Efficient Implementations of Orthogonal Matching Pursuit Based on Inverse Cholesky Factorization

Based on the recently proposed efficient inverse Cholesky factorization, we propose three efficient implementations of Orthogonal Matching Pursuit (OMP), and compare them with the existing implementations of OMP by theoretical and empirical analysis. The proposed implementation 1 theoretically needs the least computational complexity, and is the fastest in the simulations for almost all problem sizes. Among the implementations that store the Gram matrix of the dictionary, the proposed implementation 1 needs the least memories in the k-th iteration (k > 1). As the memory-saving variants of the proposed implementation 1, the proposed implementations 2 and 3 save the memories for the Gram matrix at the expense of higher computational complexity, and in the simulations they are faster than the existing implementations for most problem sizes. With respect to the existing efficient implementation that does not store the Gram matrix, the proposed implementation 2 needs less computational complexity and a little more memories, while the proposed implementation 3 needs the same complexity and less memories.