报告题目：A Linear Reaction-Diffusion System with Interior Degeneration for Color Image Compression

主 讲 人：哈尔滨工业大学 张达治副教授 博士生导师

报告时间：9月8日（周六）上午10:00--11:00  

报告地点：数理楼221

报告摘要：We considers colorization-based image compression in RGB color space. In compression, we store only the compressed luminance component of the original color image and a few representative pixels extracted from the original color image. In decompression, by explicitly introducing the relation between the luminance component and the original color image into diffusion equations, a linear reaction-diffusion system with Perona-Malik type diffusion coefficient is proposed to reconstruct R, G and B channels simultaneously. The Perona-Malik type diffusion coefficient is a function of the luminance component and leads to interior degenerations, in general. It yields anisotropic smoothing in the restored color image and constrains the geometry of the restored image to follow the geometry of the luminance component. The existence and uniqueness of solutions for the proposed system with a specific class of diffusion coefficients are proved in a weighted Sobolev space. The selection of representative pixels has a big impact on reconstruction results. We also propose a local-optimal strategy that splits the original color image into a series of different size subimages and searches the optimal representative pixel in each subimage. Comparisons with recent colorization-based image compression methods, as well as transform-based JPEG and JPEG2000 standards are performed to show the potential for successful compression applications of the proposed method.

个人简历：张达治，男，1977年2月出生，哈尔滨工业大学数学系，副教授，博士生导师，计算数学研究所副所长，计算数学硕士点负责人，理学院人工智能与数据科学研究中心副主任，黑龙江工业与应用数学学会副秘书长，全国大学生数学建模竞赛黑龙江赛区组委会副秘书长，哈尔滨工业大学数学建模竞赛负责人。主要科研方向：图像处理，偏微分方程数值解，大数据分析与预测，目前已在相关领域发表SCI检索论文20余篇，主持或承担国家级科研项目5项。