Applications of Sparse Representation, Low Rank Approximation and Dictionary Learning to Image Processing and Pattern Recognition

稀疏表示、低秩逼近和字典学习在图像处理和模式识别中的应用

• 批准号: RGPIN-2015-06254
• 负责人: Bui, Tien
• 金额: $ 1.31万
• 依托单位: Concordia University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=590944
• 关键词: Applications; Sparse; Representation; Low; Rank

Many problems in image processing and pattern recognition can be modeled by using an energy minimization framework in the context of the variational principle. On the other hand there are other approaches to image processing based on partial differential equations (PDEs) and on the theory of multi-resolution analysis. In the last few years, there has been tremendous progress in the development of the multi-resolution analysis, wavelet transforms, directional filtering and sparse representation. Both the energy minimization and the multi-resolution theories have tremendous successes in image processing and related areas. However, there has been little work on the combination of these theories in a mathematically coherent manner. We plan to study models that can take into account both approaches by forming energy functional that contains the texture component represented by filters, and the cartoon-like components represented the boundary curves. Innovative combination of these models with machine learning methods will lead to new powerful techniques for image processing, pattern recognition and computer vision.

图像处理和模式识别中的许多问题可以通过在变分原理的上下文中使用能量最小化框架来建模。另一方面，有其他方法来图像处理的基础上偏微分方程（PDE）和多分辨率分析的理论。近年来，在多分辨率分析、小波变换、方向滤波和稀疏表示等方面取得了巨大的进展。能量最小化和多分辨率理论在图像处理及相关领域都取得了巨大的成功。然而，很少有工作的结合，这些理论在数学上连贯的方式。我们计划研究的模型，可以考虑到这两种方法，形成能量泛函，其中包含的纹理组件表示的过滤器，和卡通般的组件表示的边界曲线。这些模型与机器学习方法的创新结合将为图像处理，模式识别和计算机视觉带来新的强大技术。