000 04493nam a22005535i 4500
001 978-981-10-3205-9
003 DE-He213
005 20181204134231.0
007 cr nn 008mamaa
008 170202s2016 si | s |||| 0|eng d
020 _a9789811032059
_9978-981-10-3205-9
024 7 _a10.1007/978-981-10-3205-9
_2doi
040 _aISI Library, Kolkata
050 4 _aQA403.5-404.5
072 7 _aPBKF
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBKF
_2thema
082 0 4 _a515.2433
_223
100 1 _aSkopina, Maria.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aMultivariate Wavelet Frames
_h[electronic resource] /
_cby Maria Skopina, Aleksandr Krivoshein, Vladimir Protasov.
264 1 _aSingapore :
_bSpringer Singapore :
_bImprint: Springer,
_c2016.
300 _aXIII, 248 p. 2 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aIndustrial and Applied Mathematics,
_x2364-6837
505 0 _aChapter 1. Bases and Frames in Hilbert Spaces -- Chapter 2. MRA-based Wavelet Bases and Frames -- Chapter 3. Construction of Wavelet Frames -- Chapter 4. Frame-like Wavelet Expansions -- Chapter 5. Symmetric Wavelets -- Chapter 6. Smoothness of Wavelets -- Chapter 7. Special Questions.
520 _aThis book presents a systematic study of multivariate wavelet frames with matrix dilation, in particular, orthogonal and bi-orthogonal bases, which are a special case of frames. Further, it provides algorithmic methods for the construction of dual and tight wavelet frames with a desirable approximation order, namely compactly supported wavelet frames, which are commonly required by engineers. It particularly focuses on methods of constructing them. Wavelet bases and frames are actively used in numerous applications such as audio and graphic signal processing, compression and transmission of information. They are especially useful in image recovery from incomplete observed data due to the redundancy of frame systems. The construction of multivariate wavelet frames, especially bases, with desirable properties remains a challenging problem as although a general scheme of construction is well known, its practical implementation in the multidimensional setting is difficult. Another important feature of wavelet is symmetry. Different kinds of wavelet symmetry are required in various applications, since they preserve linear phase properties and also allow symmetric boundary conditions in wavelet algorithms, which normally deliver better performance. The authors discuss how to provide H-symmetry, where H is an arbitrary symmetry group, for wavelet bases and frames. The book also studies so-called frame-like wavelet systems, which preserve many important properties of frames and can often be used in their place, as well as their approximation properties. The matrix method of computing the regularity of refinable function from the univariate case is extended to multivariate refinement equations with arbitrary dilation matrices. This makes it possible to find the exact values of the Hölder exponent of refinable functions and to make a very refine analysis of their moduli of continuity.
650 0 _aFourier analysis.
650 0 _aFunctional analysis.
650 0 _aMathematics.
650 1 4 _aFourier Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12058
650 2 4 _aFunctional Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12066
650 2 4 _aApplications of Mathematics.
_0http://scigraph.springernature.com/things/product-market-codes/M13003
650 2 4 _aSignal, Image and Speech Processing.
_0http://scigraph.springernature.com/things/product-market-codes/T24051
700 1 _aKrivoshein, Aleksandr.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aProtasov, Vladimir.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9789811032042
776 0 8 _iPrinted edition:
_z9789811032066
776 0 8 _iPrinted edition:
_z9789811098178
830 0 _aIndustrial and Applied Mathematics,
_x2364-6837
856 4 0 _uhttps://doi.org/10.1007/978-981-10-3205-9
912 _aZDB-2-SMA
942 _cEB
950 _aMathematics and Statistics (Springer-11649)
999 _c426665
_d426665