HYBRID FRACTIONAL FOURIER AND DUAL TREE COMPLEX WAVELET TRANSFORM FOR IMAGE DENOISING

Abstract

Denoising plays an important role in image processing which is used to recover a signal/image that has been corrupted by noise. In this Thesis we have shown various denoising algorithms based on spatial and frequency domain filtering, Discrete Wavelet Transform, Dual Tree Complex Wavelet Transform (DTCWT) and Fractional Fourier Transform (FrFT). Based on the study of various algorithms a new hybrid FrFT and DTCWT algorithm has been proposed. After a thorough study of various denoising techniques, these techniques are then implemented in MATLAB for different types of noises such as Gaussian, Salt and Pepper and Speckle Noise at various noise levels and there simulation results are compared based on Mean Square Error (MSE) criteria and visual interpretation and it has been shown that denoising algorithms depends on the type of noise present in image, hence it is necessary to have prior knowledge about the type of noise present in image so as to select the appropriate denoising algorithm. Combining the advantages of DTCWT and FrFT, a new hybrid algorithm has been proposed and it proves to be best when noise is of Gaussian or Speckle type whereas Median filter proves to be best when noise is of Salt and Pepper type