Noisy signal compression based on optimal search in wavelet bintree

This paper presents a wavelet based simultaneous de-noising and compression scheme for noisy signals. The orthogonal wavelet transform (OWT), used in the traditional signal coding and denoising, is translation variant, which hinders its performance in the signal processing. It is also interesting if an optimal waveform can be selected from a family of wavelet bases to best transform a set of functions for efficient compression. In this paper the wavelet bintree decomposition (WBD), a translation invariant transform, is proposed and an optimal family of wavelet bases is selected. The bases better de-correlate the input signal than the OWT and represent the signal compactly. Wavelet thresholding is then applied on wavelet coefficients for denoising. Thresholding is similar to the quantizing of a zero-zone in a lossy encoding procedure. In this paper a signal adaptive nearly optimal threshold is computed for denoising and the wavelet coefficients after the thresholding are quantized for compression. Experiments show that the presented encoding scheme outperforms the OWT-based method.