KSVD Decomposition: Dictionary Learning Algorithm for Sparse Representation

KSVD is a dictionary learning algorithm based on sparse representation. The algorithm's name originates from its requirement of multiple iterations (K times), with each iteration employing Singular Value Decomposition (SVD) to refine the dictionary. The primary objective of KSVD is to reconstruct signals from given sparse representations by learning optimal atoms in the dictionary. During each iteration, the algorithm selects one atom and updates its corresponding sparse coefficients through SVD-based optimization. In code implementation, this involves iterating through dictionary columns while fixing other atoms, then applying SVD to minimize representation error for the selected atom's support set. Through repeated iterations and updates, KSVD progressively optimizes both the dictionary and sparse representations, achieving superior signal reconstruction performance. Key implementation aspects include atom-column iteration strategies, error matrix computation for sparse coefficients, and rank-1 approximation via SVD to preserve sparsity constraints.