Filterbank-based fast parallel algorithms for 2-D DHT-based real-valued discrete Gabor transform

Novel and fast parallel algorithms for the 2-D DHT-based real-valued discrete Gabor transform (RDGT) and its inverse transform are presented based on 2-D filterbanks. A 2-D analysis filterbank is designed for the 2-D RDGT and a 2-D synthesis filterbank is designed for the 2-D inverse RDGT. The parallel channel in each of the two filterbanks has a unified structure and can apply the 2-D fast DHT (discrete Hartley transform) to reduce its computational load. The computational complexity of each parallel channel is very low and is independent of the oversampling rate. The computational complexity of the proposed parallel algorithms is analyzed and compared with that of the existing fastest parallel algorithms for the 2-D RDGT and its inverse transform. The results indicate that the proposed parallel algorithms are attractive for real tune image processing.