Fourier power spectrum. In this paper, based on a rigid statistics framework, we present a new significance test method which can extract the intrinsic feature of a geophysical time series very well. We show...
Article
In this paper, we will show that the Fourier support of a wavelet ψ possesses the minimal measure if and only if the conditions |[^(y)]| = cE\vert \widehat{\psi}\vert = {\chi }_{E} and |E| = |[`(E)]| = 2p\vert E\vert = \vert \overline{E}\vert = 2\pi hold simultaneously. If a wavelet ψ satisfies the first condition |[^(y)]| = cE\vert \widehat{\p...
Article
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In 2006, Saito and Remy proposed a new transform called the Laplace Local Sine Transform (LLST) in image processing as follows. Let f be a twice continuously differentiable function on a domain Ω. First we approximate f by a harmonic function u such that the residual component v=f−u vanishes on the boundary of Ω. Next, we do the odd extension for v...
Article
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In this paper, we give a new method of constructions of non-tensor product wavelets. We start from the one-dimensional scaling functions to directly construct the two-dimensional non-tensor product wavelets. The wavelets constructed by us possess very simple, explicit representations and high regularity, and various symmetry (i.e., axial symmetry,...
Article
It is well known that the global frequency domain Ω of any orthonormal wavelet has a hole which contains the origin, viz. the frequency domain Ω possesses a ring-like structure Ω = S \ S * (0 ∈ S * ⊂ S). We show that under some weak conditions, the set S and the hole S * are determined uniquely by Ω, where the size of the hole S * satisfies 0 ∈ S 4...
Article
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In this paper, we discuss the continuous extension and wavelet approximation of the detected object on a general domain of R2. We first extend continuously the image to a square T and such that it vanishes on the boundary @T. On T \ , the extension has a simple and clear representation which is determined by the equation of the boundary @. We expan...
Article
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In this paper, we give integral representations of partial sums of the periodic wavelet frame series and then, based on it, we study convergence and the Gibbs phenomenon of the periodic wavelet frame series.
Article
Since the extension principles of constructing wavelet frames were presented, a lot of symmetric and compactly supported wavelet frames with high vanishing moments have been constructed. However the problem of constructing periodic wavelet frames with the help of extension principles is open. In this paper, we will construct tight periodic wavelet...
Article
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The concept of frames for L 2 (ℝ) is a generalization of the concept of orthonormal bases. The Weyl-Heisenberg frames are a kind of important frames. It is generated by translations and modulations of a single function and is extensively used in time frequency analysis. Here, we study the convergence of the Weyl-Heisenberg frame series.
Article
Let {φ k } 1 ∞ be a frame for the Hilbert space H. The purpose of this paper is to present an approximation formula of any f∈H by a linear combination of finitely many frame elements in the frame {φ k } 1 ∞ and to show that the obtained approximation error depends on the bounds of the frame and the convergence rate of the frame coefficients of f as...
Article
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In 2006, Saito and Remy presented a new algorithm called polyharmonic local sine transform (PHLST) in image processing as follows. Let f be a twice continuously differentiable function on a domain . First we approximate f by a polyharmonic function u such that the residual component v = f u vanishes in the boundary of . Next, we do the odd extensio...
Article
We investigate the measures of frequency bands of scaling functions and wavelets, and solve an open problem. Furthermore, we give conditions for which the measures of frequency bands of scaling functions are less than 8π 3 and the measures of frequency bands of wavelets are less than 4π. We also discuss the densities around the origin and the diame...
Article
Full-text available
The polyharmonic local cosine transform (PHLCT), presented by Yamatani and Saito1 in 2006, is a new tool for local image analysis and synthesis. It can compress and decompress images with better visual fidelity, less blocking artifact s, and better PSNR than those processed by the JPEG-DCT algorithm. Now, we generalize PHLCT to the high-dimensional...
Article
Based on the research of the supports of dimension functions for band-limited wavelets, we show that if the Fourier transform of a band-limited wavelet is continuous at every boundary point of the support of its Fourier transform, then this band-limited wavelet is associated with a multiresolution analysis.
Article
We characterize the support G of the Fourier transform of the band-limited scaling function and give an approach to the construction of the scaling function. Based on the relations of translates of three point sets G, 12G and G∖12G, we reveal an essential difference of scaling functions corresponding to MRA, weakly translation invariant MRA and tra...
Article
In 2000, Papadakis announced that any orthonormal wavelet must be derived by a generalized frame MRA (GFMRA). In this paper, we give a characterization of GFMRAs which can derive orthonormal wavelets, and show a general approach to the constructions of non–MRA wavelets. Finally we present two examples to illustrate the theory.
Article
Pointwise convergence and uniform convergence for wavelet frame series is a new topic. With the help of band–limited dual wavelet frames, this topic is first researched.

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