Analysis of T-Orthogonal greedy algorithm in noisy measurement

Abstract

Abstract We define the Tikhonov Orthogonal Greedy algorithm (T-OGA), a variant of the orthogonal greedy algorithm, to study the recovery of sparse signals from noisy measurements. We establish sufficient conditions for T-OGA to recover sparse signals via restricted isometry property (RIP) inherited from frames. We introduce various concepts such as match matrix, match vector, and residue vector to execute T-OGA. Various technical lemmas have been established to prove our main theorem. In the execution of T-OGA, we employ Tikhonov regularization with regularization parameter λ to solve the minimization problem for the N-sparse solution. In our main result, we proved that if a frame satisfies the RIP of order N + 1 with isometry constant τ and ( τ + λ ) < 1 3 N , then T-OGA can recover every N-sparse signal in the atmost N iterations.