Image Processing Based On Fractional Wavelet Transform

Image denoising and image fusion have always been hot issues in the field of digital image processing.In recent years,fractional wavelet transform has become a new signal processing method.Its definition is based on wavelet transform and fractional Fourier transform.It extends multi-resolution analysis to time-fractional frequency domain and becomes a new time-frequency domain analysis method.Therefore,the application of fractional wavelet transform to image denoising and image fusion has a very broad development prospect.The main research work of this paper is as follows:(1)Image denoisingTraditional threshold function denoising is mainly hard threshold function denoising and soft threshold function denoising,but these threshold functions are discontinuous or continuous but not smooth at the threshold point.Therefore,a fractional wavelet image denoising method based on improved threshold function is proposed in this paper.First,the noise signal is decomposed by the fractional wavelet transform,then the coefficients in the fractional wavelet domain of each layer are processed by the improved threshold function,and finally the denoised signal is obtained by the reconstruction of the processed coefficients.The simulation results show that compared with the existing soft threshold and hard threshold methods,the proposed method has a larger SNR and smaller MSE after denoising,and a satisfactory visual effect is obtained.It is a practical denoising method.(2)Image fusionWith the rapid development of image acquisition technology,the requirements of modern image processing system for image fusion are increasing.In order to solve the problem of image blurring caused by different focal points of multi-focus images,this paper proposes a multi-focus image fusion method based on fractional wavelet and improved fusion rules.Firstly,two source images A and B are input,and the source images are decomposed into high frequency and low frequency coefficients by using discrete fractional wavelet transform.Secondly,due to the different characteristics of each coefficients,the local regional gradient information criterion was selected as the low frequency fusion rule,and the neighborhood variance weighted average criterion was selected as the high frequency fusion rule to obtain the fusion coefficients.Finally,the fusion image is obtained by inverse fractional wavelet transform.Experimental results show that the proposed method is effective and superior in both visual quality and quantitative evaluation.