Pseudo-Polar Fourier Transform Theory And Applied Research

Computer technology has been importantly developed in image processing and computer vision field. At present, their application has infiltrated many aspects of life and production. Mathematics always play a decisive role in the development of image processing,, it has infiltrated the various branch of image processing .In this thesis we summarized the Wavelet analysis and Ridgelet theory, we introduced the wavelet transform, the Multi-Resolution Analysis, several common Ridgelet transform and Pseudo-Polar FFT principle, we discussed the computational complexity of Pseudo-Polar fast Fourier transform and the application of Pseudo-Polar fast Fourier transforms.Ridgelet transform can be seen as the wavelet transform in Radon domain. The discrete Radon transform is the key to Ridgelet transform algorithm. Recently, Donoho and others proposed a new Ridgelet transform algorithm, known as Pseudo-Polar FFT. Pseudo-Polar FFT is obtained by the 1D Fractional FFT and the 1D fast Fourier transformation, each has fast algorithm transform. So Pseudo-Polar fast fourier transform can be obtained. However, it is not the true ridgelet transform, we still have to study the conversion from the pseudo-polar Fourier transform to polar Fourier transform. Donoho and others proposed the over-sampling PPFFT algorithm with zero padded to realize the conversion.In this thesis, we propose a new over-sampling algorithm based on zeros padded PPFFT. This algorithm replaces zero padded with the wavelet zero high-frequency amplification image to realize the over-sampling.