Wavelet Construction Theory And Its Applications In Hyperspectral Remote Sensing Image Denoising And Compression

Wavelets achieve good property in both time and frequency resolution, and analyse signals in multiresolution. Therefore, they are widely applied in mathematical theory and image processing. Hyperspectral remote sensing imagery is a newly developed remote sensing technology in recent decades. It can describe ground objects more comprehensively and explicitly. In the process of imaging and transit, hyperspectral remote sensing images are interfered by many complicated factors, which will introduce a lot of noise and affect image analysis. Hence, it is emergent to research denoising algorithms for hyperspectral remote sensing images. The high resolution of hyperspectral remote sensing image achieves by the cost of massive data, which is a great challenge for the transit and storage of hyperspectral data. Hence, compression algorithm with high performance is one of the focuses in the field of hyperspectral image processing. This thesis studies wavelet construction theory and boundary extension algorithm for multi-dimesional wavelet. Wavelet analysis combined with denosing and compression technology for hyperspectral remote sensing image is studied as well.The main work and innovation are embodied as follows.1. Given the shape of an ideal filter, a wavelet filter construction method to approximate the ideal filter is proposed. Firstly, free parameters are determined in the meaning of least square, by minimizing the error between analysis filter and ideal filter. Then a perfect reconstructed general solution for sythesis filter is calculated by Bezout theorem. Finally, the free parameters for sythesis filter can be determined by least square design. In this method, the length of filter and the degree of vanishing moment are taken as free parameters, which can be designed at ease. We prove that the error between the constructed filter and the ideal filter is convergent at an exponential rate as the degree of filter polynomial goes large, and estimate the upper and lower boundaries of the rate.2. Based on a family of quincunx wavelets, a boundary extension method is proposed which can achieve perfect reconstruction at boundaries. That the extension method can achieve perfect reconstruction at boundaries nonexpansionally is proved. This extension method has significant meanings for image compression.3. A wavelet denoising method based on soft threshold function is proposed. The value of soft threshold is estimated by an iterative method. The convergence of this method is proved. The convergence rate is estimated and the computational time is analized. Numerical experiment shows that the algorithm is competitive to the MAD method, and the computational time is much less than MAD method.4. To tackle the denosing problem that the noise level of hyperspectral remote sensing image is relatively low and the noise variance is varying with the spectral bands, a three-dimensional hybrid denoising algorithm in derivative domain is proposed. At first, hyperspectral image is transformed into spectral derivative domain where the subtle noise level is elevated, and the affect of background is eliminated effectively. And then in derivative domain, a wavelet based threshold denoising method BayesShrink algorithm is performed in the two-dimensional spacial domain, and the spectrum is smoothed by Savitzky-Golay filter. At last, the data smoothed in derivative domain is integrated along the spectral axis and corrected for the accumulated errors brought by spectral integration. Experimental results show that the proposed algorithm can reduce the noise efficiently for hyperspectral remote sensing image.5. Hyperspectral image compression algorithms are studied. Two lossless compression algorithms and a lossy compression algorithm are proposed.(i) Considering the significant spectral correlation in adjacent bands of hyperspectral images, a hyperspectral image lossless compression algorithm based on multi-band prediction is proposed. In the process to calculate the multi-band prediction coefficients, the matrix of linear system to solve the prediction coefficients in current band has many components which are the same as the previous band. Therefore, a fast algorithm can be designed which saves computational time for solving prediction coefficients.(ii) A hyperspectral image lossless compression algorithm based on optimal recursive bidirection prediction is proposed. Since the spectral correlation factors in different bands are quite different, two different coding modes are chosen. For the bands whose spectral correlation is significant, using recursive bidirection prediction can achieve excellent compression performance. For the bands whose spectral correlation is not significant, bzip2 algorithm is used instead of spectral prediction. By coding with different modes, satisfactory compression performance is achieved and computational time is saved.(iii) A hyperspectral image compression algorithm based on prediction between bands to remove spectral redundancy and rate pre-allocation is proposed. At first, the standard error of error image of each band is computed by DPCM, and then the rate for SPIHT coding of each band is allocated by the value of the standard error. At last, each band is linear predicted based on minimal square error, and coded via SPIHT algorithm according to the pre-allocated rate. The rate pre-allocation algorithm is reasonable for it makes use of both the information of each band and the correlation between neighboring bands, and achieves ideal compression efficiency.