Dual-Tree Complex Wavelet Transform and Its Image Denoising Algorithm

In this article, we investigate the dual-tree complex wavelet transform and its applications in image denoising. The dual-tree complex wavelet transform serves as a mathematical tool that analyzes signal frequency and amplitude characteristics, enabling effective feature extraction and noise removal. In image processing applications, this transform is widely employed for denoising through a multi-scale decomposition approach. The algorithm typically involves decomposing the input image into multiple subbands using wavelet filters, followed by applying thresholding techniques (such as soft or hard thresholding) to eliminate noise components while preserving image details and features. From an implementation perspective, key functions would include wavelet decomposition using quadrature mirror filters, subband coefficient thresholding based on noise estimation, and inverse wavelet reconstruction. Furthermore, the dual-tree complex wavelet transform finds additional applications in image compression and feature extraction, making it a versatile tool in computer vision and image processing domains with significant practical value.