冲击噪声抑制技术的研究与应用

Noises, in general as the signals of un-interest, coexist with the signal of interest (SOI) and researchers have battled with them for centuries to recover the SOIs. In the most of research developments, Gaussian noise is assumed due to its simplicity. In this project, however impulsive noise, as an extension of Gaussian noise, is the focus of this work. Impulsive noise has always been a difficult problem in signal processing to handle due to the fact that it is undefined under second moments in statistics. Therefore, traditional methods designed for Gaussian noise might fail under impulsive noise case. In this project, certain properties on impulsive noise are analyzed first. Based on the obtained results, one property standing out which will be utilized in algorithm development is nearly sparse since impulsive noise presents a few spikes and has lots of small values. Assume the SOI is stationary, we will develop a new joint signal and noise estimation method to cancel the impulsive noise by exploiting the nearly-sparse property of the noise. Another main focus of this approach is how to develop an efficient solver to handle large scale problem. When the SOI is time-varying, to track its changes, adaptive filter techniques are utilized to reduce the negative impact from impulsive noise and at the same time to reconstruct the SOI. The main challenge of this approach is to develop a robust method to achieve fast convergence rate and low steady errors. To demonstrate the effectiveness of our algorithms, besides theoretic analysis and computer simulations, we intend to process real-world data in audio recordings from our collaboration partner in Poland. Due to aging and mishandling, clicks, pops and crackles in the gramophone records are often present. In our research, those clicks are modeled as impulsive noise. Therefore, those recordings are perfect data source to verify our algorithms. We apply for this project hoping that our research results can benefit other researchers and progress noise reduction algorithms in applications as well.

噪声抑制一直是人们的研究热点。高斯噪声并不能很好的描述信号的剧烈变化而有其局限性。本项目，我们研究一种更为广泛的噪声-冲击噪声。作为高斯噪声的推广，研究如何有效的进行冲击噪声抑制更有实际意义。首先我们将系统的分析冲击噪声的特点。我们发现其近似稀疏性可为我们所用。为了充分利用这个特点，首先，假定感兴趣的信号是非时变，设计出联合的信号恢复和噪声抑制算法。同时利用共轭梯度算法设计一个有效的求解算法来适应大规模数据的问题。通过联合算法的研究，利用噪声性质提高信号的恢复质量。当感兴趣的信号是时变信号时，利用自适应滤波器方法，不但可以跟踪信号也同时能够跟踪噪声的变化情况。通过在冲击噪声下的自适应算法研究，可以提高滤波器的稳健性，算法的收敛速度和降低稳态误差。为了更好的验证和推广冲击噪声抑制算法，将有划痕等破坏的唱片作为含有冲击噪声的数据源。通过对原始唱片的恢复， 能够进一步提高冲击噪声抑制问题的研究。

噪声作为一个负面的因素无时无刻都在影响着人们的生产生活。因此研究如何降低噪声对人们的影响具有重要的意义。在本项目的研究中，针对冲击噪声，采用了多种降噪方案。1) 利用冲击噪声的特点，完成了噪声和有用信号的联合恢复算法，2) 针对混合噪声，给出了级联的降噪方案，3)在语音和图像恢复等问题上，所设计的方案得到了验证。本研究的意义在于：作为前端处理，为后端的语音识别，图像分析等应用处理提供了坚实的基础。