Extension of the concept of wavelet to vector functions

Spartak Rafayelyan; Edward Danielian; Jaakko T. Astola; Karen O. Egiazarian

doi:10.1117/12.467999

22 May 2002 Extension of the concept of wavelet to vector functions

Spartak Rafayelyan, Edward Danielian, Jaakko T. Astola, Karen O. Egiazarian

Proceedings Volume 4667, Image Processing: Algorithms and Systems; (2002) https://doi.org/10.1117/12.467999
Event: Electronic Imaging, 2002, San Jose, California, United States

Abstract

Let L_n² equals L² (R) X L² (R) X ... X L² (R)/n. It is shown how to construct a system of functions {(phi) _k (x)} equals {(phi) _k⁽¹) (x), (phi) _k⁽²) (x), ..., (phi) _k⁽ⁿ) (x)} from L_n² which satisfies the following conditions: (1) After normalization it forms a Riesz basis in L_n²; (2) For any given set of functions [f₁(x), f₂(x), ..., f_n(x)] (summation) L_n² the representations f_j(x) equals (Sigma) /k c_k (DOT) (phi) _k^(j) (x), x (summation) R, j equals 1,n, hold, where the coefficients c_k are defined from {(phi) _k (x)} and [f₁(x), f₂(x),..., f_n(x)].

Citation Download Citation

Spartak Rafayelyan, Edward Danielian, Jaakko T. Astola, and Karen O. Egiazarian "Extension of the concept of wavelet to vector functions", Proc. SPIE 4667, Image Processing: Algorithms and Systems, (22 May 2002); https://doi.org/10.1117/12.467999

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KEYWORDS

Wavelets

Commercial off the shelf technology

Electroluminescence

Image processing

Mathematics

Signal processing

Time-frequency analysis

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