面向低信噪比的自适应压缩感知方法

Adaptive compressive sensing toward low signal-to-noise ratio scene

在压缩感知工程应用中,信号往往被噪声和干扰所影响,常规的压缩感知方法难以达到理想的重构效果,特别是低信噪比应用场景中,稀疏重构往往会失效.分析了压缩感知中噪声对重构性能的影响,从理论上解释了压缩感知中的噪声折叠原理,并在此基础上提出了一种基于方向性测量的自适应压缩感知方案.该方案通过后端信号处理系统估计出噪声的相关信息并反馈至压缩感知前端,前端根据反馈的噪声信息调整测量矩阵,从而改变感知矩阵的方向,自适应地感知稀疏谱,从而有效地抑制信号噪声.仿真实验表明,所提的自适应压缩感知方法对稀疏信号重构性能有较大的提升.

As an alternative paradigm to the Shannon-Nyquist sampling theorem, compressive sensing enables sparse signals to be acquired by sub-Nyquist analog-to-digital converters thus may launch a revolution in signal collection, transmission and processing. In the practical compressive sensing applications, the sparse signal is always affected by noise and interference, and therefore the recovery performance reduces based on the conventional compressive sensing, especially in the low signal-to-noise scene, the sparse recovery is usually unavailable. In this paper, the influence of noise on recovery performance is analyzed, so as to provide the theoretical basis for the noise folding phenomenon in compressive sensing. From the analysis, we find that the expected noise gain in the random measure process is closely related to the row and column of the measurement matrix. However, only those columns corresponding to the support for the sparse signal contribute to the sparse vector. In the traditional Shannon-Nyquist sampling system, an antialiasing filter is applied before the sampling process, so as to filter the noise beyond the passband of interest. Inspired by the necessity of antialiasing filtering in bandpass signal sampling, we propose a selective measurement scheme, namely adapted compressive sensing, whose measurement matrix can be updated according to the noise information fed back by the processing center. The measurement matrix is specially designed, and the sensing matrix has directivity so that the signal noise can be suppressed. The measurement matrix senses only the spectrum of interest, where the sparse spectrum is most likely to lie. Moreover, we compare the recovery performance of the proposed adaptive scheme with those of the non-adaptive orthogonal matching pursuit algorithm, FOCal underdetermined system solver algorithm, and sparse Bayesian learning algorithm. Extensive numerical experiments show that the proposed scheme has a better improvement in the performance of the sparse signal recovery. From the viewpoint of implementation, the measurement noise should be taken into consideration in the system, and more efficient algorithms will be developed for source pre-estimation at lower signal-to-noise ratio.