Research Of The Theory And Application Of Fractioanl Wavelet Transform

Fractional wavelet transform combines the characteristic of fractional fourier transform and wavelet transform, which is determined by its definition. Fractional wavelet transform overcomes the disadvantages of single wavelet transformation. Fractional wavelet transform has flexibility of containing an adjustable order, which leads to better effect in practical application. Nowadays, fractional wavelet transform has been getting more and more widely used.Firstly, the theory of fractional wavelet transform is researched in this thesis and the realization of fractional wavelet transform is introduced. Then, fractional wavelet transform is applied to image processing and its effectiveness and advantage on image processing is verified. In this thesis, fractional wavelet transform is applied to multispectral image and panchromatic image fusion, image defog and image denoising. An algorithm is proposed for each application direction. During the research of these algorithms, we study the choice of optimal decomposition series and optimal fractional order. At the same time, comparing with other algorithms by taking a series of experiments, the effectiveness and advantage of proposed algorithms is verified. In the aspect of image fusion, the advantage of proposed algorithm is balancing definition and spectral fidelity of fused image. We use the method of modifying high-frequency coefficients to improve the definition of fused image and the improvement of spectral fidelity is realized by histogram match. In the aspect of image defog, the algorithm is based on the idea of homomorphic, and its advantage is balancing definition and color fidelity of defogged image. We use contrast limited adaptive histogram equalization to enhance the definition of defogged image, and the color fidelity of defogged image is realized by HSV color model. In the aspect of image denoising, an algorithm of image threshold denoising based on fractional wavelet transform is proposed, we make some improvements on the basis of traditional wavelet threshold denoising method, and the advantage of this algorithm is getting better denoising effect by adjusting fractional order.