Tight Wavelet Frames for Data Compression

研究者和他的同事研究了如何使用紧小波框架进行图像/数据压缩的问题。他们把这个问题与压缩感知、密码学、纠错码、丢失数据的修补和恢复、量化展开的一致性恢复等许多有用的等价问题联系起来，从而可以借用等价问题的思想和数学方法来研究基于紧小波框架的图像/数据压缩。他们将使用虚拟组件方法、有限状态机、正交贪婪算法的新变体、p在0和1之间的lp优化以及谐波帧来解决数据压缩问题。初步结果表明，它们非常有前途。所提出的研究的一个最终目标是建立灵活的方法来构造多元紧小波框架所需的属性数据压缩，并使它们可用于应用程序。图像和数据压缩是互联网、多媒体通信和数据存储/传输必不可少的。15年前，FBI建立了一个标准，使用小波函数压缩所有指纹进行存储和处理。紧小波框架的构造比正交小波函数更灵活。研究人员和他的同事将研究如何使用紧小波框架进行图像和数据压缩。预期的科学结果将使人们能够更好地理解如何在冗余线性系统中找到最稀疏的数据表示。其结果将直接影响到现代设计的通信系统，如移动的电话，数码相机，数字广播以及多媒体数据的紧凑表示的方法。

The investigator and his colleague study the problem how to use tight wavelet frames for image/data compression. They have related the problem to many useful equivalent problems such as compressed sensing, cryptography, error correcting codes, in-painting or recovery of lost data, and consistent recovery from quantized expansions so that the ideas and mathematical techniques from the equivalent problems can be borrowed to study the image/data compression based on tight wavelet frames. They will use the method of virtual components, finite state machine, new variations of orthogonal greedy algorithm, lp optimization with p between 0 and 1, and harmonic frames to tackle the data compression problem. Preliminary results show that they are very promising. An ultimate goal of the proposed research is to build flexible methods for constructing multivariate tight wavelet frames with required properties for data compression and make them available for applications. Images and data compression is absolutely necessary for internet, multimedia communication, and data storage/transmission. Fifteen years ago, FBI established a standard using a wavelet function to compress all finger prints for storage and processing. Tight wavelet frames are more flexible to construct than orthonormal wavelet functions. The investigator and his colleague will study how to use tight wavelet frames for image and data compression. The expected scientific results will enable better understanding how to find the most sparse representation of data in redundant linear systems. The results will have immediate impact on the modern design of communication systems like mobile telephony, digital camera, and digital broadcasting as well as on the methods of multimedia data compact representation.