A Greedy Algorithm that aims to find the sparsest solution (i.e., one with the fewest non-zero entries) to
,
where the full row rank matrix
with
generates an underdetermined system.
The optimization problem is described as:
OMP works by first finding the support:
of the solution, and then solving the least squares problem:
x = OMP(A, y, tolerance)OMP is guaranteed to provide the exact solution (zero tolerance) if this solution exists, and satisfies:
where the mutual coherence measures
the dependence between different columns of the system matrix, and is defined as:
Bruckstein, Alfred M., David L. Donoho, and Michael Elad. "From sparse solutions of systems of equations to sparse modeling of signals and images." SIAM review 51.1 (2009): 34-81.