This paper introduces an adaptive wavelet transform based on the lifting scheme, which is applied to signal denoising. The wavelet representation using orthogonal wavelet bases has received widespread attention. Recently the lifting scheme has been developed for the construction of biorthogonal wavelets in the spatial domain. Wavelet transforms are performed through three stages: the first stage or Lazy wavelet splits the data into two subsets, even and odd, the second stage calculates the wavelet coefficients (highpass) as the failure to interpolate or predict the odd set using the even, and the third stage updates the even set using neighboring odd points (wavelet coefficients) to compute the scaling function coefficients (lowpass). In this paper, we adaptively find some of the prediction coefficients for better representation of signals and this customizes wavelet transforms to provide an efficient framework for denoising. Special care has been given to the boundaries, where we design a set of different prediction coefficients to reduce the prediction error.