Table 13 Bayesian approach seeking dictionary

Alg. 2: Use Bayesian method to find the dictionary D of similar block group

Input: Similar block group \( {\overline{Y}}_n,n=1,2,..N \), K Gaussian distribution {N(μ_k, ∑_k)}K = 1, 2, …, k through GMM leaning.

Output: Gaussian component of similar block group \( {\overline{Y}}_n \) corresponded dictionary D.

Step1. initialization n = 1,k = 1.

Step2. Apply the formula \( \ln P\left(k\left|\overline{Y}\right.=\right)\sum \limits_{m=1}^M\ln N\left({y}_m\left|\overline{0},{\sum}_k\right.\right)-\ln C \) to calculate \( \ln P\left(k\left|\overline{Y}\right.\right) \) when taking the k-th Gaussian component.

Step3. Repeat step 2, total of K times for calculating \( \ln P\left(k\left|\overline{Y}\right.\right) \) values.

Step4. Compare \( \ln P\left(k\left|\overline{Y}\right.\right),k=1,2,\dots, k \), get the maximum \( \ln P\left(k\left|\overline{Y}\right.\right) \), its corresponding Gaussian distribution can describe similar block group Y_n, its covariance matrix is ∑_k.

Step5. For SVD decomposition, get dictionary D_n of similar block group Y_n.

Step6. Repeat steps 2–5, a total of N times, until the output N is a dictionary D.