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Image coding with geometric wavelets
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DOI：10.1109/TIP.2006.887727.png)
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Abstract
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This paper describes a new and efficient method for low bit-rate image coding which is based on recent development in the theory of multivariate nonlinear piecewise polynomial approximation. It combines a binary space partition scheme with geometric wavelet (GW) tree approximation so as to efficiently capture curve singularities and provide a sparse representation of the image. The GW method successfully competes with state-of-the-art wavelet methods such as the EZW, SPIHT, and EBCOT algorithms. We report a gain of about 0.4 dB over the SPIHT and EBCOT algorithms at the bit-rate 0.0625 bits-per-pixels (bpp). It also outperforms other recent methods that are based on sparse geometric representation. For example, we report a gain of 0.27 dB over the Bandelets algorithm at 0.1 bpp. Although the algorithm is computationally intensive, its time complexity can be significantely reduced by collecting a global GW n-term approximation to the image from a collection of GW trees, each constructed separately over tiles of the image.
Keywords:
image coding
nonlinear approximation
piecewise polynomial approximation
sparse geometric representations
wavelets and multiresolution processing
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