This paper presents a wavelet transform (WT) based on simultaneous de-noising and compression scheme for noisy signal. Due to the downsampling in decomposition process, the orthogonal wavelet transform (OWT) is translation variant, which significantly hinders its performance in coding and denoising. In this paper the wavelet bintree decomposition (WBD), which is equivalent to a translation invariant WT, is first formed and an optimal downsampling route is then traversed among all the routes of the bintree. The WT with the optimal route would most effectively decorrelate and compactly represent the signal. During the process of noisy signal encoding, wavelet thresholding based denoising is performed. Thresholding is similar to the quantization of a zero-zone in lossy encoding procedure. We applied a signal-adaptive threshold to the wavelet coefficients and quantized the coefficients outside the zero-zone. Experiments show that the proposed scheme significantly outperforms the OWT-based method.