- 學位論文
應用壓縮感知之稀疏取樣微波及毫米波全息成像術
Sparsely-Sampled Microwave and Millimeter-Wave Holographic Imaging Using Compressed Sensing
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摘要
為了顯著減少近距離微波及毫米波成像系統之量測時間，並以更精確的脈衝響應描述毫米波雷達成像的架設環境，本論文首先提出整合壓縮感知技術於微波成像系統之訊號處理流程;接著提出對於成像所需之點擴散函數的雷達量測與去雜訊流程。最後再將所提出之結合壓縮感知的微波及毫米波成像技術利用所架設的雷達量測環境進行實作驗證。 在過往的時域諧波成像技術的研究中，為了順利重建目標散射物的三維影像，須在一給定的平面孔徑上進行平面機械掃描來量測反射自目標物的散射場。然而這樣的量測相當耗時且難以實際部署於應用場域。壓縮感知理論是針對可壓縮，或具稀疏性的訊號而設計的新式取樣技術。此技術能在取樣率小於取樣定理給定的條件下仍可高清還原出待測訊號。基於散射場於空間頻域中受到衰減波成分的物理侷限，而具有頻譜稀疏性，因此壓縮感知可用來降低反射係數的空間取樣點數。本研究結合上述理論於電磁模擬環境中，針對弱散射體可在保留29%(含以上)資料點的情況下順利成像。相較之下，若減少取樣點後不使用壓縮感知算法而直接進行成像，則影像品質將急遽下降。除了提出了還原空間中散射場之演算法外，針對微波成像背後之逆散射問題理論，本論文也比較了我們實驗室前期研究採用的數值濾波器與傳統的奇異值分解正則化對於微波成像品質的影響與解算速度差異。 時域諧波微波成像雖然能夠準確地重建弱散射體的影像，但在實際量測時所需的網絡分析儀卻是昂貴的實驗器材。因此，在量測部分，本研究改採用商用、低成本的雷達開發板作為毫米波的輻射源及接收器。此開發板所發射與解調的訊號為調頻連續波，這樣的訊號在成像應用中，無法如使用反射係數般解出散射體的定量特性，而僅以解出散射體與背景之間的對比為目標。為了精確地量測雷達量測環境中的點擴散函數並將其應用於成像問題，吾人提出使用截斷奇異值分解的點擴散函數去雜訊流程來算得高品質的點擴散函數。此點擴散函數在定性微波成像時，可以得出解析解無法算得之散射體細節。最後，吾人結合壓縮感知與去雜訊點擴散函數進行成像，在保留30%(含以上)空間取樣點的情況下仍可得到良好的成像品質。
並列摘要
Scanning-based microwave and millimeter-wave (MMW) imaging systems require a long measurement time and a large number of spatial sampling points to reconstruct images with high fidelity. The analytical expression of the impulse response of such a system is also insufficient to model realistic effects of the incident fields. To provide solutions for these difficulties, first, we propose a processing flow to integrate the compressed sensing (CS) scheme into the holographic imaging problem to relax the required spatial samples for successful reconstructions of images. Next, the measurement and calibration technique of the point spread function (PSF) is proposed and implemented to model the imaging environment's impulse response accurately. Finally, a practical MMW imaging system is built based on a commercial MMW radar module to demonstrate the solution procedure combining CS and the calibrated PSF. In previous works, the electric fields scattered by dielectric objects in the form of scattering parameters (S-parameters) are recorded in a mechanical raster-scanning manner, which is inefficient and difficult to implement in practical scenarios. CS is a useful technique that can measure compressible or sparse signals with a sample rate lower than that suggested by the sampling theorem. Because the spatial S-parameter signals exhibit a compressible nature in its spatial-frequency spectrum, the valuable information of the S-parameter can be acquired with fewer sample points by the concept of CS. Incorporating CS with the microwave imaging problem, the least required samples to reconstruct the images of the targeted scatterers with reasonably high quality can be estimated to be as low as 29% of the full data. The mathematical techniques behind the inverse scattering problem are also discussed and compared. It is shown that the numerical filtering by the propagating property of electromagnetic plane waves is an intuitive and robust method that can be used for faster image reconstruction compared to the general singular value decomposition (SVD)-based regularization. While using S-parameters as the input of the inverse problem creates 2D or 3D images of the targeted scatterers with high fidelity, bulky and expensive vector network analyzers (VNAs) are needed to perform such measurements. On the other hand, cost- effective and commercially available frequency-modulated continuous-wave (FMCW) radar modules lead to simpler and more compact solutions for MMW imaging. Yet the focus will be shifted to qualitative imaging. With the aim of capturing the accurate impulse response of the radar imaging system, the measurement and calibration method of the PSF is proposed to obtain faithful contrast images of the targeted scatterers. For experimental verification, we built a MMW imaging system by mounting a commercially available 77-GHz FMCW radar module from Texas Instruments onto a 3- axis mechanical scanner. With that, the scattering responses of the targeted scatterers and the raw PSF in a near-field scanning aperture can readily be acquired. It is shown that by combining the compressed sensing and the calibrated PSF in the imaging post-processing, high-quality contrast images can be retrieved with as low as 30% of the full measurement data.
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