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We examine the central issues of invertibility, stability, artifacts, and frequency-domain characteristics in the construction of nonlinear analogs of the wavelet transform. The lifting framework for wavelet construction motivates our analysis and provides new insight into the problem. We describe a new type of nonlinearity for use in constructing nonlinear transforms: a set of linear predictors that are chosen adaptively using a nonlinear selection function. We also describe how earlier families of nonlinear filter banks can be extended through the use of prediction functions operating on a causal neighborhood. We present preliminary results for a synthetic test image.
Signals, Systems & Computers, 1997. Conference Record of the Thirty-First Asilomar Conference on (Volume:1 )
Date of Conference: 2-5 Nov. 1997