Researcher: | William Chen |
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Advisor: | Edward A. Lee |
Sponsors: | NSF Graduate Fellowship and the Ptolemy Project |
Two-dimensional filterbanks have more degrees of freedom than in the one-dimensional case. In two dimensions, the frequency domain is periodic in each dimension. That is, a fundamental tile is replicated to fill or pave the plane. In a critically sampled 2-D filter bank, the subband channels cover the fundamental tile, but do not overlap.
In this project, we apply computational geometry techniques to the design of non-separable analysis/synthesis filterbanks for two-dimensional signals. First, there is no unique way to divide the frequency plane. So, we start our search space by specifying a canonical set of filters with 3-, 4-, 5-, and 6-sided convex passbands. That is, we look for all such triangles, trapezoids, pentagons, and hexagons, and then design the filterbank minimizing phase, amplitude, and aliasing distortion. Using these canonical filterbanks, we can build a tree structure to create more complex and concave geometries. Second, 2-D filterbanks can be designed with either separable or nonseparable filters. While separable filters can be decomposed to a 1-D filter design problem [2], nonseparable filters are often used because they better reflect the property of 2-D signals. Furthermore, nonseparable filters can be designed to have frequency responses that better match a particular class of 2-D signals, e.g. directional sensitivity [3].
Some possible applications of 2-D filterbanks include subband image coding, image enhancement, and image analysis.