Over the last decade perceptually based image compression has gained significant importance. This is because it relies on Human Visual Perception (HVP) in measuring the reconstruction quality in the compression process, as humans are the end users for images. Visual data that is perceived by humans can be characterized in terms of three parameters, Magnitude, Phase and Orientation of the spatial frequency content. While existing perceptually based image compression techniques exploits the first parameter, the novel contribution of this paper is its focus on the use of phase data for perceptually based texture compression. In this paper a HVS based texture characterization approach is applied to measure the perceived (by humans) phase coherence in the image. Then images are more compressed after removing the unperceived phase redundancy. Finally subjective tests are performed to measure the reconstruction quality of the proposed compression approach. The proposed compression algorithm has been applied in the JPEG2000 framework. Simulation results that demonstrate the efficiency of the proposed approach are presented.