Denoising via adaptive lifting schemes

The lifting scheme is an effective method that provides flexible solutions for designing new perfect reconstruction filter bands. However, most of the existing applications of lifting are based upon stationary assumptions. As such, existing schemes tend to fit the data with a single, pre- determined model. These methods do not exploit the full flexibility provided by lifting. By exploiting the temporal interpretation of lifting, we incorporate adaptive filtering with the lifting scheme to cope with signals whose characteristics vary with time. In this paper, we study the proposed adaptive lifting scheme and its ability to decorrelate subbands. The decorrelation behavior is related proposed adaptive lifting scheme and its ability to decorrelate subbands. The decorrelation behavior is related to the coherence between the subbands, and simulations indicate improved decorrelation when compared with deterministic lifting. Our adaptive filterbank may be used in a thresholding scheme that can yield improved noise reduction capabilities compared to conventional wavelet thresholding schemes. We present a condition under which the proposed adaptive lifting denoising scheme can outperform a similar wavelet thresholding. Simulations are presented that indicate there is an SNR value at which the performance of adaptive lifting denoising surpasses wavelet denoising.