Access

You are not currently logged in.

Access JSTOR through your library or other institution:

login

Log in through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Journal Article

Multiresolution Approximations and Wavelet Orthonormal Bases of L2(R)

Stephane G. Mallat
Transactions of the American Mathematical Society
Vol. 315, No. 1 (Sep., 1989), pp. 69-87
DOI: 10.2307/2001373
Stable URL: http://www.jstor.org/stable/2001373
Page Count: 19
  • Read Online (Free)
  • Download ($30.00)
  • Subscribe ($19.50)
  • Add to My Lists
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Multiresolution Approximations and Wavelet Orthonormal Bases of L2(R)
Preview not available

Abstract

A multiresolution approximation is a sequence of embedded vector spaces (Vj)j∈ Z for approximating L2(R) functions. We study the properties of a multiresolution approximation and prove that it is characterized by a 2π-periodic function which is further described. From any multiresolution approximation, we can derive a function ψ(x) called a wavelet such that $(\sqrt{2^j}\pi(2^jx - k))_{(k,j)\in Z^2}$ is an orthonormal basis of L2(R). This provides a new approach for understanding and computing wavelet orthonormal bases. Finally, we characterize the asymptotic decay rate of multiresolution approximation errors for functions in a Sobolev space Hs.

Page Thumbnails

  • Thumbnail: Page 
69
    69
  • Thumbnail: Page 
70
    70
  • Thumbnail: Page 
71
    71
  • Thumbnail: Page 
72
    72
  • Thumbnail: Page 
73
    73
  • Thumbnail: Page 
74
    74
  • Thumbnail: Page 
75
    75
  • Thumbnail: Page 
76
    76
  • Thumbnail: Page 
77
    77
  • Thumbnail: Page 
78
    78
  • Thumbnail: Page 
79
    79
  • Thumbnail: Page 
80
    80
  • Thumbnail: Page 
81
    81
  • Thumbnail: Page 
82
    82
  • Thumbnail: Page 
83
    83
  • Thumbnail: Page 
84
    84
  • Thumbnail: Page 
85
    85
  • Thumbnail: Page 
86
    86
  • Thumbnail: Page 
87
    87