Real-valued discrete Gabor transform for image representation

In this paper, we extend the 1-D real valued discrete Gabor transform (RDGT), proposed in our previous work, to the 2-D case for image representation and discuss how to apply the discrete Hartley transform (DHT) to compute the 2-D RDGT coefficients of an image and to reconstruct the original image from the coefficients efficiently. Meanwhile, as in the 1-D case, the 2-D RDGT also bears a simple relationship with the complex valued discrete Gabor transform (CDGT) so that the 2-D CDGT coefficients can be directly obtained from the 2-D RDGT coefficients, Moreover, through experiments, we shall show that the 2-D RDGT coefficients have much more degree of information decorrelation than the 2-D CDGT coefficients because both the magnitudes and the phases of the complex coefficients need to be separately quantized.