Wavelet Domain Median Filtering Denoising Method

In the field of signal processing, we propose a denoising method based on wavelet domain median filtering. This approach effectively removes both Gaussian white noise and impulse noise by transforming signals into the wavelet domain and applying median filtering within this transformed space. The implementation typically involves three key steps: first, performing wavelet decomposition using functions like wavedec() to obtain detailed coefficients; second, applying median filtering to high-frequency subbands using medfilt1() for 1D signals or medfilt2() for 2D signals; and finally, reconstructing the denoised signal through inverse wavelet transform using waverec(). This method reduces noise interference while preserving signal edges and sharp features, resulting in clearer and more accurate signals. With broad application prospects in practical implementations, this technique can be effectively employed for denoising various signals including audio, images, and video data through appropriate parameter tuning of wavelet types and decomposition levels.