Two-dimensional speckle tracking methods have shown great promise in imaging tissue motion and deformations in the vicinity of blood vessels offering the promise of new methods for detecting and staging of vascular disease. However, vessel wall echo reverberations overwhelm the echoes (scattering) from the blood and result in loss of flow information in large regions within the vessel. In this paper, we present a design approach for a time-varying dereverberation inverse filter for echo data within the vessel. The design approach is motivated by the fact that the reverberation pattern varies significantly with the pulsatory motion of the vessel wall. Minute changes in the location/orientation of the vessel wall with respect to the imaging beam result in measurable changes in the speckle-specular echo mixture at the vessel wall and the observed periodicities in the reverberation pattern within the vessel. Therefore, a time-varying inverse filter is necessary to remove the reverberation components appropriately during the heart cycle. A maximum likelihood approach for optimizing the inverse filter parameter is presented. The performance of the dereverberation algorithm is illustrated using pulse-echo data from realtime imaging of the carotid artery of a healthy volunteer.