2-D DHT-based fast Gabor transform for image processing

The 2-D Gabor transform has been recognized as being useful in diverse areas such as image compression, texture analysis, image segmentation, and image recognition; however, its real time applications have been limited due to the high computational complexity of the traditional 2-D complex-valued discrete Gabor transform (CDGT) algorithms. In this paper, 2-D discrete Hartley transform (DHT)-based real-valued discrete Gabor transform (RDGT) is presented, which can utilize the fast DHT algorithm for fast computation and has a simple relationship with the CDGT such that the 2-D CDGT coefficients can be directly computed from the 2-D DHT-based RDGT coefficients. Due to this simple relationship, the 2-D DHT-based RDGT also offers a faster and more efficient method to compute the 2-D CDGT. In addition, an efficient algorithm for the fast computation of the biorthogonal analysis window given a synthesis window is also presented. The results indicate that the proposed algorithms for the RDGT are attractive for real time image processing.