The definition of analytic signal and the computation algorithm for instantaneous frequencies and instantaneous amplitudes have important significance in signal processing domain.The quaternionic analytic signal is an appropriate extension of 1D analytic signal to 2D case.Whereas

the existing phase definition of quaternionic analytic signal isn't fit for extracting instantaneous frequencies of images.According to the properties of quaternionic analytic signal

a novel phase definition of quaternionic analytic signal is proposed in this paper and two decomposition tools are utilized to test the effectiveness of the definition.The experimental results of synthetic and natural textures indicate that the new definition is more coincident with image intrinsic characters and advantageous for image analytic feature extraction and classification.