A Study On Constructive Methods For Shearlets And Its Applications In Image Processing

Wavelet transform is a method of multi-resolution analysis.It is a multi-direction and non redundant decomposition,which is widely used in the field of image processing and signal processing and so on.Low frequency subbands and high frequency subbands in three directions that is horizontal,vertical and diagonal directions are obtained by wavelet decomposition.The low frequency subband is the approximation of the source image,including the main energy of the source image,and the high frequency subband contains details of the images in different scales and directions.Wavelet transform is a new mathematical tool,it has good time-frequency analysis ability,as for the high frequency,time domain step length with stepwise refinement is adapted,which focus on any detail of the object,so it is also known as the mathematical microscope.However,the traditional wavelet transform can only capture the horizontal,vertical and diagonal information.It can not be a good representation of the line singularity of the image.There are some limitations in dealing with two-dimensional signals.In this paper,the construction method for finite discrete shear waves by means of fourier transform and time-frequency analysis.A new method for shear wave is provided by constructing several auxiliary functions.Further the shearlets on cone and low frequency are constructed.Finite discrete shearlet transform has good localization and shift invariance.in order to improve the fusion accuracy for multi-focus image and infrared visible image fusion,a new image fusion algorithm based on finite discrete shearlet transform(FDS T)and contrast with image gradient information correlation factor is proposed.Firstly,the registration images are decomposed by FDST.The low frequency sub-band coefficients and high frequency sub-band coefficients being of different scales and directions are obtained.The fusion principle of low frequency sub-band coefficients was implemented on the method of image gradient information correlation factor for weighting.As for the high frequency sub-band coefficients,combining the high frequ-ency and low frequency sub-band coefficients with contrast and using contrast as the criterion for choosing the metric coefficients,can be adopted as the fusion rule.Finally,The low frequency information and high frequency information were reconstructed to image by finite discrete shearlet inverse transform,both subjective visual evaluation and objective performance assessments of the fusion results are implemented.The results indicate that the algorithm is superior to other fusion algorithms on subjective visual effects and objective evaluation.Aiming at the deficiency of the current image fusion process,four different image fusion strategies are proposed.In order to show the effectiveness of the fusion strategy and the superiority for the finite discrete shearlet transform,there are some simulation experiments on multi-focus images and infrared and visible images.Firstly,the fusion results of the same fusion strategy in different transform domains are compared,the wavelet transform used here such as discrete wavelet transform(DWT),nonsubsampled contourlet transform(NSCT),non-subsampled dual tree complex wavelet transform(UDTCWT),non-subsampled shearlet transform(NSST),finite discrete shearlet transform(FDST).Secondly,the fusion results for different fusion strategies in the same transform domain are compared.Finally,the comparison of different fusion algorithms is provided.The test results indicate that the algorithm not only has a good subjective visual effect but also its quality indexes has been increased accordingly compared with other fusion algorithms.It sufficiently shows that the algorithm is superior to other current fusion algorithms.