LEADER 04891nam 22007215 450 001 9910163081703321 005 20220330191458.0 010 $a981-10-3205-X 024 7 $a10.1007/978-981-10-3205-9 035 $a(CKB)3710000001045767 035 $a(MiAaPQ)EBC4799563 035 $a(DE-He213)978-981-10-3205-9 035 $a(PPN)198866860 035 $a(EXLCZ)993710000001045767 100 $a20170202d2016 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aMultivariate wavelet frames$b[electronic resource] /$fby Maria Skopina, Aleksandr Krivoshein, Vladimir Protasov 205 $a1st ed. 2016. 210 1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2016. 215 $a1 online resource (258 pages) 225 1 $aIndustrial and Applied Mathematics,$x2364-6837 311 $a981-10-3204-1 320 $aIncludes bibliographical references and index. 327 $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. 330 $aThis book presents a systematic study of multivariate wavelet frames with matrix dilation, in particular, orthogonal and bi-orthogonal bases, which are a special case of frames. Further, it provides algorithmic methods for the construction of dual and tight wavelet frames with a desirable approximation order, namely compactly supported wavelet frames, which are commonly required by engineers. It particularly focuses on methods of constructing them. Wavelet bases and frames are actively used in numerous applications such as audio and graphic signal processing, compression and transmission of information. They are especially useful in image recovery from incomplete observed data due to the redundancy of frame systems. The construction of multivariate wavelet frames, especially bases, with desirable properties remains a challenging problem as although a general scheme of construction is well known, its practical implementation in the multidimensional setting is difficult. Another important feature of wavelet is symmetry. Different kinds of wavelet symmetry are required in various applications, since they preserve linear phase properties and also allow symmetric boundary conditions in wavelet algorithms, which normally deliver better performance. The authors discuss how to provide H-symmetry, where H is an arbitrary symmetry group, for wavelet bases and frames. The book also studies so-called frame-like wavelet systems, which preserve many important properties of frames and can often be used in their place, as well as their approximation properties. The matrix method of computing the regularity of refinable function from the univariate case is extended to multivariate refinement equations with arbitrary dilation matrices. This makes it possible to find the exact values of the Hölder exponent of refinable functions and to make a very refine analysis of their moduli of continuity. 410 0$aIndustrial and Applied Mathematics,$x2364-6837 606 $aFourier analysis 606 $aFunctional analysis 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aSignal processing 606 $aImage processing 606 $aSpeech processing systems 606 $aFourier Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12058 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aApplications of Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M13003 606 $aSignal, Image and Speech Processing$3https://scigraph.springernature.com/ontologies/product-market-codes/T24051 615 0$aFourier analysis. 615 0$aFunctional analysis. 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 0$aSignal processing. 615 0$aImage processing. 615 0$aSpeech processing systems. 615 14$aFourier Analysis. 615 24$aFunctional Analysis. 615 24$aApplications of Mathematics. 615 24$aSignal, Image and Speech Processing. 676 $a515.2433 700 $aSkopina$b Maria$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755992 702 $aKrivoshein$b Aleksandr$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aProtasov$b Vladimir$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910163081703321 996 $aMultivariate Wavelet Frames$92129507 997 $aUNINA