Image Denoising: A Critical Component in Image Processing

Image denoising stands as a fundamentally important component in the field of image processing. During the denoising process, engineers frequently face the challenge of balancing noise suppression with the preservation of crucial image details. Wavelet transform has proven to be an extremely valuable signal processing tool, achieving remarkable success in signal denoising applications. In traditional orthogonal wavelet transform-based denoising methods, reconstructed images often exhibit oscillatory artifacts near edge regions, resulting in edge distortion. Furthermore, under conditions of significant noise contamination, these methods tend to produce blurred edge effects. The implementation typically involves thresholding wavelet coefficients using algorithms like VisuShrink or SureShrink, where hard or soft thresholding functions are applied to the transformed coefficients before reconstruction. However, by employing redundant wavelet transforms (also known as stationary or undecimated wavelet transforms), we can effectively overcome the limitations inherent in orthogonal wavelet denoising approaches. Redundant wavelet transform maintains translation invariance by eliminating the downsampling operation, which allows for more accurate edge preservation and reduced artifacts. This enhancement leads to substantial improvements in denoising algorithm performance, particularly in preserving fine details and structural information while effectively removing noise components. The implementation typically involves applying the same filters at each scale without decimation, followed by coefficient thresholding and reconstruction through averaging all shifted versions.