Compressed sensing (CS) is a pioneering sub-Nyquist sampling technique that reconstructs signals from far fewer measurements than traditional acquisition schemes. Considerable amount of research has been carried out over the years to develop powerful algorithms that can accomplish optimal recovery. However, they vary considerably in their ease of implementation, speed of recovery and noise resilience. This work presents the Sparsity Independent Regularized Pursuit (SIRP) which achieves an admirable trade-off between these key features. Further, it requires no prior knowledge of exact sparsity level and possesses a regular structure, making it amenable to low cost hardware solutions. Experimental investigations reveal the competitiveness of SIRP with existing state-of-art in regard to successful recovery and significant speed-up. The algorithm also attains superior results on a considerably large image recovery problem, which demonstrates its suitability to real world applications.