针对信号编码纠错的框架理论研究

发布时间：2018-04-28 13:49

本文选题：框架 + 编码　；参考：《电子科技大学》2014年硕士论文

【摘要】：在信号传输和重构过程中,由数据丢失和量化等原因引起的误差是不可避免的。基于框架编码的使用能够很好的解决这一类问题。框架最吸引人的性质是它的冗余性,它在应用中至少有两个优点:第一,使得框架及对偶框架的构造灵活;第二,在信号传输中发生数据丢失可以加强数据的鲁棒性。根据这一性质,本文主要研究了包含量化噪音的最优对偶框架的选择问题;另外针对融合框架在数据传输中的应用,我们研究了融合框架的局域对偶框架构造其对偶框架系。针对信号在传输过程中的数据丢失问题,利用框架的冗余性可以使信号完全重构,如果无法完全重构则可以通过选择适当框架尽量减少重构误差。本文针对信号传输过程中数据丢失问题研究了新的量化噪音模型下使得信号重构误差最小的最优对偶框架,获得了正则对偶框架是唯一最优对偶框架的充分必要条件。当编码框架是紧框架时,我们给出正则对偶框架是最优对偶框架的充分必要条件。结合实际应用,当我们知道丢失数据个数为1,但是不知道具体哪一个数据丢失时用均方差的平均值(______1MSE)代替均方差(1MSE)。当编码框架是均匀紧框架时,我们获得正则对偶框架不是最优对偶框架的充分条件。通过一个具体计算框架的最优对偶框架的实例,比较灰度图像在不同对偶框架解码下的重构效果,我们知道量化噪音模型下的最优对偶框架的重构误差是最小的。高能物理实验中数据传输是很重要的一个部分,利用融合框架编码传输的数据能够提高数据传输的效率。针对这一应用,研究了Hilbert空间中满足一定条件下的融合框架。通过融合框架系的融合框架算子的矩阵表示,给出用局域对偶框架构造对偶框架系的算法。在高能物理实验中用这个对偶框架系解码。最后给出仿真实例展示研究结果的实用性和有效性。
[Abstract]:In the process of signal transmission and reconstruction, errors caused by data loss and quantization are inevitable. The use of frame coding can solve this kind of problem well. The most attractive property of the framework is its redundancy, which has at least two advantages in application: first, it makes the framework and dual frame structure flexible; second, data loss in signal transmission can enhance the robustness of data. According to this property, this paper mainly studies the selection of the optimal dual frame containing quantized noise, and for the application of the fusion framework in data transmission, we study the local dual frame of the fusion framework to construct its dual frame system. Aiming at the problem of data loss in the process of signal transmission, the redundancy of the frame can make the signal completely reconfigurable, and if the frame can not be completely reconstructed, the reconstruction error can be reduced by selecting the appropriate frame as far as possible. In this paper, we study the optimal dual frame with minimum signal reconstruction error in a new quantized noise model for data loss during signal transmission, and obtain the necessary and sufficient conditions for the regular dual frame to be the unique optimal dual frame. When the coding frame is compact, we give a necessary and sufficient condition for the regular dual frame to be the optimal dual frame. Combined with practical application, when we know that the number of lost data is 1, but we do not know which data is lost, we use the average of the mean square deviation (MSE) to replace the mean square error (MSE). When the coded frame is uniformly compact, we obtain a sufficient condition that the regular dual frame is not the optimal dual frame. Through an example of calculating the optimal dual frame of the frame, we compare the reconstruction effect of the gray image under different dual frames. We know that the reconstruction error of the optimal dual frame under the quantization noise model is the smallest. Data transmission is a very important part in high energy physics experiment. The efficiency of data transmission can be improved by using fusion frame coding to transmit data. In view of this application, the fusion framework in Hilbert space under certain conditions is studied. Based on the matrix representation of the fusion frame operator of the fusion frame system, an algorithm for constructing dual frame system using locally dual frames is presented. In high energy physics experiments, this dual frame is used to decode. Finally, a simulation example is given to demonstrate the practicability and effectiveness of the research results.
【学位授予单位】：电子科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN911.22

【共引文献】