Fractional M-Band Wavelets And Research On Image Fusion Algorithms Based On Shearlet Domain

Since wavelet transform possesses excellent characteristics in time domain and frequency domain, they have been playing an important role in engineering and technology as well as image processing. With the expansion of the research object, the wavelet transform also exposes its limitations in some problems. The wavelet analysis is inefficient for processing signals whose energy is not well concentrated in the frequency domain. Secondly, wavelet transform is lack of direction and shift invariant, so it can not be the optimal sparse representation of the image. Combined with time frequency analysis method and fractional Fourier transform, the characteristics of the fractional multi-resolution analysis and fractional M-band orthogonal wavelets are studied in this paper. It is necessary to use the multiscale geometric analysis and theory of shearlet to process pictures, the image fusion algorithm is presented based on the theory of Shearlet domain.Combined with a novel construction method of fractional wavelets, the concept of multi-scale multi-resolution analysis and fractional M-band wavelet are proposed. We provide a construction method for fractional M-band scaling function and wavelet function. It focuses on the properties of fractional M-band orthogonal wavelet. Researching the characteristics of fractional multi-resolution analysis, a sufficient and necessary condition of fractional M-band orthogonal wavelet bases can be given. Finally we describe the decomposition and reconstruction algorithm of fractional M-band wavelet.In order to improve the fusion accuracy of infrared image and multi-focus image, we propose a new image fusion method based on non-subsampled shearlet(NSST) and weighted area feature. Firstly we uses non-subsampled shearlet transform to decompose the source image with different scales and directions, low frequency coefficients and high frequency sub-band coefficients can be obtained. In the low frequency portion, we adopt an improved gradient projection of nonnegative matrix decomposition for low frequency fusion. The fusion strategy of high frequency sub-band coefficients based on combination of weighted area regional energy and variance is proposed. Then we can reconstruct fusion image by using non-sampling shearlets inverse transformation. The experimental results show that this method can well retain the useful information of multiple images from the aspect of subjective vision. The comparison results are given with other fusion methods from the aspect of objective evaluation such as entropy, mulual information and weighted edge information.Finally, in order to improve the accuracy of multi-focus image fusion, combining with good localization and shift invariance of Finite Discrete Shearlet Transform, a new image fusion algorithm based on Finite Discrete Shearlet Transform(FDST)and improved contrast is proposed. Firstly, the registration multi-focus images are decomposed by FDST, and the low frequency sub-band coefficients and high frequency sub-band coefficients of different scales and directions are obtained. The fusion principle of low frequency sub-band coefficients is based on the method of regional average energy matching degree. As for high frequency sub-band coefficients, sum of contrast can be adopted as the fusion rule, which combines with low-frequency coefficients and high- frequency coefficients. Finally,low frequency information and high frequency information are reconstructed to image by Finite Discrete Shearlet Inverse Transform, and both subjective visual evaluation and objective performance assessments of the fusion results are implemented. Simulation results indicate that the proposed algorithm is superior to other fusion algorithms on subjective visual effects and objective evaluation.