Dictionary Update Algorithm in Dictionary-Learning-Based Speech Enhancement

The dictionary update algorithm in dictionary-learning-based speech enhancement is called the Approximate K-SVD algorithm. This algorithm employs a method based on the Orthogonal Matching Pursuit (OMP) algorithm for sparse coding to compute coefficient matrices. The core concept involves an iterative process to update the dictionary, thereby improving speech enhancement performance. The algorithm's fundamental principle represents speech signals as linear combinations of several atoms from the dictionary, achieved through sparse coding computations for the coefficient matrix. Each dictionary update iteration typically involves: 1) fixing the dictionary to compute sparse coefficients using OMP, which sequentially selects the most correlated atoms through greedy iteration; 2) updating dictionary atoms one by while keeping coefficients fixed, using singular value decomposition (SVD) to optimize atom-column pairs. Through progressive dictionary optimization, the algorithm enhances dictionary quality and subsequently improves speech enhancement performance. The implementation requires careful handling of normalization constraints and convergence criteria to ensure stable learning.