MATLAB Implementation of Wavelet Denoising with Code Examples

Wavelet denoising is a signal and image processing method based on wavelet transform that effectively separates noise from useful information by analyzing signal characteristics at different scales and directions. In MATLAB implementation, key steps typically include: performing multi-scale wavelet decomposition on the original image using functions like wavedec2 to obtain coefficients across different frequency bands; applying threshold processing to adjust high-frequency coefficients through functions such as wthresh or custom thresholding algorithms to suppress noise components; and finally reconstructing the denoised image using waverec2 or similar reconstruction functions. Traditional soft-thresholding (wthresh(type,'s')) or hard-thresholding methods may lose some detail information during noise removal, while directional wavelets like Dual-Tree Complex Wavelet Transform (implemented via dtcwt2) can better capture edge and texture features through multi-directional decomposition. These advanced wavelets provide more precise discrimination between noise and true signals, thereby improving denoising performance through directional selectivity. In MATLAB, the Wavelet Toolbox offers built-in functions for wavelet decomposition and reconstruction, allowing users to combine them with custom threshold strategies using threshold calculation functions like thselect or bayes/threshold optimization algorithms. For directional wavelets, implementation may require additional toolboxes or custom computational modules for handling complex wavelet transforms. This approach adapts well to different noise types (Gaussian noise, salt-and-pepper noise etc.) and demonstrates excellent performance in preserving image details through adaptive threshold selection algorithms. Wavelet denoising finds applications not only in image processing but also in signal denoising and compressed sensing. The success of the algorithm depends on proper selection of basis functions (db, sym, coif wavelets etc.) and threshold strategies, while MATLAB's flexibility and rich function library facilitate efficient implementation and testing through functions like wden, wdencmp, and custom scripting capabilities for parameter optimization.