## A Filter Bank Approach for Directional Multiresolution Image Representations

#### Minh DoUniversity of Illinois at Urbana-ChampaignElec & Comp Eng

Inspired by the recent results in harmonic analysis and natural scene
statistics, we have sought for new true'' two-dimensional representations
that can deal more effectively with typical images having smooth
contours. Our approach is based on the development of directional and
multiresolution image expansions using non-separable filter banks, in much
the same way that wavelets were constructed from filter banks. The result
is in a new multiresolution, local and directional representation for
images, named contourlets, using iterated multidimensional filter banks.
Contourlets provide a non-separable extension of wavelets and
multiresolution techniques that can capture the directional information --
an important and unique feature of multidimensional signals. The
contourlet transform has been demonstrated to achieve a sparse
representation for typical images with smooth contours. Furthermore, by
utilizing ideas from harmonic analysis, visual perception, computer vision,
and discrete signal processing, we look for a new fruitful interaction
between these fields.

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