Wavelet approaches to still image denoising

This paper describes three wavelet-based methods for noise reduction of still images: (i) hyperbolic shrinkage with a level-dependent thresholding policy; (ii) hyperbolic shrinkage with a two-dimensional cross-validation-based thresholding; and (iii) block SVD-wavelet denoising. All three methods make use of hyperbolic shrinkage rather than conventional soft shrinkage. As the thresholding of wavelet coefficients is concerned, at each level of wavelet decomposition, the first method employs a level-dependent universal threshold determined by the coefficient variance and the number of the coefficients at that level; while the second method extends Nason´s (1994) cross-validation approach to the 2-D case. In the third method, an image is divided into several subimages (blocks) and singular value decomposition (SVD) is applied to each block. The singular values obtained are then truncated and each pair of singular vectors are treated as 1-D noisy signals and are denoised using a wavelet-based method. The subimages are then reconstructed using the truncated singular values and denoised singular vectors.