本論文提出一個以點與塊限制之疊代式壓縮感知演算法來解決聲源識別與特性問題。聲場模型是基於等效聲源法(equivalent source method, ESM)，此反算問題是一個線性欠定問題 (underdetermined problem)，傳統上使用凸優化(convex optimization)來解決但運算效率不佳且不能處理連續分佈的聲源，因此本論文提出以牛頓法 (Newton’s method) 配合特殊修剪程序之演算法，修剪程序使用一個二元遮罩 (binary mask) 達到促進稀少性的限制，並且可以應用在二維和非同調聲源上。在後處理部分，聲學參數如聲壓，粒子速度、平均聲強、聲功率及輻射圖可以由先前等效聲源法得到的等效聲源基底計算出。此外，部分聲場分解 (partial field decomposition) 也被實現。本論文以模擬與實驗驗證此演算法，並探討了基底不匹配 (basis mismatch) 的議題。結果顯示此疊代式感知壓縮演算法與凸優化相比有極好的聲場影像表現以及較少的運算時間。

In this thesis, an iterative Compressive Sensing (CS) algorithm is proposed to solve acoustical source characterization problems with point and/or block sparsity constraints. The inverse problems are formulated with the Equivalent Source Method (ESM) as linear underdetermined systems of equations. Conventional approaches based on convex optimization can be computationally expensive and fail to deal with continuously distributed source. To overcome these drawbacks, an iterative algorithm adapted from the Newton’s method with a special pruning process incorporated is developed. The pruning process employs a binary mask that admits sparsity-promoting constraints of two dimensional and incoherent block sources. In the post-processing, acoustic variables including sound pressure, particle velocity, sound intensity, sound power, and radiation pattern can be calculated on the basis of the equivalent source amplitudes obtained previously using the ESM. In addition, partial field decomposition can also be implemented. Numerical and experimental investigations are conducted to validate the proposed technique. Basis mismatch issues are examined. The results have demonstrated that the iterative CS method achieved superior imaging performance with little computational cost, as compared to conventional convex optimization package.

摘 要.....................................................................................................i
ABSTRACT..............................................................................................ii
誌 謝...................................................................................................iii
TABLE OF CONTENT...........................................................................iv
LIST OF TABLE.......................................................................................v
LIST OF FIGURE...................................................................................vi
I. INTRODUCTION 1
II. ACOUSTIC INVERSE PROBLEMS 3
A. Equivalent source method (ESM) and the array model 3
B. Underdetermined linear system 3
III. ITERATIVE CS ALGORITHM 7
A. Sparsity constraints 7
B. Newton’s (NT) method 8
IV. POST-PROCESSING 13
A. Acoustic variables 13
B. Partial field decomposition 15
V. NUMERICAL SIMULATION 16
A. Two speech sources 16
B. Basis mismatch issue 17
C. Baffled circular rigid piston 17
VI. EXPERIMENTAL INVESTIGATION 36
A. A loudspeaker and a hand cutter 36
B. A fan and a hand cutter 37
VII. CONCLUSIONS 49
REFERENCES 50

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