消除干擾訊號在壓縮場域上:基於投影的方法

Abstract

由於壓縮式感測技術需要在整個訊號空間中量測訊號，因此往往包含了不需要的訊號成分，但對基於壓縮式感測的系統卻很容易受到雜訊以及干擾的影響，因此之前有研究提出在壓縮域上以正交投影消除干擾的方法[1]，但是這方法會造成受限保距常數增加而使得訊號重建效能衰減。因此本篇論文提出了兩種以投影矩陣去消除干擾的架構，保證能在維持受限保距常數下去消除干擾訊號。 首先本篇論文對於[1]的消除干擾方法提出了另一種觀點並且由此改寫架構，從數學分析以及模擬結果可以證實在低訊雜比環境下我們提出的方法其重建效能會略有改善。另外我們提出斜投影消除干擾方法，並當目標訊號與干擾成分所對應的子空間的最小主要角夠大時，在模擬結果中可以知道此方法的重建效能與[1]相比會有明顯的改善。

Compressive sensing (CS) based signal acquired by systems capture the entire signal space; however, it often includes undesired signal. Since CS-based systems are very sensitive to interference and noise, a scheme had been proposed to cancel the interference by using the orthogonal projection in compressive domain. Still, this scheme leads to an increase of the restricted isometry constant (RIC) for the set of the signals of interest, and causes the decay of the reconstruction performance. Hence, in this thesis, we study two schemes of inteference cancellation by using projection, which will maintain the RIC on the set of potential signals of interest. First, based on the method in [1], we rewrite the scheme to cancel the interference. The mathematical analysis and simulation results manifest that the proposed method slightly improves the performance of reconstruction in [1]. Moreover, we proposed another interference cancellation method based on oblique projection. The simulation results show that the performance will be obviously improved when the minimum principal angle is bigger than the subspaces between the desired and interference signals.