Filter banks with nonlinear lifting steps for lossless image compression

Most natural images are well modeled as smoothed areas segmented by edges. The smooth areas can be well represented by a wavelet transform with high regularity and with fewer coefficients which requires highpass filters with some vanishing moments. However for the regions around edges, short highpass filters are preferable. In one recently proposed approach, this problem was solved by switching filter banks using longer filters for smoothed areas of the images and shorter filters for areas with edges [1]. This approach was applied to lossy image coding resulting in a reduction of ringing artifacts. As edges were predicted using neighboring pixels, the nonlinear transforms made the decorrelation more flexible. In this paper we propose a time-varying filterbank and apply it to lossless image coding. In this scheme, we estimate the standard deviation of the neighboring pixels of the current pixel by solving the maximum likelihood problem. The filterbank is switched between three filter banks, depending on the estimated standard deviation.