A fast oversampling orthogonal method for the discrete two dimensional S-transform computing

The S-transform provides both the true frequency and globally referenced phase measurements characteristic of the Fourier transform and also generates local spectra, as does the wavelet transform. But the computational requirements of the 2D S-transform have limited its application in digital images processing in time. In order to reduce the processing time and memory requirement, we present a fast oversampling orthogonal method to compute the discrete 2D S-transform. Our method combines Brown´s oversampling method with Drabycz´s orthogonal method and reduces the time and memory consuming dramatically. We calculated the 2D discrete S-transform of the typical 24 bits bmp image in 0.05 seconds and the memory requirement is 8 times of the original image size. 256×256 24 bits bmp image in 0.05 seconds and the memory requirement is 8 times of the original image size.