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Highly nonlinear approximations for sparse signal representation

稀疏信号表示的高度非线性近似

基本信息

批准号：
EP/D062632/1
负责人：
L Rebollo-Neira
金额：
$ 21.01万
依托单位：
Aston University
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2006
资助国家：
英国
起止时间：
2006 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FD062632%2F1
关键词：
Highly nonlinear approximations sparse signal

项目摘要

The problem of best approximating a target signal by superposition of elementary signals, called atoms, which are drawn from a large and redundant set called dictionary is, in general, a Nonpolynomial (NP)-hard problem. The mathematical methods for signal representation within this framework are referred to as `highly nonlinear approximations'.Such types of signal representations have been proved to be very powerful even when addressed by heuristic algorithms in the line of pursuit approaches, which do not seek for the optimal solution with regard to sparseness. The basic matching pursuit approach, for instance, is used for images, audio and video coding, as well as for biomedical applications. We have recently proposed a number of greedy strategies which significantly improve upon the original matching pursuit approach. Our strategies, effectively implemented by adaptive biorthogonalisation techniques, evolve by stepwise selection of atoms through the following operations:i)Forward steps to increase the number of atoms in the signal decomposition by selecting them one by one from the dictionary.ii)Backward steps for deleting atoms one by one from the signal decomposition and adapting the remaining representation.iii)Swapping operations to interchange atoms in the decomposition with atoms from the dictionary (For more information see http://www.ncrg.aston.ac.uk/Projects/BiOrthog)The success of the techniques evolving by stepwise selection of single atoms motivates the endeavour of designing well founded advanced greedy methodologies evolving by simultaneous selection of multiple atoms. One can certainly envisage the enormous gain in the sparseness of a representation that such technique should be able to produce. The consequent increment in complexity will be compensated by designing algorithms specially devised for parallel implementation. Furthermore, from the information collected by such new techniques it is expected to gather an insight leading to new heuristic methodologies of low complexity.

通过基本信号(称为原子)的叠加来最佳地逼近目标信号的问题通常是一个非多项式(NP)困难的问题，这些基本信号是从称为字典的大而冗余的集合中提取的。在此框架内用于信号表示的数学方法被称为高度非线性近似。这种类型的信号表示已被证明是非常强大的，即使在追逐方法中使用启发式算法时也是如此，这些启发式算法不寻求关于稀疏性的最优解。例如，基本匹配追踪方法用于图像、音频和视频编码以及生物医学应用。我们最近提出了一些贪婪策略，这些策略在最初的匹配追逐方法上有了显着的改进。我们的策略，通过自适应双正交化技术有效地实现，通过通过以下操作逐步选择原子来进化：i)通过从词典逐个选择原子来增加信号分解中的原子数量的前进步骤。ii)用于从信号分解中逐个删除原子并适配剩余表示的反向步骤。iii)交换操作以将分解中的原子与来自词典的原子互换(有关更多信息，参见http://www.ncrg.aston.ac.uk/Projects/BiOrthog)The通过逐步选择单个原子而发展的技术的成功激发了设计通过同时选择多个原子而进化的有根有据的高级贪婪方法的努力。人们当然可以想象，这种技术应该能够产生的表示的稀疏性将带来巨大的收益。随之而来的复杂性增加将通过设计专门为并行实现而设计的算法来补偿。此外，从这些新技术收集的信息中，有望收集导致低复杂性的新启发式方法的洞察力。