基于贝叶斯压缩感知的信号时频表示重构机理与方法研究

Time-frequency analysis has been widely used in military and civilian areas, such as in radar, sonar, and communications. However, in traditional time-frequency analysis, the bilinear Wigner-Ville distribution is suffered from the tradeoff between cross term suppression and high time-frequency concentration, and the suppression of cross terms will decrease the time-frequency concentration; in the linear short-time Fourier transform, there exists the tradeoff between the time resolution and the frequency resolution, and the time-frequency resolution is low. Compressive sensing is combined with time-frequency analysis to solve the above problems. In the time-frequency representation reconstruction based on the compressive sensing, the Wigner-Ville distribution can achieve suppressed cross terms with high time-frequency concentration, and the linear short-time Fourier transform can achieve high time resolution as well as high frequency resolution. Under the framework of Bayesian compressive sensing, this project will research on the compressive sensing based time-frequency analysis, mainly including: 1) investigate the adaptive selection method of the sample domain/sample quantities, to provide the theoretical analysis for achieving time-frequency representation reconstruction with suppressed cross terms and high time-frequency concentration; 2) employ the structured sparsity as the prior, to improve the precision of the time-frequency representation reconstruction; 3) combine the compressive sensing with the signal pre-processing methods, to construct the low-complexity and robust reconstruction algorithm for noisy signals. Based on the above research, we aim to improve the mechanism of the compressive sensing based time-frequency representation reconstruction, and provide the theoretical basis for application areas such as in radar imaging.

时频分析方法广泛应用于雷达、声纳、通信等国防及民用领域。传统双线性时频分析方法中，交叉项抑制与高时频聚集性存在矛盾，交叉项抑制以牺牲时频聚集性为代价；线性时频分析方法中，时间分辨率和频率分辨率存在矛盾，时频表示的时频聚集性较差。基于压缩感知进行时频表示重构，能够抑制双线性时频分布中的交叉项同时获得较高时频聚集性，并使线性时频分布在获得高时间分辨率的同时保持较高的频率分辨率，有效解决上述的两个问题。本项目将基于贝叶斯压缩感知进行时频分析研究，主要包括：研究样本区间/样本数量的自适应选择方法，为获得高时频聚集性的时频表示重构提供依据；将信号时频域的结构化稀疏信息作为先验信息，提高时频表示重构的精度；将压缩感知与信号预处理方法结合，针对被噪声污染的信号构建运算复杂度低、稳健性高的重构算法；通过对上述关键问题的研究，完善基于压缩感知的时频表示重构机理和方法，为其在雷达成像等领域的应用提供理论依据。

时频分析方法是处理时变信号的有效工具，广泛应用于雷达、声纳、通信等领域。本项目将基于压缩感知进行时频分析研究，主要完成工作如下：（1）研究了基于压缩感知的信号时频表示重构机理，通过选择信号模糊域的少量样本，完善利用压缩感知的信号时频表示重构算法，完成了基于压缩感知的时频表示重构。（2）基于梯度方法对压缩感知系统进行了优化，设计了一种迭代方法用于确定最优字典，推导了梯度下降算法以求解优化感知矩阵问题。与其它常见的压缩感知方法相比较，本项目提出的方法能在不同信噪比情况下获得较小的均方误差值。（3）提出了一种基于稀疏性的方法，解决了频域中自矫正的采样率转换误差较大的问题，从而提高了采样率转换的准确性。该方法能显著降低均方误差，尤其能有效降低相位谱的均方误差。（4）基于压缩感知的应用：基于压缩感知，对MIMO 雷达系统中的DOA估计进行了探讨，提出的nuclear norm minimization 框架在低信噪比的情况下，知框架能够提供更优的DOA估计性能及更高的角度分辨率；基于结构化贝叶斯压缩感，对数字水印的嵌入和提取进行了研究，分别针对载体图片和水印图片进行压缩感知测量，实现了两种不同的数字水印嵌入及提取方法，并对载水印图片进行了高斯噪声、椒盐噪声、滤波、压缩、裁剪等不同形式的水印攻击测试；基于贝叶斯压缩感知框架，对语音中的欠定分离进行了初步探讨，本项目提出的方法能较好地恢复语音信号；针对雷达数据不足的情况下，利用压缩感知全变分优化Total Variation Optimization方法对ISAR雷达成像进行重构，重构的MIG25飞机图具有更好的重构效果及噪声抑制能力。（5）基于压缩感知的系统设计：设计了基于压缩感知的图片压缩和加密GUI系统，主要解决海量图片的存储空间利用率低和图片数据安全问题；为快速安全进行移动设备端海量数据的云端备份，基于压缩感知理论，在移动端Andriod系统上，通过高斯随机矩阵进行压缩测量，实现了信号的压缩存储和加密，从而节省了信号处理、存储和传输所需要的资源，提高了移动端数据的上传速度和安全性。