Detailed imaging of blood flow may improve the understanding of brain functions. The state-of-the-art non-invasive flow imaging of the brain is limited to a one-dimensional Doppler setting. We propose a method to estimate the two-dimensional flow vector in the fine vascular network of the brain by using a speckle tracking technique. The framework of Orthogonal Matching Pursuit is used for speckle tracking and modified to include prior constraints to guide the matching process among two frames, called as Guided Orthogonal Matching Pursuit. Prior constraint is in the form of a directional constraint which determines the probability of vector flow in all the directions according to the orientation of the vessels. The orientation of the vessels is computed using Power Doppler Imaging. In this work, the proposed method for two-dimensional vector estimation is compared with the standard block matching technique of Normalized Cross-Correlation. We see that the variance of the final velocity estimates has reduced when compared to the standard speckle tracking method and the direction of blood flow is found within the curvature of the vessel.