為了提高數(shù)字水印抗擊各種圖像攻擊的性能和保持圖像的穩(wěn)健性和不可見(jiàn)性，提出了一種基于離散小波變換（DWT），SVD（singular value decomposition）奇異值分解水印圖像和原始載體圖像的離散余弦變換（DCT）的自適應(yīng)水印嵌入算法，主要是將水印圖像的兩次小波變換后的低頻分量潛入到原始圖像分塊經(jīng)過(guò)SVD分解的S分量矩陣中，同時(shí)根據(jù)圖像的JPEG壓縮比的不同計(jì)算各個(gè)圖像塊的水印調(diào)節(jié)因子。實(shí)驗(yàn)證明該算法在抗擊JPEG壓縮、中值濾波、加噪等均具有很好的魯棒性，嵌入后的圖像的PSNR達(dá)到38，具有良好的視覺(jué)掩蔽性
Included are the files wav1.m, wav2.m, wavecoef.mat and readme.
wav2 function implements the tree structured wavelet transform of the input matrix, up to the given level of decomposition. Wav2 uses another function called wav1, which takes the well known wavelet transform of the given matrix. Daubechies wavelet coefficients are used for wavelet transform operation wahich is saved in wavcoeff.mat.
平均因子分解法，適用于正定矩陣First, let s recall the definition of the Cholesky decomposition: Given a symmetric positive definite square matrix X, the Cholesky decomposition of X is the factorization X=U U, where U is the square root matrix of X, and satisfies:
(1) U U = X
(2) U is upper triangular (that is, it has all zeros below the diagonal).
It seems that the assumption of positive definiteness is necessary. Actually, it is "positive definite" which guarantees the existence of such kind of decomposition.
