The emerging theory of compressive sensing (CS) provides a new sparse signal processing paradigm for reconstructing sparse signals from the undersampled linear measurements. Recently, numerous algorithms have been developed to solve convex optimization problems for CS sparse signal recovery. However, in some certain circumstances, greedy algorithms exhibit superior performance than convex methods. This paper is a followup to the recent paper of Wang and Yin (2010), who refine BP reconstructions via iterative support detection (ISD). The heuristic idea of ISD was applied to greedy algorithms. We developed two approaches for accelerating the ECME iteration. The described algorithms, named ECME thresholding pursuits (EMTP), introduced two greedy strategies that each iteration detects a support set I by thresholding the result of the ECME iteration and estimates the reconstructed signal by solving a truncated least‐squares problem on the support set I. Two effective support detection strategies are devised for the sparse signals with components having a fast decaying distribution of nonzero components. The experimental studies are presented to demonstrate that EMTP offers an appealing alternative to state‐of‐the‐art algorithms for sparse signal recovery.