Underperformance in higher frequency signal regions denoising is a common problem for many denoising methods. Wavelet transforms are, generally, less prone to the problem than the pure spatial or frequency domain transforms, but there is still much room for improvements. In this paper, we propose a point-wise adaptive wavelet transform for signal denoising applications. It is very efficient in denoising higher frequency regions, without compromising the performance on smooth, lower frequency, regions. The transform uses statistical method of intersection of confidence intervals rule to adapt to local signal properties. Its performance was extensively tested on various signal classes. The results proved validity of theoretical assumptions and showed significant performance improvements when compared to other denoising methods.