Implementation of Three Denoising Algorithms: BLS-GSM, BM3D, and NLM

Image denoising is a crucial and common problem in image processing, aiming to recover clean original images from noisy inputs. BLS-GSM, BM3D, and NLM are three classical image denoising algorithms, each with unique features applicable to different noise scenarios. BLS-GSM (Bayesian Least Squares - Gaussian Scale Mixture) is a wavelet-based denoising method. It assumes that image coefficients in the wavelet domain follow a Gaussian scale mixture distribution and employs Bayesian estimation theory to model and remove noise. This algorithm is particularly effective for additive white Gaussian noise. In implementation, the method typically involves wavelet decomposition, statistical modeling of coefficients, and Bayesian shrinkage estimation. BM3D (Block-Matching 3D) is an efficient denoising algorithm based on block matching and collaborative filtering. The core concept involves searching for similar image blocks, stacking them into 3D arrays, and performing filtering in the transform domain. BM3D effectively suppresses noise while preserving image details, demonstrating excellent performance against both Gaussian and salt-and-pepper noise. The algorithm implementation generally includes block grouping, 3D transformation, thresholding, and inverse transformation steps. NLM (Non-Local Means) is a non-local averaging denoising method that leverages self-similarity in images by computing weighted averages of pixel neighborhoods. Unlike traditional local filtering approaches, NLM searches for similar structures across larger image regions, better preserving texture and edge information. The implementation typically involves calculating similarity weights between patches and performing weighted averaging operations. When evaluating denoising performance, PSNR (Peak Signal-to-Noise Ratio) and SSIM (Structural Similarity Index) are two commonly used metrics. PSNR measures noise suppression effectiveness by calculating the mean squared error between denoised and original images, where higher values indicate better quality. SSIM focuses more on structural information, providing a more accurate reflection of perceptual image quality differences. These three algorithms each have strengths and limitations: BLS-GSM is suitable for wavelet-domain denoising, BM3D excels in high-noise environments, while NLM performs better on texture-rich images. Selecting the appropriate denoising algorithm requires consideration of specific noise types and image characteristics.