Based On Wavelet And Partial Differential Equations In Image Processing

The image is an important way to obtain information,in order to obtain informationmore quickly and easily, the image processing is necessary. Nowdays,the image ismostly storaged by digital, Digital Image Processing is a young interdisciplinary theory,becomes richer and more,widely get a lot of people’s concern and attention.As an information processing tool which has good time-frequency analysis andmulti-resolution analysis capabilities,wavelet analysis plays an important role in thetheory of digital image processing. As a theory which has a long history, Partialdifferential equations and image processing find a meeting point. They have theirrespective advantages, so do some flaws, but these can’t deny that they are powerful.Today, the combination between wavelet analysis and partial differential equations areapplied in image processing is one of the hot. In this paper, we study the waveletanalysis and partial differential equations combination in image denoising, the main jobinclude:(1) Introducing the classical theory of wavelet analysis, including the definition ofthe wavelet, wavelet series, continuous and discrete wavelet transform andmultiresolution analysis. For its application to image denoising, we introduced twoalgorithms---wavelet thresholding and local Wiener filtering, and compared the result oftheir numerical experiments.(2) Studying the evolution of the heat equation and variational problems which arethe theory of partial differential equations in image processing. Understanding the filteriteration and scale space. Having a systematic grasp of partial differential equations inimage processing problems. Numerical experiments to do with the ordinary heatequation algorithm and the PM model algorithm.(3) Investigating in-depth the relationship between wavelet thresholding functionand heat diffusion equation based on understanding the theory of the existing waveletanalysis and partial differential equations.They can be deduced between each other, sowe can get new threshold function and the divergence function,then they will be used indenoising algorithm.Finally,we put forward a new algorithm that using the thermal diffusion to replace the process of reducing wavelet coefficients in the wavelet thresholddenoising.The final results of the numerical experiments show that the combination ofwavelet transform and partial differential equations method is better than use a wayindividually to get results, but not very stable, need continue to research.