采用频域紧支集正交小波基消除瞬态散射回波中的高斯白噪声干扰

Recovery of Signal from Transient Scattered Response Contaminated by Gaussian White Noise Based on Orthogonal Bases of Compactly Supported Wavelets in Frequency Domain

本文提出一种采用频域紧支集正交小波基的非线性柔性阈值滤波方法，该方法利用频域紧支集小波基的良好频谱特性和信号压缩能力，有效地消除了高斯白噪声对瞬态散射回波的干扰．文中以一人工合成瞬态回波，实测球体瞬态晚期响应和1：72的B-58飞机模型的散射回波为例，对本文方法的有效性作了检验，并将其与傅立叶滤波、样条拟合消噪小波变换极大模算法及采用Daubechies基的非线性柔性阈值滤波法作了比较，显示了本文方法的优越性．

In this paper, a nonlinear soft-thresholding method based on orthogonal bases of compactly supported wavelets in frequency domain is proposed to recover signal from transient scattered response contaminated by Gaussian white noise. Two poverties of this kind of wavelet basis are responsible for the effectiveness of the proposed method:one is its compact support in frequency domain, the other is its great capability in data compression. The effectiveness of the proposed method is verified with a synthetic transient scattered response,measured response of a sphere and response of a model aircraft B-58 having the scale ratio of 1: 72 with additive Gaussian noise. The results obtained by the method are compared with those of Fourier truncation, spline smoothing, maximum modulus algorithm of wavelet and nonlinear soft-thresholding based on compactly supported wavelet bases in time domain. The superiority of the proposed method is thus demonstrated.