Stability and Robustness of Weak Orthogonal Matching Pursuits

A recent result establishing, under restricted isometry conditions, the success of sparse recovery via orthogonal matching pursuit using a number of iterations proportional to the sparsity level is extended to weak orthogonal matching pursuits. The new result also applies to a pure orthogonal matching pursuit, where the index appended to the support at each iteration is chosen to maximize the subsequent decrease of the squared norm of the residual vector.