Image compression by rectangular wavelet transform

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dc.creatorZavadsky, Vyacheslav
dc.date2004-06-04
dc.date.accessioned2026-07-07T03:21:24Z
dc.date.available2026-07-07T03:21:24Z
dc.descriptionWe study image compression by a separable wavelet basis $\big\{ψ(2^{k_1}x-i)ψ(2^{k_2}y-j),$ $ϕ(x-i)ψ(2^{k_2}y-j),$ $ψ(2^{k_1}(x-i)ϕ(y-j),$ $ϕ(x-i)ϕ(y-i)\big\},$ where $k_1, k_2 \in \mathbb{Z}_+$; $i,j\in\mathbb{Z}$; and $ϕ,ψ$ are elements of a standard biorthogonal wavelet basis in $L_2(\mathbb{R})$. Because $k_1\ne k_2$, the supports of the basis elements are rectangles, and the corresponding transform is known as the {\em rectangular wavelet transform}. We prove that if one-dimensional wavelet basis has $M$ dual vanishing moments then the rate of approximation by $N$ coefficients of rectangular wavelet transform is $\mathcal{O}(N^{-M}\log^C N)$ for functions with mixed derivative of order $M$ in each direction. The square wavelet transform yields the approximation rate is $\mathcal{O}(N^{-M/2})$ for functions with all derivatives of the total order $M$. Thus, the rectangular wavelet transform can outperform the square one if an image has a mixed derivative. We provide experimental comparison of image compression which shows that rectangular wavelet transform outperform the square one.
dc.identifierhttps://arxiv.org/abs/cs/0406008
dc.identifierhttp://arxiv.org/abs/cs/0406008
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/32184
dc.subjectComputer Vision and Pattern Recognition
dc.titleImage compression by rectangular wavelet transform
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