Nonlinear Wavelet Transforms for Image Coding via Lifting

Nonlinear Wavelet Transforms for
Image Coding via Lifting

Roger Claypoole Geoffrey M. Davis Wim Sweldens Rich Baraniuk

Abstract: We examine the central issues of invertibility, stability, artifacts, and frequency-domain characteristics in the construction of non-linear 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 non-linearity for use in constructing non-linear transforms: a set of linear predictors that are chosen adaptively using a non-linear selection function. We also describe how a previously studied family of non-linear 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.

Status: Submitted to IEEE Transactions on Image Processing, 1999.

Dates:
August 1999: Submitted
September 1999: Posted

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Wim Sweldens <wim@bell-labs.com>