Tight Wavelet Frames for Data Compression

研究者和他的同事研究了如何使用小波帧进行图像/数据压缩的问题。他们将该问题与许多有用的等价问题联系起来，如压缩感知、密码学、纠错码、丢失数据的绘制或恢复，以及量化展开的一致恢复，以便从等价问题中借鉴思想和数学技术来研究基于紧密小波帧的图像/数据压缩。他们将使用虚拟分量方法、有限状态机、正交贪心算法的新变体、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。本研究的最终目标是建立灵活的方法来构造具有数据压缩所需属性的多元紧小波帧，并使其可用于应用。图像和数据压缩对于互联网、多媒体通信和数据存储/传输是绝对必要的。15年前，联邦调查局建立了一个标准，使用小波函数压缩所有指纹以进行存储和处理。紧小波框架比标准正交小波函数构造更灵活。研究者和他的同事将研究如何使用紧小波帧进行图像和数据压缩。预期的科学结果将有助于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。研究结果将对移动电话、数码相机、数字广播等现代通信系统的设计以及多媒体数据压缩表示方法产生直接影响。

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.