Strong convergence of alternated inertial CQ relaxed method with application in signal recovery

This article proposes a strong convergence CQ relaxed iterative method with alternated inertial extrapolation step in a real Hilbert space. The propose method converges strongly under some suitable and easy to verify assumptions. Moreover, the proposed method does not require the prior knowledge of the operator norm or estimate of the matrix norm. Instead, the stepsize is self-adaptive with a simple selection procedure that does not involve any linesearch procedure. Numerical experiments to illustrate the computational performance together with implementation of the proposed method in signal recovery application is presented. Additionally, comparison of the method with some existing iterative methods in the literature is performed.