Real-valued Discrete Gabor Transform And Its Application In Image Compression

Gabor transform can attain optimum localization at spatial and frequency domain, especially that the 2-D Gabor elementary function has properties similar to simple cell receptive field profiles (RFP) in visual cortex of the great majority of mammalians, namely that the RFP of simple cells can be best modeled by 2-D Gabor elementary function, has attracted a lot of theoretical and applicable researches. Therefore, by using the image representation via 2-D Gabor transform, the characteristic of human vision system could be combined with the strategy of image compression encoding efficiently.This dissertation firstly introduces the theory of time-frequency analysis and reviews the development of Gabor transform. Because Gabor transform is nonorthogonal, it is impossible to calculate the Gabor transform coefficients simply through the inner product projection. This makes it very complex to calculate the Gabor transform coefficients and restricts the real-time applications of Gabor transform. In recent years, many approaches have been proposed. Generally, these methods for calculating the Gabor transform coefficients all involve complex operation. In order to simplify the calculation, the theory of real-valued discrete Gabor transform has been proposed by Professor Tao. This dissertation will firstly introduces the traditional complex-valued Gabor transform based on the auxiliary biorthogonal function method presented by Bastiaans, and then discuss the real-valued discrete Gabor transform (RDGT) in detail and its fast algorithms. By replacing the complex-valued Gabor elementary functions of the complex-valued discrete Gabor transform (CDGT) with real-valued Gabor elementary functions, a significant computation of the RDGT can be saved as compared with the computation of the CDGT. The similarity between the RDGT and the discrete Hartley transform (DHT) allows the RDGT to utilize the fast DHT algorithms for fast computation.This dissertation also introduces the 2-D real-valued discrete Gabor transform (2-D RDGT) and its fast algorithm based on 2-D DHT, and applies the 2-D RDGT in image compression. In compression process, we used two different coding methods to select and quantize the transform coefficients:zonal coding and threshold coding. By the comparison of the two coding results, we found that the threshold coding is more adaptive. To measure the compression quality, we also made comparison with DCT transform and wavelet transform, which demonstrates that 2-D RDGT is more attractive in the recovery of image details. We can see that the 2-D RDGT can be well used in many other areas of image processing, such as texture segmentation, feature extraction and identification.