基於均勻稀疏採樣散射場資料及插值方法之D頻段單輸入多輸出電磁成像技術

Abstract

本研究針對D頻段（110–170 GHz）單輸入多輸出成像系統，探討在均勻稀疏採樣條件下的散射場及影像重建技術，並評估不同插值方法的成像品質與適用範圍。在高頻成像應用中，由於天線製造及系統硬體限制，滿足最小奈奎斯特取樣標準（四分之一波長）的全採樣條件往往難以實現，因此適當的數值重建方法對於恢復影像品質至關重要。 本研究比較團隊先前開發的有理薄板樣條（Rational Thin-Plate Spline, RTPS）插值方法與廣泛應用之雙立方（Bicubic）插值方法，評估其在不同均勻稀疏取樣條件下的成像效果。我們首先透過數值模擬驗證這兩種方法在不同測試物配置（單球體、雙球體、五球體陣列）下的表現，並分析不同取樣間隔對影像品質的影響。此外，我們進一步探討當系統採用外插來補足未取樣數據時，兩種插值方法在重建結果上的差異，發現 RTPS 在須採用外插時能維持較佳的空間連續性，而 Bicubic 因無法外插，必須使用零填充（Zero-padding），導致邊界影像品質下降。 此外，本研究架設了一套150-GHz量測系統，並透過該系統的量測數據進行重建與分析，以驗證先前的模擬結果。經過比較，評估兩種插值方法的抗噪性，並總結其優缺點及適用場景。最終的結果證實，本研究架設之150-GHz量測系統之成像品質與模擬大致吻合，進一步確立了 RTPS 與 Bicubic 插值方法在不同稀疏取樣條件下的成像特性。

This study focuses on the image reconstruction techniques for a D-band (110–170 GHz) single-input multiple-output (SIMO) imaging system under uniform sparse sampling conditions. It evaluates the imaging quality and applicability of different interpolation methods. In high-frequency imaging applications, achieving fully sampled data that meets the minimum Nyquist sampling standard (λc/4) is often infeasible due to limitations in antenna fabrication and system hardware. Therefore, appropriate numerical reconstruction methods are essential for restoring image quality. This study compares the Rational Thin-Plate Spline (RTPS) interpolation method, previously developed by our research team, with the widely used bicubic interpolation method, assessing their performance under different uniform sparse sampling conditions. Numerical simulations were first conducted to evaluate both methods across various target object configurations (single sphere, dual spheres, and five-sphere arrays) and to analyze the impact of different sampling intervals on image quality. Additionally, we investigated the differences between these interpolation methods when extrapolation is required to compensate for missing sampled data. The results indicate that RTPS maintains better spatial continuity in extrapolation scenarios, whereas bicubic, which lacks extrapolation capability and relies on zero-padding, suffers from reduced image quality at the boundaries. Furthermore, a 150-GHz experimental measurement system was established in this study, and the acquired measurement data were reconstructed and analyzed to validate the earlier simulation results. A comparative evaluation was conducted to assess the noise resistance of both interpolation methods, summarizing their advantages, limitations, and applicable scenarios. The final results confirm that the image quality of the 150-GHz measurement system closely aligns with the simulation, further establishing the interpolation characteristics of RTPS and bicubic under different sparse sampling conditions.