高致死率的乳癌一直是女性健康的潛在威脅，尋求一兼具低輻射量、高解析度及較簡單的影像重建機制之診斷儀器成為競逐的目標。其中藉由乳房不同組織與微波作用後其回波在振幅等物理量(參數)上具差異特性以判斷是否有腫瘤的微波乳房成像受到研究學者高度重視，本論文即提出了結合傾斜投影信號處理技術及檢測器於乳房腫瘤偵測中，以提升微波成像品質。傾斜投影是基於子空間的方法，其將向量分解為位於兩個子空間之一中的兩個分量，即目標子空間和雜波/干擾子空間，與傳統的正交投影相比，該投影不需要兩個子空間彼此正交，此技巧能更彈性的應用於乳房腫瘤與雜訊間的複雜場景中。另外，本論文應用了一具有在複雜度低，且在低SCNR下偵測性能與廣用的廣義似然比率檢驗(generalized likelihood ratio test，GLRT)性能接近的Rao-test作為檢測器。模擬結果顯示，在不同的對比度、不同的訊雜比、不同的取樣點數等等不同的場景下，所提出的結合傾斜投影技巧及Rao-test檢測器的方法與現有常用的乳房腫瘤偵測技巧相較，獲致了較佳的信號-雜波-雜訊比(signal-clutter-noise ratio，SCNR)。另外，利用傾斜投影的特性，本文也提出了一較不受因腫瘤大小、形狀等因素影響的共變異數矩陣估測技巧，利用此技巧所估得的共變異數矩陣可直接應用於後端的檢測器中，此方法避免了傳統上待測者於健康時需要事先建立相關的乳房之資料庫以估得共變異數矩陣的做法，以更利於臨床上的應用。

Breast cancer has been a potential threat to women's health. It is thus of importance to seek for less expensive signal processing-based solutions based on microwave images to provide similar reconstructed image quality. The crux of using microwaves to detect breast tumors is the dielectric-properties contrast that exists between malignant and normal breast tissues at microwave frequencies. In the thesis, we propose a new scheme which combine the oblique projection and Rao detector for breast tumor detection to improve the quality of microwave imaging. Oblique projection is a subspace based approach, which decomposes a vector into two components lying in either the subspaces, i.e., target subspace or clutter/interference subspace. However, in contrast to the conventional orthogonal projection, this projection does not require the two subspaces to be orthogonal to each other. Also, based on the characteristics of the oblique projection, we consider a new covariance matrix estimated method which does not require to determine beforehand. Afterward, the Rao detector is employed. Simulation results show that performance of proposed approach attains similar and sometimes even superior performance as the widespread GLRT detector with yet even lower complexity.

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