Tissue Characterization by Information-theoretic Entropy of Ultrasound Signal

傳統的超音波灰階影像，俗稱B-mode(Brightness-mode)，已廣泛的運用在臨床醫學，主要功用在於定性呈現生物組織結構形態與輪廓。然而，超音波灰階影像的亮度會受到許多因素影響，如系統增益、動態範圍、與操作者經驗等。此外，為避免斑點效應(speckle effect)影響影像品質，通常在現有醫用超音波系統中，較微弱的超音波逆散射訊號會被濾除，但需注意的是，超音波逆散射訊號與組織內部散射子的特性，例如大小、形狀、密度、濃度等有關，因此散射訊號的濾除會使得灰階影像無法提供散射子定量訊息，這對於疾病早期偵測，或者組織良惡性判定有某程度上的困難。 基於超音波逆散射訊號的本質為隨機訊號，因此在過去許多研究者皆使用統計模型來描述超音波逆散射訊號的機率密度函數，以輔助灰階影像於臨床診斷之不足。這些統計模型主要包括Rayleigh、K、homodyned K、generalized K、以及Nakagami模型。其中又以Nakagami統計模型最能描述不同種類的超音波散射分佈。但在某些情況下，如訊號存在非線性效應、或者訊號經過非線性處理後，逆散射訊號便不再遵守Nakagami統計分佈，這限制了統計模型使用上的廣泛性與通用性。 為解決此問題，本研究提出以超音波逆散射訊號的訊息理論熵來定量組織特性。訊息理論熵的優勢在於它本身不受限於訊號僅能遵循某種特定的統計模式的條件下，也能反映出組織內部的散射子特性。為探索這個想法，我們以仿體實驗方式來進行驗證。首先進行超音波影像掃描系統之架設，此系統掛載不同頻率之超音波換能器進行影像掃描。之後我們製作不同散射子濃度之仿體，並使用系統對仿體進行資料擷取與灰階成像。同時對影像包絡訊號進行訊息理論熵的計算，採用三種訊息理論熵(i.e. Shannon, Renyi, Tsallis entropy)，以探討訊息理論熵隨散射子濃度變化之趨勢與結果，並與Nakagami統計模型做比較，評比利用不同方法判讀散射子濃度的優勢與缺點，以及這些方法與超音波頻率之間影響為何，整理出無本質斑點效應與具本質斑點效應的仿體之特性化結果。驗結果顯示，利用Nakagami統計模型定量仿體組織的結果顯示，在低頻聚焦式探頭下能顯示的動態範圍最佳，但是隨著頻率提高時，相同濃度範圍下所能顯示的動態範圍會縮小，主要原因在於訊號的機率分佈會隨著頻率增加往pre-Rayleigh分佈靠近。而以訊息理論熵來定量組織特性的結果，以Tsallis entropy在不同組織特性 鑑別濃度的效果最佳，除了具有高動態範圍優勢，隨著頻率提高能增加對應散射子濃度的線性程度，且在具本質斑點效應的影響下，仍然可以應用在濃度較高的組織上。The conventional ultrasound gray scale image the so-called B-mode image (Brightness-mode), has been widely applied in the clinical medicine. Its primary purpose is to qualitatively present the structure, shape and contour of the biological tissue. However, the brightness of the B-mode image is would be affected by many factors, such as system gain, dynamic range, operator’s experience and etc. Besides, in order to avoid the speckle effect on the image quality, the weaker backscattering signal is typically removed in the existing medical ultrasound systems. Note that ultrasound backscattering signal is related to the properties of scatterers in tissues, such as, size, shape, density and concentration. Therefore, the filtering of scattering signal makes the B-mode image difficult to provide the quantitative information of scatterers, which in turn influences the early detection and classification on benign and malignant tissues.ased upon the fact that the essence of ultrasound backscattering signal belongs to random signals, many researchers explored using statistical models to describe the probability density function of backscattering echoes to complement the deficiency of B-scan. The statistical models mainly include Rayleigh, K, homodyned K, generalized K, and Nakagami, in which Nakagami statistical model can encompass all scattering conditions in ultrasound. But, under certain circumstances, the backscattered statistics do not obey the Nakagami distribution anymore once there are some nonlinear effects or processing on the backscattering signals. This limits the practical applications of statistical models.n order to solve the problem, this study proposed using information-theoretic entropy of ultrasonic backscattering signal to quantify the properties of tissue. The superiority of information-theoretic entropy lies in that it can reflect the scatterer properties without any limitation due to statistical models on the backscattering echoes. To explore the idea, we carried out experiments on phantoms. First of all, we set up ultrasound image scanning system, which holds the ultrasonic transducer with different frequencies for image scanning. Subsequently, we made phantoms with different scattering concentrations and deal with data acquisition and gray image formation. Meanwhile, we use the envelope signals to calculate three information-theoretic entropies (i.e. Shannon, Renyi, Tsallis.) to explore the entropies as a function of scatterer concentrations. The results between using Nakagami models and entropies will be compared and discuss the effects of ultrasonic frequencies and background speckles on the performance of entropy to characterize tissues. he show the Nakagami parameter has a better dynamic range to detect the variation of scatterer concentration when low frequency focused transducer was used. With the increase in frequency, the dynamic range decreased in the same range of scatterer concentration as frequency increases. The main reason is that the probability distribution of signal will be close to pre-Rayleigh distribution with increasing the ultrasound frequency. Tsallis entropy has an outstanding performance to quantify the scatterer concentration. Besides a high dynamic range, its relationship with scatterer concentration would become more linear by increasing ultrasonic frequency. Meanwhile, under the influence of background speckle effect, it also can be applied to tissues with higher scatterer concentration.中文摘要 ibstract iii錄 v索引 vii索引 ix謝 x一章 緒論 1.1 前言 1.2 研究背景 3.3 文獻回顧 4.3.1 超音波逆散射訊號統計模型 4.3.2 超音波訊息理論熵 6.4 研究目的 8二章 理論基礎 10.1 超音波簡介 10.1.1 聲波傳遞的基本原理 10.1.2 聲速與衰減 12.1.3 反射與折射 13.1.4 超音波探頭構造與聲場 14.1.5 超音波影像之軸向解析度 16.1.6 超音波影像之側向解析度 18.2 超音波散射分析 20.2.1 超音波散射現象 20.2.2 分析單一散射子之散射現象 20.2.3 分析多散射子之散射現象 22.3 逆散射統計模型 25.3.1 Rayleigh統計分佈 25.3.2 Rician統計分佈 26.2.3 K統計分佈 27.3.4 Nakagami統計分佈 28.4 訊息理論熵原理 29.4.1 訊息理論熵之基本原理 29.4.2 訊息理論熵之計算 30三章 實驗材料與方法 31.1 超音波影像系統架構 31.1.1 馬達掃描方式 33.1.2 程式設計流程與操作介面 34.2 實驗仿體製作 36.2.1 無本質斑點效應之仿體 37.2.2 存在本質斑點效應之仿體 37.3 數據處理步驟 40.3.1 超音波逆散射訊號處理 40.3.2 Nakagami參數計算 40.3.3 訊息理論熵計算 41四章 實驗結果與討論 42.1 無本質斑點效應之仿體 42.1.1 B-mode影像與訊號機率密度函數 42.1.2 定量參數分析 53.1.3 討論 59.2 存在本質斑點效應之仿體 62.2.1 B-mode影像與訊號機率密度函數 62.2.2 定量參數分析 66.2.3 討論 70五章 結論與未來展望 71.1 結論 71.2 未來展望 72考文獻 7