压缩感知中字典学习算法的研究及应用

发布时间：2018-04-13 15:59

本文选题：压缩感知 + 字典学习　；参考：《天津大学》2014年硕士论文

【摘要】：压缩感知理论是近年来提出的一种信号压缩编码理论,它突破了奈奎斯特采样定理的极限,能以随机采样的方式用更少的采样数据优质的恢复出原始信号。信号的稀疏表示是压缩感知理论的基础和前提,因此如何找到合适的稀疏字典,实现信号的最优稀疏表示,成为该领域的重要研究目标。在众多稀疏字典中,基于字典学习的自适应过完备稀疏字典摆脱了固定结构,使得字典中的原子尺度和特性更加接近原始信号本身。然而已有字典学习算法存在耗时过长的问题,因此提高字典学习速度的研究有着重要的意义。近年来,无线多媒体传感器网络中的视频编解码方法得到了越来越多的重视。该领域的研究主要针对两大问题:(1)如何降低编码端的复杂度;(2)如何抵抗信道误码。压缩感知理论在该领域的应用,可以很好的解决上述问题,应用字典学习算法则可提高视频重构精度,因此将压缩感知和字典学习应用于视频编解码中,有很大的应用前景。本文主要包括以下三个研究内容:(1)分析各类稀疏字典的特点,并将其应用于压缩感知理论中,通过实验对字典结构、稀疏表示能力和重构精度等方面做了详细对比;(2)基于字典学习耗时过长的问题,提出了一种改进的字典学习算法IK-SVD,在稀疏表示环节引入了系数复用思想,在字典更新环节对SVD分解方法进行简化,从而减小时间损耗。实验数据表明,该算法将字典学习时间缩短了1/3以上;(3)针对传统编码方式在无线多媒体传感器网络中的局限性,提出了一种基于字典学习的压缩感知视频编解码模型,该模型采用压缩感知理论将计算复杂度从编码端转移到了解码端,字典学习算法的加入实现了视频重构精度的提高。理论分析和仿真实验表明该模型是可行并且有效的。
[Abstract]:Compression sensing theory is a signal compression coding theory proposed in recent years. It breaks through the limit of Nyquist sampling theorem and can recover the original signal with less sampling data by random sampling.Sparse representation of signals is the basis and premise of compressed sensing theory. Therefore, how to find appropriate sparse dictionaries and realize optimal sparse representation of signals has become an important research goal in this field.Among many sparse dictionaries the adaptive overcomplete sparse dictionaries based on dictionary learning get rid of the fixed structure and make the atomic scale and characteristics of the dictionary closer to the original signal itself.However, existing dictionary learning algorithms are time-consuming, so it is very important to improve the speed of dictionary learning.In recent years, more and more attention has been paid to video coding and decoding in wireless multimedia sensor networks.The research in this field focuses on two major problems: 1) how to reduce the complexity of the encoder and how to resist the channel error.The application of compressed perception theory in this field can solve the above problems well. The application of dictionary learning algorithm can improve the accuracy of video reconfiguration. Therefore, the application of compression perception and dictionary learning in video coding and decoding has great application prospects.This paper mainly includes the following three contents: 1) analyzing the characteristics of all kinds of sparse dictionaries, and applying them to the theory of compression perception.In this paper, the sparse representation ability and reconstruction accuracy are compared in detail. Based on the problem of long time consuming in dictionary learning, an improved dictionary learning algorithm, IK-SVD, is proposed, which introduces the idea of coefficient reuse in sparse representation.The SVD decomposition method is simplified in dictionary update to reduce time loss.Experimental data show that the algorithm shortens dictionary learning time by more than one third. Aiming at the limitation of traditional coding methods in wireless multimedia sensor networks, a compressed perceptual video codec model based on dictionary learning is proposed.In this model, the computational complexity is transferred from the coding end to the decoding end using the compression sensing theory, and the precision of video reconstruction is improved with the addition of dictionary learning algorithm.Theoretical analysis and simulation results show that the model is feasible and effective.
【学位授予单位】：天津大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN919.81;TN911.7

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