Gabor Atomic Decomposition Using OMP Algorithm

The Orthogonal Matching Pursuit (OMP) algorithm is an efficient signal decomposition method particularly suitable for sparse representation problems. Compared to the traditional Matching Pursuit (MP) algorithm, OMP significantly improves decomposition speed and accuracy by introducing an orthogonalization step. In implementation, OMP typically involves iteratively selecting the atom that has the highest correlation with the current residual signal, followed by orthogonal projection to update the residual.

In Gabor atomic decomposition, the OMP algorithm rapidly matches optimal atoms and obtains high-precision decomposition results through iterative residual signal optimization. The key advantage of OMP lies in its orthogonalization processing of selected atoms after each iteration, which avoids redundant computations commonly occurring in MP algorithms and substantially enhances computational efficiency. Code implementation typically involves maintaining an active set of atoms and solving least squares problems at each iteration to update coefficients.

In practical applications, the OMP algorithm demonstrates excellent performance in signal denoising and feature extraction. Particularly when processing non-stationary signals, Gabor atomic decomposition combined with OMP can better capture time-frequency characteristics. Compared to MP algorithms, OMP not only converges faster but also produces sparser decomposition coefficients, resulting in superior signal reconstruction quality. The algorithm's efficiency can be further optimized through techniques like precomputed dictionaries and optimized matrix operations.