An Analysis Dictionary Learning Algorithm under a Noisy Data Model with Orthogonality Constraint

Algorithm 1

OIHT-ADL.

Input: Observed data 𝐘∈𝑅^𝑀×𝐾, the initial dictionary Ω₀∈𝑅^𝑃×𝑀, 𝜆,𝛾,𝛼, the number of iterations 𝑐

Output: Dictionary Ω

Initialization: Set Ω≔ Ω₀

For  𝑡=1,…,𝑐  do

 (i) Fixing Ω, compute Ω𝐘

 (ii) Update the analysis coefficients 𝐙 using (14)

 (iii) Fixing 𝐙, update the dictionary Ω using (16)

 (iv) Normalize rows in Ω using (17)

End