Multivariate wavelet frames in various function spaces and their applications

各种函数空间中的多元小波框架及其应用

• 批准号: 228051-2009
• 负责人: Han, Bin
• 金额: $ 1.6万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=503771
• 关键词: Multivariate; wavelet; frames; various; function

With the advance of technology, nowadays we are living in a world which is full of digital data sets such as digital images and videos. In order to process, store, and transmit data efficiently, a mathematical model with desirable properties is in high demand to sparsely and economically represent various types of data sets. In fact, modern information technology is built on many advanced mathematical tools coupled with fast computational algorithms. As a multiscale-based representation simulating the procedure that our human eyes use to analyze images, a wavelet or framelet has proved to be an effective computational tool for sparsely representing a wide range of digital data sets. For example, wavelet-based methods are now standard tools for image compression and signal denoising.

随着技术的进步，我们现在生活在一个充满数字数据集的世界，例如数字图像和视频。为了有效地处理、存储和传输数据，迫切需要一种具有理想特性的数学模型来稀疏且经济地表示各种类型的数据集。事实上，现代信息技术是建立在许多先进的数学工具加上快速计算算法。作为一种模拟人眼分析图像过程的基于多尺度的表示方法，小波或小框架已被证明是一种有效的计算工具，可以稀疏地表示各种数字数据集。例如，基于小波的方法现在是图像压缩和信号去噪的标准工具。