中文摘要：

针对信号和图像去噪声问题,利用小波及剪切波理论,分别对信号及图像稀疏表示。通过软阈值算法将其重构,实现去噪声过程。根据小波和剪切波的不同结构,分析了剪切波与小波的去噪声过程,通过信噪比对比了二者的恢复效果。通过数值算例分析了消失矩对小波去噪声结果的影响,为去噪声问题中如何选择小波基提供先验信息。

英文摘要：

Aim at the solution to signal and image denoising problems, the sparse representation of signal and image is given based on the theory of wavelet and shearlet. Then a soft threshold algorithm is used to reconstruct the object in order to achieve the denoising. According to different structures of wavelet and shearlet, the denoising processes are analyzed and compared by SNR to evaluate the efficiency. Furthermore, numerical examinations are taken to analyze the influence of vanishing moments to denoising results, which will provide the prior information for how to choose the wavelet basis.