發(fā)布時間：2018-04-28 13:49

  本文選題：框架 + 編碼��； 參考：《電子科技大學(xué)》2014年碩士論文

【摘要】：在信號傳輸和重構(gòu)過程中,由數(shù)據(jù)丟失和量化等原因引起的誤差是不可避免的�；诳蚣芫幋a的使用能夠很好的解決這一類問題�？蚣茏钗说男再|(zhì)是它的冗余性,它在應(yīng)用中至少有兩個優(yōu)點:第一,使得框架及對偶框架的構(gòu)造靈活;第二,在信號傳輸中發(fā)生數(shù)據(jù)丟失可以加強數(shù)據(jù)的魯棒性。根據(jù)這一性質(zhì),本文主要研究了包含量化噪音的最優(yōu)對偶框架的選擇問題;另外針對融合框架在數(shù)據(jù)傳輸中的應(yīng)用,我們研究了融合框架的局域?qū)ε伎蚣軜?gòu)造其對偶框架系。針對信號在傳輸過程中的數(shù)據(jù)丟失問題,利用框架的冗余性可以使信號完全重構(gòu),如果無法完全重構(gòu)則可以通過選擇適當(dāng)框架盡量減少重構(gòu)誤差。本文針對信號傳輸過程中數(shù)據(jù)丟失問題研究了新的量化噪音模型下使得信號重構(gòu)誤差最小的最優(yōu)對偶框架,獲得了正則對偶框架是唯一最優(yōu)對偶框架的充分必要條件。當(dāng)編碼框架是緊框架時,我們給出正則對偶框架是最優(yōu)對偶框架的充分必要條件。結(jié)合實際應(yīng)用,當(dāng)我們知道丟失數(shù)據(jù)個數(shù)為1,但是不知道具體哪一個數(shù)據(jù)丟失時用均方差的平均值(______1MSE)代替均方差(1MSE)。當(dāng)編碼框架是均勻緊框架時,我們獲得正則對偶框架不是最優(yōu)對偶框架的充分條件。通過一個具體計算框架的最優(yōu)對偶框架的實例,比較灰度圖像在不同對偶框架解碼下的重構(gòu)效果,我們知道量化噪音模型下的最優(yōu)對偶框架的重構(gòu)誤差是最小的。高能物理實驗中數(shù)據(jù)傳輸是很重要的一個部分,利用融合框架編碼傳輸?shù)臄?shù)據(jù)能夠提高數(shù)據(jù)傳輸?shù)男�。針對這一應(yīng)用,研究了Hilbert空間中滿足一定條件下的融合框架。通過融合框架系的融合框架算子的矩陣表示,給出用局域?qū)ε伎蚣軜?gòu)造對偶框架系的算法。在高能物理實驗中用這個對偶框架系解碼。最后給出仿真實例展示研究結(jié)果的實用性和有效性。
[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.
【學(xué)位授予單位】：電子科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：TN911.22

【共引文獻】

相關(guān)碩士學(xué)位論文 前1條

1 段小明;基于小波配點法的偏微分方程數(shù)值解[D];電子科技大學(xué);2013年

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本文編號：1815529