4 December 2000 Directional complex-wavelet processing
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Abstract
Poor directional selectivity, a major disadvantage of the separable 2D discrete wavelet transform (DWT), has previously been circumvented either by using highly redundant, nonseparable wavelet transforms or by using restrictive designs to obtain a pair of wavelet trees. In this paper, we demonstrate that superior directional selectivity may be obtained with no redundancy in any separable wavelet transform. We achieve this by projecting the wavelet coefficients to separate approximately the positive and negative frequencies. Subsequent decimation maintains non-redundancy. A novel reconstruction step guarantees perfect reconstruction within this critically- sampled framework. Although our transform generates complex- valued coefficients, it may be implemented with a fast algorithm that uses only real arithmetic. We also explain how redundancy may be judiciously introduced into our transform to benefit certain applications. To demonstrate the efficacy of our projection technique, we show that it achieves state-of-the-art performance in a seismic image- processing application.
© (2000) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Felix Fernandes, Rutger van Spaendonck, Mark J. Coates, C. Sidney Burrus, "Directional complex-wavelet processing", Proc. SPIE 4119, Wavelet Applications in Signal and Image Processing VIII, (4 December 2000); doi: 10.1117/12.408642; https://doi.org/10.1117/12.408642
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