訊息理論熵最佳化估算探討：理論、模擬與生物組織應用

Optimal Estimation of Ultrasonic Information-theoretic Entropy: Principle, Simulation, and Applications to Biological Tissue

胡瑞成(Rui-Cheng Hu)

指導教授 ： 張建成

國立臺灣大學/工學院/應用力學研究所/碩士(2010年)

https://doi.org/10.6342/NTU.2010.01564

摘要

為克服B-mode影像不能作定量分析，和統計模型只能處理未經非線性處理之訊號的缺點，有學者提出使用訊息理論熵計算超音波的逆散射訊號，作為定量散射濃度的工具，原因有二：一者訊息理論熵不受限於統計模型；二者有學者證實訊息理論熵，即使面對非線性處理過的訊號，依然可定量組織散射濃度。

傳統訊息理論熵會與類比轉數位器(analogy-to-digital converter, ADC)的動態範圍有關，熵值隨動態範圍增加而上升，非是定值；且動態範圍過大時，熵值會進入飽和。為克服此問題，Hughes學者定義只跟波形性質相關的Shannon entropy：「連續波形的Shannon entropy」，此定義下的熵值即使進入飽和，其相對大小仍存。

本研究即以連續波形的熵為主，針對其估算參數作相關效應的最佳化探討，同時以散射濃度定量及生物組織應用作熵值效能的測試。實驗結果發現，無論是散射濃度定量，或生物組織燒灼區域辨識，新定義的熵都有相當不錯的表現。

此外，本研究對於「連續波形的Shannon entropy」之「傅立葉級數法」，定義出相關的估算參數，並對參數對熵值估算之影響進行探討，尋求最佳化的計算條件。無論是數值模擬、超音波模擬或是組織燒灼實驗都可發現，並非需很嚴苛的計算條件(嚴格的參數設定、很長的計算時間或很高的計算資源…等等)才有最佳效果。工程上的應用也是尋求最佳效果和最適當的計算量，方是最好的估算參數設定之最佳化。因此本論文對熵計算之傅立葉級數法的最佳化條件，提供一個較有效率的尋求方向。

關鍵字

訊息理論熵 ； Shannon entropy ； 散射濃度定量 ； 組織燒灼和傅立葉級數法

並列摘要

To solve the problem that the parameter value of B-mode images can not be for quantitative analysis, and to overcome the shortcoming that statistical models can not deal with non-linear processing signals. Some researchers have suggested that we can use the information-theoretic entropy for calculation of the backscattering ultrasound signals, and quantify the scattering concentration. There are two reasons: first, information-theoretic entropy is not restricted to statistical models; second, some researchers have confirmed that the estimated value of information-theoretic entropy of non-linear processing signals can still quantify the concentration of tissue scattering.

Traditional entropy value increases with increasing of dynamic range of ADC devices (analogy-to-digital converter, ADC), and can not be a constant. Also, traditional entropy value have the saturation problem when dynamic range is too large. To overcome this problem, M.S. Hughes define a new Shannon entropy that only is relevant to the waveform property of signals. And the difference of any different "Shannon entropy of the continuous waveform" values will keep, even enter the saturation situation.

In this study, the entropy of the continuous waveform is the main research object. We would like to find the optimization of the parameters setting of the "Shannon entropy of the continuous waveform", and also test the ability of "Shannon entropy of the continuous waveform" by the quantitative experiment of scattering concentration and the experiment of biological tissue. The results show that "Shannon entropy of the continuous waveform" has a very good performance in both experiment.

In addition, this study defines relevant estimated parameters of "Fourier series method" of "Shannon entropy of the continuous waveform", discusses how those parameters affect on the estimation of entropy, and find the optimization of the parameters setting. The results of numerical simulation experiment, ultrasound simulation experiment, and tissue ablation experiment show that we can get pretty good results, but do without rigorous settings. Therefore, this study on "Fourier series method" of "Shannon entropy of the continuous waveform" provide a more efficient direction on searching estimated optimization.

並列關鍵字

information-theoretic entropy ； Shannon entropy ； quantification of tissue scattering concentration of ； tissue ablation ； and. Fourier series method

參考文獻

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