Image Compression Method Based On Partial Differential Equations

Image compression is an important branch of the field of the image processing, which is to reduce redundant information of the image data and to improve the efficiency of the data storage and data transmission. Partial differential equation (PDE) is an important mathematics analysis tool, which has been widely used in image processing techniques, such as image segmentation, filtering and so on. PED-based image compression algorithm has been gradually recognized by researchers. Comparing to traditional algorithms, PDE-based image compression algorithm takes the local information structure into account. The central theme of PDE-based method as follows:take the feature points of the image as the compressed image, fill the missing information of the image by PED-based inpainting algorithm, and get the final restored image. The traditional PDE-base inpainting algorithm just considers the information of the edge and comer of the image, and employs linear diffusion, isotropic nonlinear diffusion or boundary enhance diffusion as the image decompression method. In the thesis, the structure information of the edge and corner of the image is considered, and the crease point is introduced. An improved compressing algorithm is put forwards through considering the combination of the information structure of the feature points above, which can control the compression ratio effectively. Additionally, an improved decompressing introduced can get better restored result.The thesis is organized as follows:Firstly, the information of the edge and corner is analyzed and the crease point is introduced. The information structure of the characteristic points is extracted from the image, and various combinations of the point information are repaired by the improved image inpainting method. Finally, compare the results of the experiments.Secondly, take the feature points obtained as the compressed image, recover it by using linear diffusion, isotropic nonlinear diffusion, edge enhance diffusion, and our improved diffusion, and compare the results.Thirdly, according to the results of the experiments, compression ratio can be controlled effectively by the compression and decompression algorithms proposed in this thesis, meanwhile a better restoration result is received.