| 摘要: | 一位元壓縮感知（1-bit Compressed Sensing）以極低解析度的量化方式，有效簡化硬體架構並降低系統傳輸功耗，適合應用於資源受限的裝置與通訊場景。然而，量化後僅保留符號資訊的特性，使原始訊號振幅難以回復，且重建穩定性需要依靠大量測量資料，對符號翻轉等干擾也極為敏感，在實務應用上仍面臨不少挑戰。
為了解決上述問題，本文提出一種兼具高效率與穩健性的重建方法，首先，在量化階段引入非零閾值作為參考點，使系統具備還原訊號振幅的能力，進一步的，利用量化閾值於感測過程中所保留的相對資訊，設計出一套初始值估計策略，協助訊號重建能以穩定且合理的起始點出發，降低過往方法對大量觀測資料的依賴。
考量提升整體重建效率的目的，我們對稀疏訊號的非零位置進行估計，並以所估得的少量非零位置作為新的重建目標，減輕過往在高維訊號重建中所面臨的龐大運算負擔。而針對傳輸中可能發生的符號翻轉問題，本文提出一套翻轉位元修正機制，無需事先得知翻轉總數量，即可快速定位錯誤位元並修正，有效提升重建過程的整體效率與穩健性。
最後，為強化一位元壓縮感知在雜訊干擾下的適應能力，本文提出一套針對符號翻轉環境以模型為導向的深度神經網路。該方法以本文所建立的感測重建流程為基礎，擴展成具彈性的深度展開(Deep Unfolding)架構，具備雜訊環境下自適應優化參數的能力，使重建精度進一步提升。另一方面，藉由神經網路良好的訓練收斂特性，所提出架構能在少量層數內快速收斂，降低傳統方法所需的運算成本，展現應用於實務場景之潛力。
;1-bit Compressed Sensing (1-bit CS) employs extremely low-resolution quantization to reduce system power and hardware complexity, making it well-suited for resource-constrained devices and communication environments. However, by preserving only the sign information, signal amplitude becomes difficult to recover, and stable reconstruction typically requires a large number of measurements. Moreover, it is highly vulnerable to sign-flip errors, limiting practical applicability.
To address these challenges, we propose an efficient and robust reconstruction framework. A non-zero quantization threshold is introduced during sensing, enabling signal amplitude rerecovery. This threshold also preserves relative measurement information, which we leverage to design a novel initialization strategy, allowing the reconstruction to start from a stable and reasonable point without relying on excessive observations.
To further improve efficiency, we estimate the support of the signal and use a reduced set of indices as the reconstruction target, significantly lowering the computational cost associated with high-dimensional signal recovery. Additionally, to combat potential bit-flip errors in transmission, we introduce a correction mechanism that operates without prior knowledge of the flip count, achieving fast and effective recovery.
Finally, to enhance performance under noisy conditions, we develop a model-based deep neural network tailored for the sign-flip scenario. Built upon our proposed framework, it adopts a flexible deep unfolding architecture with adaptive parameter learning, enabling rapid convergence in a small number of layers and reducing training overhead. The proposed method thus demonstrates the potential for practical applications. |
